In order to explore the impact resistance of carbon fiber reinforced metal laminates modified by carbon nanotubes under high-speed conditions, this experiment mainly tested the energy absorption of aluminum plate, carbon fiber reinforced metal laminate and carbon fiber reinforced metal laminate modified by carbon nanotubes with the same thickness compared with that after complete breakdown of projectile, So as to judge the impact resistance. The experimental device is mainly composed of launcher, target box and high-speed photography system. First fix the test piece in the target box, and then spray the projectile with an air gun at high speed, and then puncture the test piece. Two high-speed cameras record the velocity of the projectile before and after passing through the test piece, as shown in Fig. 1.

The basic working principle of the experimental device is to use a high-speed camera to record the impact velocity VI of the projectile and the residual velocity VR after passing through the experimental plate. The evaluation criterion of impact resistance is the kinetic energy loss of projectile in the process of penetration -Ek:

$$
\Delta E\_k = \frac{1}{2} M\_p \left( V \mathbf{i}^2 - V\_r^2 \right) \tag{1}
$$

In this paper, three groups of test pieces were tested: pure aluminum plate, carbon fiber reinforced metal laminate without carbon nanotubes and carbon fiber reinforced metal laminate with 1 wt% carbon nanotubes.

**Fig. 1.** High speed impact test device.

# **3 Finite Element Simulation**

## **3.1 Model Establishment and Grid Division**

In the simulation, the plate size of the test piece is 60 mm \* 60 mm, as shown in Fig. 2. Orthogonal carbon fiber interlayer bonding property parameters and carbon fiber aluminum alloy interlayer bonding property parameters are shown in Tables 2 and 3 respectively. The impact projectile is made of 45# steel, the density is 7.8 g/cm3, the elastic modulus is 210 gpa, the radius R is 5 mm and the mass is 4.16 g. Considering that the number of elements affects the computer computing speed, the approximate global size of each component is 1. In the load, the contact between the projectile and the target plate adopts general contact, the contact attribute is tangential contact, normal hard contact, and the friction coefficient is 0.2. The four sides of the carbon fiber reinforced composite are completely fixed, the degrees of freedom and rotation of the projectile in three directions are limited, and the initial velocity in the negative direction of the x-axis is defined as 200 m/s. The bonding layer is very thin, so it is defined by interlayer constraints. The modeling process of carbon fiber reinforced metal laminate and carbon nanotube fiber reinforced metal laminate is exactly the same. The difference is that the mechanical properties of the bonding layer of carbon fiber reinforced metal laminate with carbon nanotubes are about 15% higher than those without carbon nanotubes.

**Fig. 2.** High speed impact finite element model

**Table 2.** Interlaminar bonding property parameters of orthogonal carbon fiber plates

**Table 3.** Bonding property parameters between carbon fiber plate and aluminum alloy

### **3.2 Simulation Results and Analysis**

Figure 3 shows the finite element simulation results of the three kinds of experimental parts after high-speed impact. It can be seen from the Fig. 3 that the aluminum plate has higher shape, smaller bullet holes and more regular edges after impact. Because of the high brittleness of carbon fiber plate, the damage of high speed impact is great, and the cracking phenomenon is great. Because of the dual properties of metal and composite material, the carbon fiber reinforced aluminum alloy composite has better impact resistance and smaller damage area after high speed impact.

**Fig. 3.** Stress nephogram of breakdown of different materials under high speed impact (a) Aluminum plate (b) Carbon fiber composites (c) Carbon fiber reinforced aluminum alloy composites

Carbon fiber composite material stress and strain contours of each layer are shown in Fig. 4 below, the carbon fiber orientations can be found on the damage form of fiber reinforced metal laminates composite materials have great influence, therefore, in practice, according to the characteristics of different structure optimization design in the form of different bearing to meet different needs.

**Fig. 4.** Hashin Criteria for different Angle carbon fiber layer damage cloud (a) 0° (b) 90°

The output speed of the projectile in the simulation process is shown in Fig. 5 below, and the kinetic energy and energy loss of the three groups of projectile are calculated by this speed, and the results are shown in Table 4 below:

By comparing the results of three groups of simulation experiments, the energy absorption of carbon fiber reinforced metal laminates is about 300 times that of aluminum alloy plates, which fully demonstrates that the impact resistance of carbon fiber

**Fig. 5.** The velocity curve of the projectile hitting different materials (a) Aluminum plate (b) Carbon fiber metal laminates (c) Carbon fiber metal laminates modified by carbon nanotubes

**Table 4.** Projectile velocity change and kinetic energy loss

reinforced metal composites has a great advantage compared with aluminum alloy. However, when 1 wt% carbon nanotubes were added to the carbon fiber reinforced metal laminates, the absorption energy was about 10 times of the original, indicating that carbon nanotubes increased the ultimate yield stress of the resin and the material in the epoxy resin, and alleviated the weakness that the composite was easy to delaminate under impact load.

# **4 Conclusion**

The impact resistance of carbon fiber reinforced metal composites and mechanical properties of carbon nanotube modified carbon fiber epoxy resin matrix were studied, and the conclusions were as follows:

**Acknowledgements.** This work was financially supported by the College Students' Innovative Entrepreneurial Training Plan Program (D202104022110228193), Aeronautical Science Foundation of China (2020Z055054002) and the Scientific Research Funds from Liaoning Education Department (JYT2020006 & JYT2020007).

# **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Comparative Analysis of the Displacement Dynamic Load Allowance and Bending Moment Dynamic Load Allowance of Highway Continuous Girder Bridge**

Kaixiang Fan(B)

School of Highway, Chang'an University, Xi'an 710064, Shaanxi, China<EMAIL_ADDRESS>
**Abstract.** The dynamic load allowance (DLA) of the bridge structure is an important parameter in the bridge design. In order to study the variation law of displacement DLA and bending moment DLA of continuous girder bridge, taking 2 × 30 m continuous girder bridge and five-axis vehicles as the research object, the road roughness was simulated by the trigonometric series approach. With the help of ANSYS and APDL language, the influence of vehicle speeds, vehicle weights and road roughness on the displacement DLA and bending moment DLA are studied. The results show that the displacement DLA showed increasing trend with the increase of vehicle speed, and bending moment DLA showed increasing first and then decreasing; With the increase of body weight, the displacement DLA and bending moment DLA show a gradually increasing trend; Displacement DLA and bending moment DLA do have numerical differences. And the value of the displacement DLA is slightly larger than the value of the bending moment DLA. It is suggested that the displacement DLA and bending moment DLA should be distinguished in engineering design and dynamic load test. The research conclusion can provide reference for bridge structure engineering design and dynamic load test.

**Keywords:** Bridge engineering · Continuous girder bridge · Vehicle-bridge interaction · Dynamic load allowance · Time-history curve

# **1 Introduction**

DLA is one of the important aspects of the application research of vehicle bridge coupling vibration analysis. There are many factors affecting the DLA of bridges, and the stress mechanism is very complex, so it has attracted more and more attention of researchers.

The DLA of the bridge structure was first a model test conducted by British and French engineers in 1844 to study the dynamic performance and bridge carrying capacity of the vehicle-bridge system. Many experts and scholars have done a lot of studies from many aspects: G G.Stokes [1], K.P.Chatterjee [2], V Kolousek [3] analyzed the coupling response of the bridge under the moving load, and derive the vehicle-bridge coupling vibration equation of the vehicle load when the vehicle load passes through the bridge structure; Song Yifan [4] found that the road roughness of bridge deck is the most significant factor affecting the dynamic action of vehicles based on analysis method of vehicle vibration response caused by pavement roughness; Shi Shangwei [5] analyzed the trend of difference and causes between the measured value and standard value of the DLA of the girder bridge. Jiang Peiwen [6] calculated the time history response of longspan continuous girder bridge under the action of multiple vehicles, and summarized the variation laws of displacement DLA and bending moment DLA based on the vehicle bridge coupling calculation method in ANSYS single environment; Zhou Yongjun [7] comprehensively considered the impact effect of vehicle load on the whole bridge, weighted the DLA at all peaks on the time history curve, and fully included the impact effect at multiple positions of the bridge structure; Denglu [8] found that the strain dynamic amplification factor is basically less than the deflection dynamic amplification factor by using the methods of theoretical derivation and numerical simulation.

In conclusion, many experts and scholars have carried out many researches on the DLA of bridges, and have made fruitful research results. But most of them are only for displacement DLA, and few researches on bending moment DLA are involved. In this paper, the coupling vibration model of the vehicle and bridge is established by ANSYS. The displacement time history curve and bending moment time curve of the bridge under different working conditions are analyzed. The change law of displacement DLA and bending moment DLA of continuous girder bridge under different vehicle speed, vehicle weight and road surface road roughness are studied.

# **2 Solution Method of Vehicle-Bridge Interaction**

Through the coordination relationship of the action force and displacement at the contact point, the equation of vehicle-bridge interaction is established as follows [9]:

$$
\begin{bmatrix} M\_{\rm b} \\ & M\_{\rm v} \end{bmatrix} \begin{Bmatrix} \ddot{\mathbf{y}}\_{\rm b} \\ \ddot{\mathbf{y}}\_{\rm v} \end{Bmatrix} + \begin{bmatrix} C\_{\rm b} & C\_{\rm bv} \\ C\_{\rm vb} & C\_{\rm v} \end{bmatrix} \begin{Bmatrix} \dot{\mathbf{y}}\_{\rm b} \\ \dot{\mathbf{y}}\_{\rm v} \end{Bmatrix} + \begin{Bmatrix} K\_{\rm b} & K\_{\rm bv} \\ K\_{\rm vb} & K\_{\rm v} \end{Bmatrix} \begin{Bmatrix} \mathbf{y}\_{\rm b} \\ \mathbf{y}\_{\rm v} \end{Bmatrix} = \begin{Bmatrix} F\_{\rm br} + F\_{\rm vg} \\ F\_{\rm vr} \end{Bmatrix} \tag{1}
$$

Where *M*,*C*,*K* are the quality, damping and stiffness matrix of the vehicle and bridge respectively; *d* is the vertical displacement, *b* and *v* are the bridge and vehicle respectively; *Fbr* and *Fvr* are the interaction force of the vehicle-bridge system respectively, the subscript *r* represents the road roughness, and *F***vg** represents the vehicle gravity.

Based on the above principle, the time-variation equation is solved by the Newmarkβ method. Using the transient analysis function of large-scale finite element program ANSYS, the vehicle bridge coupling vibration model is established by APDL language and displacement contact method, and the time-varying equation is solved by direct integration method.

# **3 Bridge, Vehicle and Road Roughness Model**

### **3.1 Bridge Model**

In order to study the displacement DLA and bending moment DLA of continuous girder bridge, 2 × 30 m continuous girder is selected the research object, the material is C50 concrete, and its section form is shown in Fig. 1.

**Fig. 1.** Cross section of bridge (unit: cm)

### **3.2 Vehicle Model**

1/2 vehicle model is selected. The vehicle layout diagram is shown in the Fig. 2, detailed parameters reference literature [10].

**Fig. 2.** 1/2 Vehicle model

### **3.3 Road Roughness Model**

Road roughness is a very important excitation source of vehicle bridge coupling vibration. In practice, the statistical characteristics of road roughness are usually described by power spectrum, and the power spectral density of pavement roughness can be fitted as

$$G\_{\chi}(n) = G\_{\chi}(n\_0) \left(\frac{n}{n\_0}\right)^{-\omega} \tag{2}$$

Where *n* is the spatial frequency; *n*0 is the reference spatial frequency; *Gx*(*n*) is the displacement power spectral density value, *Gx*(*n*0) is the coefficient of road roughness; *ω* is the frequency index, *ω* = 2.

# **4 The Method of DLA Calculation and the Working Condition Layout**

### **4.1 Working Condition Layout**

2 × 30 m continuous girder bridge is used for analysis. The effects of vehicle speed, vehicle weight and road roughness on the DLA of continuous girder bridge are considered. Among them, five speeds, five vehicle weights and three grades of road roughness are considered respectively. The specific working conditions are shown in the Table 1:

### **Table 1.** Working conditions

### **4.2 Calculation Method of the DLA**

The DLA (μ) is defined under the current specification:

$$
\mu = \frac{f\_{d.\,\max}}{f\_{s.\,\max}} - 1 \tag{3}
$$

Where *f d*.*max* is the maximum dynamic response of the vehicle when passing the bridge; *fs*.*max* is the maximum static response corresponding to the bridge structure of the same vehicle. *μd* is the displacement DLA, and *μM* is the bending moment DLA.

### **5 Results Analysis**

Based on the established calculation model and considering various influencing factors in the Table 1, the vehicle-bridge interaction calculation is carried out, and the effects of different grades of road roughness, vehicle speed and vehicle body weight on the displacement DLA and bending moment DLA in the mid-span of the first span of continuous girder bridge are analyzed. The relevant results are analyzed as follows.

### **5.1 Influence of Vehicle Speed on the Displacement DLA and Bending Moment DLA of the Continuous Girder Bridge**

In order to study the influence of vehicle speed on the displacement DLA and bending moment, the road roughness is not considered in the analysis. The analysis results are shown in the following Figs. 3, 4 and 5:

**Fig. 3.** Displacement curve at different speeds of smooth pavement

**Fig. 4.** Bending moment curve at different speeds of smooth pavement

The vehicle speed has a significant impact on the displacement DLA and the bending moment DLA of the continuous girder bridge. With the increase of the vehicle speed,

**Fig. 5.** Comparison of displacement DLA and bending moment DLA at different speeds

the change rules of the displacement DLA and the bending moment DLA are different. And the maximum value of the bending moment DLA is less than the maximum value of the displacement DLA. At the same time, the difference between the value of the displacement DLA and the value of the bending moment DLA changes with the increase of the vehicle speed. And the value of the former is about double that of the latter.

### **5.2 Influence of the Vehicle Body Weight on the Displacement DLA and Bending Moment DLA of the Continuous Girder Bridge**

In order to study the influence of vehicle body weight on the displacement DLA and bending moment DLA of continuous girder bridge, the influence of road roughness is not considered in the analysis process, and the vehicle speed is set as **v** = 20 m/s. The analysis results are shown in the Fig. 6:

The weight of vehicle body has a significant impact on the displacement DLA and bending moment DLA of continuous girder bridge. With the increase of vehicle body weight, the variation law of displacement DLA and bending moment DLA is the same, showing a gradual increasing trend, and the displacement DLA is greater than the bending moment DLA. And the value of the former is about triple that of the latter.

### **5.3 Influence of Road Roughness on the Displacement DLA and Bending Moment DLA of the Continuous Girder Bridge**

In order to study the impact of road roughness on displacement DLA and bending moment DLA of continuous girder bridge, the vehicle speed **v** = 20 m/s during the analysis. In order to avoid the influence of the randomness of the road roughness samples on the results, the DAL under 15 randomly generated road roughness samples is calculated for each working condition, and then the average value is calculated. The analysis results are shown in the Fig. 7.

The road roughness has a significant influence on the displacement DLA and bending moment DLA of the continuous girder bridge. Compared with grade A road roughness, the value of DLA under grade C road roughness is about 9 times that under grade A road

**Fig. 6.** Comparison between displacement DLA and bending moment DLA under different vehicle body weight

**Fig. 7.** Comparison between displacement DLA and bending moment DLA under different road roughness grades

roughness. With the increase of the grade of road roughness, the displacement DLA and bending moment DLA both increase gradually. At the same time, displacement DLA is slightly larger than bending moment DLA for the same grade of road roughness. And the difference between them increases with the increase of the grade of road roughness. The maximum difference between them is = 0.016.

## **6 Conclusion**

Through the calculation and analysis of the finite element model, the influence of vehicle speed, vehicle body weight and road roughness on the displacement DLA and bending moment DLA of the continuous girder bridge are studied. The conclusion of comparative analysis as follows:

# **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Temperature Distribution and Transmission in Multilayer Porous Asphalt Courses**

Hongqing Chen1, Chunfa Jiang1, Yunfei Su1, and Xiaowei Wang2(B)

1 CCCC-SHEC Third Highway Engineering CO., LTD., Xi'an, China 2 School of Civil Engineering, Xi'an University of Architecture and Technology, Xi'an, China<EMAIL_ADDRESS>
**Abstract.** The objective of this paper was to investigate the temperature distribution and the law of temperature transmission in multilayer porous asphalt courses. Three types of multilayer porous asphalt courses are designed as the same thickness of actual pavements. In order to achieve this objective, experiments were conducted in an oven with different temperature, and samples were enwrapped with an efficient insulation material except the surface. The final temperature in samples is lower by 5~10 °C than ambient temperature and reduced gradually from top to bottom. The ability of heat transmission is related to the mixture's air void and ambient temperature. The temperature transmission rate in porous asphalt mixture is lower than traditional dense graded asphalt mixture. At last, temperature transmission formulas of porous asphalt mixture are given.

**Keywords:** Porous asphalt mixture · Multilayer porous asphalt courses · Temperature distribution · Temperature transmission · Temperature reduction

# **1 Introduction**

Pavement distresses, such as rutting and moisture damage, were occurred in porous asphalt (PA) pavements during their service life because asphalt material is a typical temperature sensitive material. There is a closed relationship between pavement distresses and temperature [1–3]. When the solar radiation falls on the road surface, the surface start to warm up and heat begin to pass down. Gradually, the pavement structure was heated up to a certain temperature and forming a temperature gradient in pavement structure. The road materials and structure may appear damage in such environmental conditions for a long term. High temperature causes rutting damage, and great temperature gradient would cause cracking in pavement structures [4, 5]. Furthermore, frequent changes in temperature will exacerbate the possibility of such damage. In order to better prevent the emergence of these diseases, it is necessary to study the law of heat transfer in PA pavement.

PA pavement is a kind of open graded asphalt pavement which has a large air void (AV) content of 15%~25%, and skeleton-pore structure [6, 7]. PA pavement has the advantages of runoff mitigation, driving safety improvement, noise reduction, and et al. [8]. Asphalt types, aggregate type, porosity will affect heat-conducting property of road structure. Due to the high AV content, temperature in PA pavements is lower than traditional dense graded asphalt pavements, and PA pavements are used to mitigate the effects of urban heat island (UHI) [9]. In addition, the temperature has a significant effect on the bearing capacity and performance of PA pavement [10–12]. A variety of common damage is also directly or indirectly related to the distribution of road surface temperature. At present, many research concentrate on the temperature field under the comprehensive impact of solar radiation and temperature for dense graded asphalt pavements. In this paper, the temperature distribution and the law of temperature transmission in multilayer PA courses was investigated.

# **2 Materials and Experiment Design**

# **2.1 Materials**

PA mixture and dense graded asphalt mixtures (SUP) with different nominal maximum aggregate size (NMAS) was used in the paper, including PAC-13, PAC-16, PAC-25, SUP-20 and SUP-25. The details of these mixtures are illustrated in Table 1. Aggregates of basalt and limestone were used in this paper. Limestone was used in PAC-25, SUP-20 and SUP-25, and other mixtures used basalt. High viscosity binder (HVB) and SBS modified asphalt was used in the paper and the optimal asphalt contents is presented in Table 1. The technical properties of HVB and SBS modified asphalt are shown in Table 2.

**Table 1.** Aggregate gradations and mix design results.

**Table 2.** Properties of HVB and SBS modified asphalt.

### **2.2 Specimen Preparation**

Specimen with a diameter of 150 mm was compacted by Superpave gyratory compactor (SGC) with the height control model to obtain the target air voids. As shown in Fig. 1, three types multilayer PA courses were designed. Multilayer PA courses consist of singlelayer PA (type I), double layer PA courses (type II), and triple layer PA courses (type III). All of them consist of top layer, middle layer and bottom layer with a total thickness of 18 cm, and emulsified asphalt was used to glue each layer together. The thickness of top layer, middle layer, and bottom layer is 4 cm, 6 cm, and 8 cm, which is equal to the actual pavement.

In order to record the temperature inside the sample and study the law of heat transmission accurately, temperature sensor was put in the drill hole which is made in advance. The location is shown in Fig. 2.

**Fig. 1.** Types of samples.

**Fig. 2.** The location of sensors.

## **2.3 Test Scheme**

All the tests are performed in an oven, which can keep a constant temperature during the test. A temperature recorder is used to record the temperature through temperature sensor. In actual pavements, heat only transit from surface to bottom. In experiment, in order to simulate this situation, an efficient insulation material is applied to the sample except the top. Three temperatures of 40 °C, 50 °C and 60 °C are selected. When the oven reach the given temperature, put sample in and turn on the temperature recorder. The record interval of recorder is 10 min. The Termination condition is that the temperature change of 14 cm less than 1 °C in an hour.

# **3 Results and Discussion**

### **3.1 Temperature at Depth of 2 cm**

As we can see from the Fig. 3, firstly, the final temperature of 2 cm is lower about 5 °C than the ambient temperature no matter what temperature the sample I in. The explanation is that there will be heat losses in distribution of temperature because of the heat-transfer capability of mixture. Secondly, no matter what the temperature conditions, the early heating rate is very high and then become gentle slowly. But, the time of the first phases is different. The period in which sample warm up quickly is 150 min when the ambient temperature is 40 °C, while 50 °C is 200 min, 60 °C is 250 min. It means the ambient temperature which the mixture in is higher, the time which mixture will go through temperature changes is longer. Thirdly, the higher the temperature at which the sample is placed, the greater the rate of temperature rise. In that case, the ambient temperature of mixture is higher, it will undergo more sharp temperature changes.

**Fig. 3.** Temperature of 2 cm in sample I, II, and III

### **3.2 Temperature at 10 cm**

As shown in the Fig. 4, the following results can be achieved. When samples are placed in low temperature environment, the ability of temperature transmission of different aggregate gradations is equivalent. In the beginning, the PAC-16 mixture is better than SUP-20 mixture, gradually, the SUP-20 is better than PAC-16. When in medium or high temperature, the PAC-16 mixture shows a pretty excellent performance of temperature transmission, especially in medium temperature.

**Fig. 4.** Temperature at 10 cm in Sample I II

### **3.3 Temperature at 14 cm**

The temperature distribution at 14 cm is shown in Fig. 5. Obviously, the temperature transmission ability of PAC-25 and SUP-25 is pretty equivalent. It has been concluded in the previous results. The temperature of bituminous concrete subsurface is a little low. In lower ambient temperature, the ability of SUP and PAC is pretty close.

### **3.4 The Temperature Transmission Law**

In order to study the temperature transmission law, the following method is adopted. Firstly, the temperature of 2 cm in sample I, 10 cm in sample II and 14 cm in sample III is selected, and the corresponding ambient temperature is 40 °C 50 °C and 60 °C. Secondly, calculate the different value between ambient temperature and temperature of the above location and draw them in coordinate system. Then, connect them with a smooth curve. Lastly, fitting curve with cubic polynomials and obtain the temperature transmission formulas. Figure 6 (a) shows the temperature difference between 2 cm in sample I and ambient at the 40 °C and the fitting line of the temperature differences. Figure 6 (b) shows the temperature difference between 10 cm in sample II and 50 °C, and Fig. 6(c) shows the temperature difference between 14 cm in sample III and 60 °C.

**Fig. 6.** The fitting curve of temperature transmission

All the formulas above is concluded from few limited date and there isn't every verification. At the same time, there are lots of effects which can influence the temperature transmission. As a result, the applicability and practicability of those formulas are limited. In this paper, they are adopted to reveal the sketchy low of temperature transmission, which can provide a reference for the further research.

# **4 Conclusions**

The main conclusion of this paper can be summarized as followed:

# **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Research on Support Damage of Highway Bridge Based on Midas**

Miaomiao Fang1(B) , Yuqi Wang2, Jiaxin Liu1, and Fan Sun1

> 1 Chang'an University, Xi'an, Shaanxi, China<EMAIL_ADDRESS>
2 China Railway Shanghai Design Institute Group Co., Ltd., Shanghai, China

**Abstract.** During the operation of highway bridges, the bearing stiffness will decrease with the service life, and the mechanical properties will also change. In order to study the influence of stiffness damage on bearing. In this paper, a continuous beam bridge is selected for finite element model analysis, and the effects of stiffness damage on bearing force and bearing offset under the conditions of concrete shrinkage and creep and 30 °C temperature difference are comprehensively considered. The results show that the bearing stiffness damage has little influence on the vertical displacement, horizontal displacement and bearing capacity of the bearing, but has a great influence on the vertical compression deformation and durability of the bearing.

**Keywords:** Rubber bearing · Stiffness reduction · Mechanical performance · Support offset · Durability

# **1 Introduction**

In recent decades, with the continuous development of highway bridges in China, the traffic mileage of expressway is also increasing. Plate rubber bearing is widely used because of its simple structure, simple processing, manufacturing and installation, simple maintenance and low cost. According to the survey, the terrain of Shanxi Province is complex and the temperature difference between day and night is large. Under the influence of coal transportation, the traffic volume increases suddenly. This makes the bridges in this area overloaded seriously, resulting in the stiffness problems of 95% of the bridge bearings, and the durability of the bearings will be affected.

Chen Yanjiang et al. [1] studied the influence of recycled rubber on the durability of plate rubber bearing from the perspective of material, and came to the conclusion that the amount of recycled rubber added into the branch seat rubber can be determined by detecting the mechanical index of compression shear modulus before and after bearing aging, so as to judge the early failure of bearing; Xu Yue et al. [2] studied the influence of plate rubber bearing stiffness on the stress and deformation of bridge structure through T-beam finite element analysis. It is concluded that the loss of bearing stiffness has little influence on internal force, but has great influence on structural deformation; Huang Yueping [3], studied the influence of uneven rubber layer thickness on the durability of plate rubber bearing, and concluded that uneven rubber layer thickness will lead to the improvement of its mechanical properties, and the processing and testing process should be strictly controlled during the production and inspection of rubber bearing.

The above studies are from the perspective of materials and bridge structure stress. However, in the actual bridge operation, under the influence of environmental factors such as load and climate, the bearing stiffness will be reduced, which will have a great impact on the bearing durability and bridge durability. This paper mainly studies the stiffness damage of bearing, taking a 2 × 40 m T-beam bridge as an example, the damage of the bearing is simulated, and then by changing the bearing stiffness, the stress, stress and offset are analyzed to obtain the impact of the reduction of bearing stiffness on the bearing.

# **2 Bearing Damage Simulation**

There are two very important mechanical indexes of the bearing: compressive elastic modulus and shear elastic modulus, so the design of the bearing is inseparable from these two data. According to the above analysis, the damage of plate rubber bearing can be simplified as the change of shape coefficient and shear modulus of rubber bearing [4].

Support damage simulation can generally be carried out from the following two aspects: a. change the plane size of the support; b. Change the rubber shear modulus in the bearing. In the finite element software, the elastic connection is generally used to simulate the restraint effect of the bearing. Since the degrees of freedom in six directions

*SDx*, *SDy*, *SDz*, *SRx*, *SRy*, *SRz*, in the elastic connection are determined according to the plane size and shear stiffness g of the rubber bearing, the damage degree of the bearing can be effectively simulated by adjusting the corresponding restraint stiffness [5–13].

The stiffness calculation formula of plate rubber bearing is:

Stiffness in x-axis direction of element local coordinate system: *SDx* = *EA/L*;

Stiffness of element local coordinate system in Y, Z axis direction: *SDy* = *SDz* = *GA/L*; Rotational stiffness in x-axis direction of element local coordinate system: *SRx* = *GIp*/*L*; Rotational stiffness of element local coordinate system in Y-axis direction: *SRy* = *EIy*/*L*; Rotational stiffness of element local coordinate system in Y-axis direction: *SRz* = *EIz*/*L*.

# **3 Model Building**

The supporting bridge is a river crossing bridge. The main beam adopts C50 concrete, and its superstructure is fabricated prestressed concrete T-beam. The bearing is teflon plate rubber bearing, its differential settlement is - = 5 mm and the specification of the side fulcrum bearing is GJZF4400 × 400 × 85 mm, and the specification of the middle fulcrum support is GJZ F4550 × 550 × 130 mm. The bridge is located in the environment with large temperature difference between day and night. Rigid connection between main beam and pier; In order to comprehensively analyze the bearing stress, under the basic load combination, simulate the displacement and stress of the bearing under the combined overall temperature rise of 30 °C and overall temperature drop of 30 °C and concrete shrinkage and creep. The bridge model and model bearing reaction are shown in Figs. 1 and 2.

**Fig. 1.** Depends on the 2 × 40 m finite element model of the bridge

**Fig. 2.** Reaction value of rear support of bidirectional movable support of the model

# **4 Bearing Durability Analysis**

### **4.1 Stress and Deformation Analysis**

In order to better analyze the impact of stiffness reduction of two-way movable bearing, this paper takes longitudinal bearing, transverse bearing and two-way movable bearing for comparison, and takes a point for each type of bearing for analysis. In the environment with large temperature difference, the thermal expansion and cold contraction of concrete beam and the shrinkage and creep of concrete have a great impact on the bearing. Therefore, considering the shrinkage and creep of 10 years and the temperature difference of 30°, the stress and offset of the bearing are analyzed. The stress and offset of various bearings under different working conditions are shown in the Tables 1, 2and3 below.

It can be seen from the above table that the longitudinal displacement of the longitudinal movable bearing is large, and the temperature has a great impact on the longitudinal

**Table 1.** Forces and offsets of longitudinal movable supports under different working conditions

**Table 2.** Forces and offsets of lateral movable supports under different working conditions

**Table 3.** Forces and offsets of bidirectional movable supports under different working conditions

stress and displacement of the bearing. When the temperature rises by 30 °C, the longitudinal displacement of the bearing changes by 13.4 mm; When the temperature drops by 30 °C, the longitudinal displacement of the support changes by 16.58 mm.

The vertical displacement of the lateral movable bearing is large, but the temperature has a great influence on the lateral displacement. When the temperature rises to 30 °C, the lateral displacement of the bearing changes by 1.61 mm; When the temperature drops by 30 °C, the lateral displacement of the support changes by 1.64 mm.

The support reaction force of two-way movable bearing is small, the vertical displacement is small, and the longitudinal and transverse displacement is large. Temperature change has great influence on longitudinal and transverse displacement. The variation amplitude of longitudinal displacement is similar to that of longitudinal movable support, and the variation amplitude of transverse displacement is similar to that of transverse movable support.

According to the specification, for the support GJZF4400 × 400 × 85 mm, the limit value of two-way movable bearing along the bridge direction is 90 mm, the limit value of transverse bridge direction is 40 mm, the limit value of one-way movable bearing along the bridge direction is 90 mm, and the limit value of transverse bridge direction is 3 mm; For the support GJZF4550 × 550 × 130 mm, the limit value of unidirectional movable bearing along the bridge is 130 mm, and the limit value of transverse bridge is 3 mm. According to the results of the above analysis, the maximum longitudinal displacement of the support is 18% of the longitudinal limit and the maximum transverse displacement of the support is 55% of the transverse limit. Although the displacement meets the requirements of the specification, the lateral offset of the support is obviously larger than the longitudinal offset.

According to the above analysis results, the bearing reaction value is less than the maximum bearing capacity of the bearing, and there is nearly 30% surplus, which meets the requirements of the specification. However, with the passage of time, the bearing disease will reduce the rubber stiffness of the bearing, and the surplus in the design may be offset in the operation process, making the bearing reaction greater than the design value, resulting in the failure of the bearing.

### **4.2 Bearing Stiffness Damage Analysis**

The above analysis of the force and deflection of the support under three different conditions shows that the force of the support has a certain margin in the design. However, during the operation of the bridge, the stiffness of the support will continue to weaken, causing the surplus to be gradually offset, which will have a great impact on the durability of the support. Next, for the support of the bridge, under three different conditions, the force and displacement of the support are analyzed under the conditions of constant stiffness of the support and reduction of 20%, 40%, and 60%. Because the force and deformation changes of the two-way movable support under different working conditions are relatively large, this article takes the two-way movable support as an example to analyze the influence of the change of the stiffness of the support on the force and deformation of the support. The 10-year shrinkage and creep of the concrete, the combined temperature rise of 30 °C, and the combined temperature drop of 30 °C support offset and force are shown in Figs. 3, 4 and 5.

**Fig. 3.** 10-year shrinkage and creep of concrete

It can be seen in Fig. 3 that under the condition of shrinkage and creep of the concrete 10, the value of the support in the F(x) and F(y) directions is very small, which can be ignored and unchanged, and the support is in these three directions. The force changes are very small. However, the offset changes in the three directions of the support are different. The offset in the D(z) direction is very obvious, from −1.2065 mm to −3.0557 mm; the

**Fig. 4.** Temperature rising 30 °C

support is in the D(x) direction. Before the stiffness of the seat is reduced to 40%, the offset changes more gently, but when the stiffness is reduced to 60%, the offset of the support is larger.

**Fig. 5.** Temperature cooling 30 °C

**Fig. 6.** Comparison of three working conditions

It can be seen from Fig. 5 and Fig. 6 that under the temperature difference of 30 °C, the stress change of the bearing is roughly the same as that under the shrinkage and creep of concrete, with little change; The variation range of bearing offset in D(x) and D(y) directions is very small, but the increase range of vertical displacement is very obvious, from −1.2055 mm to −3.0548 mm.

In conclusion, the reduction of bearing stiffness weakens the bearing durability. Under the three different conditions given above, the increase of stiffness damage of bidirectional movable bearing reduces the stress in x and y directions and increases the stress in z direction, but the increase range is small; The influence on the longitudinal and transverse deformation of the bearing is very small and can be ignored, but it has a great influence on the vertical displacement of the bearing. The vertical deformation change of support under three working conditions is shown in the figure below.

It can be clearly seen from Fig. 6 that under the condition of 10-year shrinkage and creep, the stiffness of the two-way movable bearing is reduced to 60%, which is 1.8492 mm higher than the vertical extrusion deformation without reduction, with an increase of about 60.52%; Under the condition of combined temperature rise of 30 °C, the vertical extrusion deformation of the support increases by 1.8491 mm, with an increase of about 60.49%; When the combined cooling temperature is 30 °C, the vertical extrusion deformation of the support increases by 1.8493 mm, with an increase of about 60.54%. Therefore, with the passage of time, the stiffness of the support is continuously reduced and the vertical displacement of the support is continuously increased, which is not conducive to the durability of the support, and the increase of the extrusion deformation of the support is more likely to cause bulging cracks.

# **5 Conclusion**

# **References**

1. Chen, Y.J., Li, B.B., Zhao, Q.Y.: Experimental study on the effect of recycled rubber on the durability of plate rubber bearing. Highway Traf. Sci. Technol. (Applied Technology Edition) **14**(08), 120–122 (2018)

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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# **Application Analysis of Several Basement Exterior Wall Construction Schemes in Compacted Pile Foundation Treatment Engineering**

Yatuan Yan, Chen Chen(B) , Yufei Xu, Shoufu Li, Teng Wang, and Di Ding

China Construction Third Engineering Bureau Co. LTD. Northwest Branch, Xian 710065, Shaanxi, China<EMAIL_ADDRESS>
**Abstract.** Collapsible loess exists in a large area in Northwestern China. When collapsible loess exists in the ground, it is usually necessary to treat it to eliminate the collapsibility before placing the building foundation. When compacting piles are used to treat the collapsible loess foundation, there are three different construction schemes for the construction of the basement exterior wall, which are the conventional excavation scheme, the outer frame edge excavation scheme, and the unilateral support form excavation scheme. Through the detailed description of the three construction schemes, and the comparative analysis from the aspects of construction difficulty, economy, construction period, etc. It can be concluded that the conventional excavation scheme has the highest cost, the highest construction efficiency, the longest construction period, and other aspects. The frame edge excavation scheme has the lowest construction efficiency, and the unilateral formwork excavation scheme has the lowest cost and the shortest construction period.

**Keywords:** Basement exterior wall · Collapsible loess · Compacted piles · One-sided support module · Construction plan

# **1 Introduction**

Collapsible loess is a kind of soil with special properties. Microscopically, it is composed of structural units, cements and pores. The color is mostly light gray-yellow or yellowbrown, the soil quality is relatively uniform, good permeability, large pores, and easy disintegration, vertical joint development, and the mechanical properties are anisotropic. The landform and structure of loess are shown in Fig. 1. The characteristics of Collapsible loess are generally higher strength and lower compressibility when it is not wetted. When it is wetted by water under a certain pressure, the soil structure will be destroyed quickly, resulting in a large additional subsidence and a rapid decrease in strength.

Loess collapsibility is an unstable deformation with a large amount of subsidence and a fast subsidence rate. It can lead to uneven settlement of the foundation, which is more harmful to the building. It will cause the tilt of the structure, the damage of the wall in the house and the cracking of the load-bearing structure such as beams and columns. In addition, the hazards to road engineering are mainly manifested in uneven settlement after encountering water, causing large-scale cracking of municipal roads, and sinking affects road construction quality and driving safety.

It is necessary to consider the importance of the building, the degree of the possibility of the foundation being wetted by water and the strictness of the uneven settlement limit during the use period when constructing in collapsible loess areas. In order to prevent the loess foundation from collapsing, the replacement cushion method, dynamic compaction method, impact compaction method, Compacted pile method and other measures can be used to strengthen the soil to improve the bearing capacity of the soil layer. Some foundation treatment methods are shown in Fig. 2.

a) Loess landform b) Schematic diagram of loess structure

**Fig. 1.** Landform and structure of loess

a) Replacement cushion method b) Compacted pile method

**Fig. 2.** Some foundation treatment methods

Under normal circumstances, the construction of the basement exterior wall is to erect the frame after the excavation of the foundation pit reaches the specified elevation, and then support the formwork for concrete pouring. However, when there is collapsible loess in the construction zone, it is necessary to treat the collapsible loess foundation locally or wholly. When using compacted piles to wholly treat the collapsibility, the plane treatment range should exceed the outer edge of the building exterior wall by 2 m, and should not be less than 1/2 of the thickness of the treated soil layer [1]. At this time, if the outer edge of the foundation pit excavation is designed outside the compacted pile, the construction site needs a larger plane working surface. However, with the continuous advancement of the urbanization process in China, the old and new buildings are often close to each other, and measures should be taken to reduce the mutual influence between the buildings when the new buildings are under construction in the basement. However, with the continuous advancement of the urbanization process, the old and new buildings are often relatively close, and measures should be taken to reduce the mutual influence between the buildings during the construction of the new building basement [2]. For this kind of project with narrow construction site and limited space, reduce the excavation range of the foundation pit fertilizer trough, and directly carry out the compaction pile construction from the positive and negative zero elevation. It is a good way to use unilateral support for the construction of the basement exterior wall. A construction plan that effectively saves working surface and reduces the mutual influence between buildings. Based on a typical residential project in Xi'an, this article introduces in detail three construction schemes for the basement exterior wall when using plain soil compaction piles to treat collapsible loess foundations [3, 4]. Comprehensive analysis of several programs.

# **2 Overview of Construction Scheme**

For a residential project in Xi'an City, the seismic grade of shear wall of the project is grade 2, the design grade of underground garage foundation is grade C, and the basement has two layers, each with a height of 3.7 m. Some foundation soils are of grade II heavy collapsibility. The collapsible loess foundation is treated as a whole with plain soil compaction piles. The diameter of compaction piles is 400 mm, the distance between piles is 500 mm. The collapsibility treatment range is 4 m outside the raft cushion, the foundation is 400 mm thick raft, and 170 mm thick foundation cushion is set under the raft.

# **2.1 Conventional Excavation Scheme**

In order to ensure the effectiveness of foundation treatment, the conventional excavation scheme carries out pile row support construction at the edge of collapsibility treatment range, excavates all soil within collapsibility treatment range, and constructs compacted piles at elevation of pit bottom at −9.670 m after excavation. After construction of compacted piles, external frames are set up in turn, reinforcement bars of external walls are tied up, and external wall formwork is set up. Then the concrete construction of the basement outer wall is carried out [5, 6]. The schematic diagram of conventional excavation scheme is shown in Fig. 3.

**Fig. 3.** Schematic diagram of conventional excavation plan

### **2.2 Excavation Scheme for Outer Frame Edge**

Considering the installation of scaffolding for basement outer wall construction, the row pile support in this scheme is set at 2.5 m away from the outer edge of the outer wall, reserving the erection space for the outer frame and excavating all the earth inside the support. The compacted piles outside the excavation scope are drilled from the zero elevation and compacted to the elevation of −9.670 m. The above part is backfilled with plain soil. The compacted piles on the side within the excavation scope are constructed from the bottom elevation of −9.670 m pit. Schematic diagram of excavation scheme for outer frame edge is shown in Fig. 4.

### **2.3 Excavation Scheme of One-Sided Formwork**

Regardless of scaffolding during construction of basement exterior wall structure, unilateral formwork supporting technology is proposed for construction of basement exterior wall structure. In this scheme, row pile support is set 0.9 m away from outer edge of basement exterior wall, and excavation side line is close to inner side of support. Compacted piles with collapsibility treatment and expansion range are constructed from positive and negative zero elevation, compacted to −9.670 m elevation, and the above parts are backfilled with plain soil. Brick tyre film is used on the outside of the basement outer wall, and fine sand is used to fill the gap between the support and row of piles. The basement outer wall is constructed with one-sided formwork from the inside without setting up external scaffolding.

The schematic diagram of the one-sided support mode scheme is shown in Fig. 5.

**Fig. 4.** Schematic diagram of outer frame edge excavation plan

**Fig. 5.** Schematic diagram of unilateral formwork plan

# **3 Overview of Construction Scheme**

### **3.1 Economical Efficiency**

The list of quantities of the three schemes is shown in Table 1 and the economic comparison diagram is shown in Fig. 6. From the chart, it can be seen that the foundation pit of conventional excavation scheme has a large scope of outlay. Even without considering the support form, large area earthwork excavation and backfilling will cause significant increase in cost and relatively high construction cost. Due to the small excavation scope,

**Table 1.** Quantities list of exterior wall construction plan

the one-sided formwork construction scheme basically does not need soil backfilling of the fertilizer tank, and the minimum amount of earth excavation and backfilling is required. At the same time, no external erection and double-sided formwork support are required. Only the tyre form of outer wall bricks is required, thus the construction cost is relatively low. The construction cost of the outer frame edge construction scheme is between the conventional construction scheme and the one-sided formwork construction scheme [7, 8].

**Fig. 6.** Economic comparison chart of the three options

### **3.2 Difficulty of Construction**

Conventional excavation schemes increase the amount of work due to earth excavation and backfilling within 4.4 m of the outer side of the foundation, and often due to site constraints, foundation pit support is affected after foundation treatment is expanded, sometimes it is necessary to strengthen or even change the form of support, resulting in passivity of the constructor, reinforcement, formwork and support for the outer basement wall. Concrete construction is the same as inner wall construction, which cannot effectively improve work efficiency. The excavation scheme of one-sided formwork avoids the problem of ineffective earthwork excavation and backfilling outside the basement [9]. Because the exterior expanded compacted piles are struck from the ground, the length of bore holes needs to be increased. This part of work is relatively small and controllable. At the same time, the construction efficiency of the exterior wall structure is improved by using the single-sided formwork technology and the single-sided formwork frame can be rented, although it is necessary to increase the tyre form of exterior wall Costs have increased, but construction convenience has increased considerably. The foundation treatment of outer frame edge excavation scheme is partially excavated and then compacted piles are constructed. Some compacted piles are driven from the ground by the same measures as the one-sided formwork scheme, which improves the efficiency to a certain extent. However, the general formwork is still used to construct the basement outer wall structure with lower overall efficiency.

# **4 Conclusion**

Conventional excavation schemes will be affected more by pollution control, haze reduction, rainy season and other factors due to more earthwork excavation and backfilling in the expanded part of foundation treatment, thus affecting the construction period. In addition, the basement exterior wall structure is constructed by traditional technology, which is relatively time-consuming and has the longest construction period. The main difference of the excavation scheme of single-side formwork is that the exterior wall uses brick tyre mould, while the basement exterior wall structure uses single-side formwork technology, which effectively improves labour efficiency. In addition, when the expanded part of compacted piles of foundation treatment are laid from the ground, a certain construction period can be saved and the construction period is relatively shortest. The construction period of the outer frame edge excavation scheme is between the above schemes.

# **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Multilateral Boundary Blasting Theory of High and Steep Slope in Open Pit Mine and Its Application**

Junkai Chen1, Wenxue Gao1(B) , Xiangjun Hao2, Zheng Wei2, Xiaojun Zhang1, and Zhaochen Liu1

> 1 College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China<EMAIL_ADDRESS>2 Inner Mongolia Kinergy Blasting Co., Ltd., Erdos 017000, China

**Abstract.** At present, the blasting theory of high and steep rock slope mainly focuses on flat terrain, ignoring the influence of micro-terrain boundary factors on blasting effect, which leads to excessive blasting energy and affects the stability of slope. Therefore, based on the theory of multilateral boundary rock blasting, this paper deduces the calculation formula of blasting charge for high and steep rock slope under multilateral boundary conditions, and verifies it with field test. The results show that: (1) The multilateral boundary charge calculation formula directly includes micro-topography boundary conditions and blasting effect, and the rock blasting theory is based on the interaction of blasting energy provided by explosives and potential energy in medium, which effectively improves the energy utilization rate of explosives. (2) The influence of surplus blasting energy on the surrounding environment under different boundary conditions is controlled, and the explosive explosion effect is effectively controlled, so that a stable high and steep slope of open pit mine is formed after blasting.

**Keywords:** Micro-topography · Multilateral boundary · Blasting charge · High and steep slope

# **1 Introduction**

The application and research of engineering blasting technology in national economy and national defense construction has a long history. Since modern open pit mine stripping works are mostly carried out under the condition of high mountains and complex changes of wavy micro-topography, it is very important to establish blasting characteristics and blasting charge calculation theory under multilateral boundary conditions. The multilateral boundary condition refers to the boundary condition of micro-topography, which belongs to the shape geometry condition compared with the horizontal boundary condition [1].

Wang [2] systematically proposed the comprehensive theory of multilateral boundary stone blasting for the first time, and directly introduced the micro-topography into the blasting theory as a main condition. Chen et al. [3] studied quantitatively the influence of geological conditions and physical and mechanical properties of rock on the blasting effect and the effect of blasting on the stability of mountain or slope. Gu [4] proposed that the possibility of amplitude superposition should be considered when the interval time between charge bags is small, and the permissible distance of blasting vibration should be calculated according to equivalent charge. Chen et al. [5] improved the threemultiple blasting method and adopted multi-layer, multi-initiation and multi-face open terrain blasting to make the deep cutting take shape in one blast, which improved the blasting method of deep cutting facing open terrain in multi-boundary blasting theory. Xia et al. [6] made equivalent transformation of blasting vibration speed monitored on site according to Sadoski formula, and used linear regression control method to calculate blasting charge amount for subsequent construction. Huang et al. [7] uses high-speed photography technology and numerical calculation method to carry out research, and obtains that the maximum initial throwing velocity of slope rock increases, stabilizes and decreases in the direction of blasting propagation in the extended blast hole. Hu et al. [8] put forward the concept of equivalent path, which provides a new method for predicting the peak value of particle vibration velocity of bench blasting seismic wave. Gan et al. [9] built a theoretical model of iron ore crushing energy, which provides a theoretical basis for the calculation of ore crushing energy in iron mines. Yang et al. [10] proposed a liquid explosive fracturing technology based on deep-hole blasting of coal and rock, which enhanced the energy utilization rate of explosives in the direction of hard rock fracturing.

The above-mentioned research mainly focuses on the blasting theory and charge calculation of flat terrain. However, the change of boundary conditions of the microtopography is not considered enough, or only the micro-topography is considered as a factor that has an influence on the blasting effect. Since the charge calculation formula and design, method did not consider the potential energy of the rock mass itself, it caused a waste of explosive charge, easily caused geological diseases, and caused slope instability. Based on the comprehensive blasting theory of multi-boundary stonework, this paper directly introduces the micro-topography boundary conditions into the charge calculation and blasting effect, and conducts deep-hole controlled blasting to study the action law of charge, terrain conditions and blasting effect under multi-boundary conditions.

## **2 Main Role of Explosive Under Multilateral Boundary Conditions**

### **2.1 Upswing**

Upswing is also called sublation action under horizontal boundary condition. The explosive wave generated by the explosive charge explosion and the thrust of the expansion of the explosive product make the medium rise upward and then blow out to form the blasting funnel. It can be seen that the size of the blasting funnel and the quality of the throwing effect depend on the kinetic energy generated by the explosive explosion. The larger the dosage and the higher the throwing, the larger the throwing amount obtained, and the stable blasting effect. Under the condition of horizontal boundary, the drop rate is proportional to the amount of charge.

$$E \propto \mathcal{Q} \tag{1}$$

Upswing is the basis for determining the volume of the visible blasting funnel and the throwing rate of the two types of boundary conditions, the horizontal and the concave pass.

### **2.2 Collapse**

Under non-horizontal terrain conditions, the medium in the collapse funnel itself contains a certain amount of potential energy, and the blasting surface of the charge receiving bag collapses. It has a great effect on a number of technical indicators of engineering blasting, such as blasting hopper volume, throwing rate and unit consumption, etc. It is also the physical basis of multi-boundary blasting theory. According to the statistics of a large number of engineering practices, in different media, the ratio of the upper and lower damage radius is calculated by Eq. (2):

$$R\_{\mu} = \left(1 + \frac{\alpha^2}{5000 \sim 7000}\right) R\_I \tag{2}$$

In Eq. (2), *Ru* is the upper destruction radius of the blasting funnel (m). *Rl* is the lower destruction radius of the blasting funnel (m). α is the ground slope (°).

Under the inclined boundary condition, the reason why the upper destruction radius of the blasting funnel increases with the increase of the ground slope is essentially caused by the collapse. The upper damage radius increases with the slope of the ground, which is 1 to 2.6 times larger than the lower damage radius, and it is larger in soil and rock masses controlled by structural planes. From this, it can be seen that the collapse effect expands the damage range of the cartridge explosion.

### **2.3 Slump**

The high throwing rate in steep terrain is due to the existence of slump. When the medicine packet is only broken, the slump rate of the rock block is Eq. (3):

$$E\_o = 1 - \frac{1}{\xi} \left( \frac{\tan \theta}{1 - \cot \psi \tan \theta} \int \frac{\tan \alpha}{1 - \cot \psi \tan \alpha} \right) \tag{3}$$

In Eq. (3), *Eo* is the slump rate of the rock block when the medicine packet is only broken (%). ξ is the looseness coefficient of the rock, generally taken as 1.3. θ is the average angle of repose of the rock, generally around 35°, not more than 40°. ψ is the angle formed by the designed step slope line and the horizontal plane.

According to Eq. (3), it is obtained that when the cartridge only serves to break the rock mass, the slump rate of the exploded rock mass increases sharply with the steepening of the natural ground slope. Therefore, in the terrain above the steep slope (α > 50◦), the rock mass only needs to be fully broken, and its slump rate will reach the best throwing rate of the slope terrain using throwing blasting, and it has a good effect on the stability of the steep slope. In cliff topography, the slump rate can exceed 70%. Under steep terrain, no need to use throwing blasting. Because the potential energy contained in the rock mass itself has replaced the explosive energy required to throw the rock block out of the blasting funnel, the potential energy contained in the rock mass itself increases the effective utilization of explosive energy.

### **2.4 Side Throwing**

The effect of side throwing can be expressed by the increment of throwing rate, and the relationship with the natural ground slope is shown in Eq. (4):

$$
\Delta E = -77.52 \,\text{lg} \, f(\alpha) \tag{4}
$$

In Eq. (4), *E* is the increment of throwing rate (%). *f* (α) is the slump coefficient, and the calculation method is shown in Eq. (5):

$$f(\alpha) = \begin{cases} 1 - \alpha^2 / 7000 \text{ } \alpha < 30^\circ \\ 26/\alpha & \alpha < 30^\circ \end{cases} \tag{5}$$

Under multiple boundary conditions, the charge volume remains unchanged, and the increase in throwing rate increases with the steepness of the natural ground slope. The essence is that under multiple boundary conditions, the explosive kinetic energy and the potential energy of the rock are the result of the combined effect. The rock mass has a certain potential energy and a favorable throwing angle, so that the rock mass thrown from the side is not easy to fall back into the blasting funnel. Therefore, only a smaller throwing height and throwing distance are required to obtain a higher throwing rate.

# **3 Calculation Formula of Blasting Charge Under Multilateral Boundary Conditions**

### **3.1 Basic Principles and Assumptions**

### **3.2 Multilateral Boundary Dose Calculation Formula**

### (1) Theoretical calculation formula of multilateral boundary dose

According to the law of conservation of mechanical energy, the principle of functional balance and the above assumptions, the calculation formula for the multilateral boundary drug amount is obtained as follows:

$$Q = K W^3 F\_{\psi}(E, \alpha) = K W^3 \frac{10^{0.0129E}}{\left(\sqrt{0.05\alpha} + 1\right) \left(1.11 - \frac{86.133}{E} \lg f(\alpha)\right)} \tag{6}$$

In Eq. (6), *Q* is the multi-boundary blasting charge (kg). *K* is the dosage per cubic meter of standard throwing blasting (kg/m3). *W* is the minimum resistance line (m). *F*ψ (*E*, α) is the theoretical drug packet property index, which can be calculated by Eq. (7):

$$F\_{\psi}(E,\alpha) = \varphi(E) \cdot f\_{\psi}(\alpha, E) \tag{7}$$

In Eq. (7), ϕ(*E*) is the function of the throwing rate, generally ϕ(*E*) = 0.45 × 100.0129*E*, for the collapse blasting, ϕ(*E*) = 1. *f*ψ (α, *E*) is the topographic coefficient or the dose attenuation coefficient, which can be calculated by Eq. (8):

$$f\_{\emptyset}(\alpha, E) = V(\alpha) \cdot E(\alpha) \tag{8}$$

In Eq. (8), *V*(α)is the collapse factor, calculated by Eq. (9). *E*(α)is the side throwing factor, calculated by Eq. (10):

$$V(\alpha) = 2 \Big/ (\sqrt{A\alpha} + 1) \tag{9}$$

In Eq. (9), *A* is the collapse coefficient. In the calculation of multi-boundary drug dose, *A* = 0.05, and *A*α ≥ 1.

$$E(\alpha) = 1 \Big/ \left[ 1 - \frac{77.52}{E} \lg f(\alpha) \right] \tag{10}$$

In Eq. (10), *f* (α) is the slump coefficient, and the calculation method is shown in Eq. (5).

According to Eq. (8)–(10), the topographic coefficient is shown in Eq. (11):

$$f\_{\Psi}(\alpha, E) = 1 \Big/ \left(\sqrt{0.05\alpha} + 1\right) \Big[0.5 - \frac{38.76}{E} \lg f(\alpha)\Big] \tag{11}$$

The Eq. (11) to calculate the theoretical property index of the drug pack is shown in Eq. (12):

$$F\_{\Psi}(E,\alpha) = \frac{10^{0.0129E}}{\left(\sqrt{0.05\alpha} + 1\right)\left(1.11 - \frac{86.133}{E}\lg f(\alpha)\right)}\tag{12}$$

(2) Empirical calculation formula of multilateral boundary dose

$$\mathcal{Q} = K W^{\mathfrak{J}} F(E, \alpha) \tag{13}$$

In Eq. (13), *F*(*E*, α) is the property index of the drug package.

$$F(E, \alpha) = \varphi(E) \cdot f(\alpha) \tag{14}$$

### **3.3 Comparison of Theoretical Formula and Empirical Formula**

By comparing theoretical Eq. (6) and empirical Eq. (13), we can see that there are certain differences between the two, which are mainly manifested in the following two aspects:

(1) The terrain coefficient is different from the slump coefficient

The theoretical topographic coefficient refers to the slump coefficient when considering the law of lateral tossing, and takes a step forward, so that the topography or slump coefficient has a clear physical and mechanical meaning, that is, the *f*ψ (α, *E*) value reflects the effective utilization rate of blasting energy along with the topographic boundary The law of changing conditions. The terrain is favorable, the effective utilization rate of explosive energy is increased, and the amount of charge needs to be reduced. On the contrary, the terrain is unfavorable, and the utilization rate of explosive energy decreases, and the amount of charge needs to be increased like the terrain of a pass.

(2) The relationship between slump coefficient and terrain coefficient

The current empirical formula may produce the following situations in production: when the design-throwing rate *E* < 60%, the actual effect is higher and safer. When *E* > 60%∼70%, it is likely to be slightly lower, mainly in steep terrain. At this time, due to the sharp increase in slump, the actual blasting effect will not be affected. Therefore, it can be considered that the calculation Eq. (13) of the multiboundary charge is consistent with the theoretically derived formula. In the steep terrain, the principle of slump should be obeyed, and slump blasting should be used.

### **3.4 Calculating Formula of Charge for Multilateral Boundary Deep Hole Blasting**

Based on the analysis of the characteristics of rock mass blasting under multi-boundary conditions, especially the rock mass blasting of high and steep slopes, according to the calculation principle of formula (13), the formula for calculating the packing charge of deep-hole blasting columnar charge under multi-boundary conditions is obtained:

$$\mathcal{Q} = K W^{\mathcal{S}} F(E, \alpha) = K F(E, \alpha) aWh \tag{15}$$

In Eq. (15), *a* is the hole distance (m). *h* is the drilling depth (m).

The multilateral boundary charge calculation formula directly includes the terrain boundary conditions and the blasting effect. The blasting theory is based on the combination of the explosive energy provided by the explosive and the potential energy in the medium to control the excess blasting energy and excessive explosive consumption under different terrain conditions. Established the functional relationship among the explosive quantity, terrain boundary conditions and blasting effect, which is convenient for practical inspection and application of engineering blasting, and has been widely used in engineering blasting in our country.

# **4 Project Example**

### **4.1 Project Overview**

Xingguang Coal Mine is located in the west wing of Zhuozishan anticline, and its geomorphic features belong to the low mountain and hilly area of the Inner Mongolia Plateau. The terrain is relatively flat, the thickness of the loose cap layer is small, and geological disasters such as landslides and mudslides are rarely occurred. Gray-white medium and coarse sandstone with a small amount of gray-green sandy mudstone are distributed in a large area in the area. The stratum has been extensively weathered and eroded and is in integrated contact with the underlying Shanxi Formation. Sandy mudstone has weak water richness, hardens after losing water, easy to crack, and has little water content. The softening coefficient of various types of rocks varies greatly, ranging from 0.21 to 0.83, with an average of 0.40. Except for coal, all kinds of rocks are basically easy to soften rocks. The mine is a gas mine, and there is no outburst of coal and gas.

### **4.2 Deep Hole Blasting Design Under Multilateral Boundary Conditions**

According to the multilateral boundary blasting theory, the open-pit mine blasting design is carried out. The deep hole loosening millisecond delayed blasting construction is used to control the direction of the minimum resistance line of blasting, avoid facing the direction of residential houses and various buildings, and take safety protection measures. The environmental conditions of the blasting area are good, and the rock is drilled once and blasted to reach the design depth to ensure the construction progress. In order to control the blasting flying rocks, ensure the length of the blockage during construction, press sandbags at the orifices, and cover the wicker if necessary. At the same time, the millisecond delayed detonation technology is used to limit the maximum amount of detonating charge in a period to control the impact of blasting vibration and flying rocks on the surrounding environment. The blasting design parameters are as follows:

## **4.3 Detonation Network**

The network of digital electronic detonator is used in blasting, in which the outermost row near the side slope is firstly detonated, and then detonated hole by hole from outside to inside. Delay time setting: delay time between holes is 25 ms, and delay time between rows is 60 ms. The schematic diagram of initiation network is shown in Fig. 1.

**Fig. 1.** Initiation network diagram of bench blasting.

## **4.4 Blasting Effect and Analysis**

In this mining area, the multilateral boundary blasting theory is studied for deep-hole controlled blasting. The blasting of 76848 m3 and 73438 m3 is studied by multi-boundary design method and empirical design method respectively. Combined with the actual situation in the field, groups of measuring points are arranged at the horizontal distance of 70 m, 90 m, 110 m and 130 m respectively. Through the analysis of waveform diagram of vibration time history of four groups of measuring points (Fig. 2), the amplitude of blasting vibration velocity produced by multilateral boundary design method is less than that of empirical design. Under the same conditions, the multi-boundary design method uses less explosives, improves the energy utilization rate of explosives, makes the construction safer, and has less influence on the surrounding disturbance.

**Fig. 2.** Vibration monitoring waveform diagram.

Based on the theory of multi-boundary rock blasting and the formula of explosive charge calculation, the design and construction of rock mass blasting on high and steep slope of mine have been fully considered, and the blasting effect has been significantly improved. Field monitoring and camera show that blasting vibration and flying rocks have been effectively controlled; the fragmentation of blasting pile meets the design requirements, and all broken rock mass collapses within the design range (Fig. 3 and Fig. 4).

(a) Multilateral boundary design method (b) Experiential design method **Fig. 3.** Comparison of blasting fragmentation.

(a) Multilateral boundary design method (b) Experiential design method

**Fig. 4.** High and steep slope formed after blasting.

# **5 Conclusions**

Multi-boundary blasting theory considers the influence of topography and geological conditions on charge blasting. The blasting engineering practice of Xingguang Coal Mine in Inner Mongolia Kinergy Blasting Co., Ltd. shows that based on the analysis of blasting characteristics of charge under multi-boundary conditions, the following conclusions are drawn:

# **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Laboratory Model Test of Eco-Concrete Slab Slope Protection**

Hao Chen(B) , Fengchi Wang, Gang Xu, and Lilong Guo

School of Civil Engineering, Shenyang Jianzhu University, Shenyang, China<EMAIL_ADDRESS>
**Abstract.** In order to study the protective effects of eco-concrete slope and the influencing factors of eco-concrete slope deformation. The displacement characteristics and ultimate bearing capacity of the slope model under different geometric parameters are obtained through the laboratory model test of eco-concrete slope protection, and the influence laws of slope deformation under different protection slope conditions are summarized, as well as the influence laws of soil compaction, soil moisture content and slope ratio on the horizontal displacement restraint capacity and stability of the slope. Compared with the unprotected slope, the ultimate load of the reinforced concrete slab slope and the ordinary concrete slab slope are increased by 2.2 times and 2.4 times respectively, and the horizontal displacement restraint capacity of the slope is increased by 29.3% and 51.6% respectively. The moisture content, compactness and slope gradient of slope soil have a certain influence on the deformation restraint capacity of slope protected by vegetation concrete slab.

**Keywords:** Eco-concrete · Moisture content · Compactness · Slope gradient

## **1 Introduction**

In the traditional concrete slope protection project, ordinary concrete can effectively improve the stability of the slope, while also causing the balance of the slope ecological environment to be broken. In order to avoid sacrificing the ecological environment in exchange for urban development, in the early 1990s, many experts and scholars developed a new type of concrete-vegetable concrete that can maintain the high-strength properties of concrete while also taking into account the biocompatibility.

After continuous research by scholars at home and abroad, certain results have been achieved in the preparation of vegetation concrete [1–3], water permeability [4–6] and alkali reduction technology [7, 8]. However, the eco-concrete can protect the slope The extent of the impact still needs to be studied.

This test is designed as a scaled test to simulate the damage of the slope model, to study the protection effect of the eco-concrete slope and the factors affecting the deformation of the eco-concrete slope. Through the experiment, the displacement characteristics and ultimate bearing capacity of the slope model under different geometric parameters are obtained. According to the force, the slope failure load, the maximum settlement and the horizontal displacement of the slope are obtained, which provides a reference for the application of the eco-concrete slab on the slope.

# **2 Test overview**

# **2.1 Experiment Material**

The cement used in the test is P.O 42.5 grade ordinary Portland cement, and the ultrafine ore powder is obtained by crushing the ore of AnShan Iron and Steel Group. The water reducing agent is a polycarboxylic acid water reducing agent liquid, and the designed usage amount is 0.5%. The coarse aggregate of eco-concrete is recycled concrete aggregate.

## **2.2 Test Plan**

The test includes the following four working conditions, and the specific scheme is shown in Table 1. The planting soil suitable for plant growth in the local suburbs of ShenYang was selected as the test soil sample to be filled into the slope model groove as the main filling material for the slope. The specific model slot is shown in Fig. 1.

**Table 1.** The model test scheme

## **2.3 Specimen Production**

Before the soil sample is prepared, the test soil sample is air-dried and crushed first, and the soil sample is sieved with a 10mm square hole sieve. Calculate the mass of the soil samples required for each group of test models according to the standard of 90% compaction, multiply it by the loss coefficient of 1.1, weigh it, and mix with water.

Randomly test the moisture content of the soil sample, and fill the model slope in layers when the moisture content is close to ±2% of the optimal moisture content

**Fig. 1.** The test model tank

value. The weight of the compaction hammer is M = 13.5 kg, the drop distance is H = 685.5 mm, the total length of the guide rod is L = 800 mm, and the diameter of the compaction backing plate is ϕ = 153 mm. The filling height of each layer is 20 cm, and 40 compaction points are set in the filling section of each layer, and each layer is compacted 3 times. Each compaction ensures staggered compaction.

### **2.4 Sensing Element Layout and Loading**

During the test, the column tension and compression load cell was used to collect the vertical load, and the load cell range was 0–200 kn. The YHD displacement sensor is used to measure the slope displacement, and the comprehensive layout of the displacement sensor is shown in Fig. 2.

**Fig. 2.** The displacement sensor layout scheme

The loading phase is divided into the initial loading phase and the destruction loading phase. In the primary loading stage, the vertical load is applied at a loading speed of 5 KN/min. The vertical deformation of the specimen is detected by Disp1 and Disp2. When the values of Disp1 and Disp2 are stable and the difference between the two does not increase, the next First class load. In the loading stage of the destruction period, the loading speed is 1 KN/min. When the load reading appears "falling back", record the peak load stress at this time as the load design value. Stop loading until the first-level load value is reached, and collect the displacement count value after the compression deformation and stress redistribution inside the model soil (about 10 Min) are completed. Begin to apply the lower load. When there are obvious cracks in the slope, reduce the load loading level and increase the number of data observations until the slope is damaged on a large scale and the peak load no longer increases.

# **3 Effect Analysis of Eco-Concrete Slope Protection**

For the unprotected slope test,eco-concrete slope test and ordinary concrete slope test, the relationship between displacement and load at different positions of the slope is shown in Fig. 3, 4 and 5.

From the point of view of the vertical settlement of slope, slope ecological concrete and ordinary concrete slope compared with no protective slope, slope vertical settlement aspects appear very big contrast, the vertical settlement of the slope changed little, considering this is the laboratory scale experiments, the actual situation of the ecological concrete slope and no protective slope vertical settlement will be bigger; Compared with the unprotected slope, the concrete slab will have greater vertical settlement due to its larger weight during the experiment. The maximum settlement measured in the experiment is 10 mm, which is acceptable compared to the model size.

From the point of view of the horizontal displacement of the slope, with the increase of the vertical load, the trend of the horizontal displacement of the slope with different disposal methods is roughly the same. As can be seen from Table 2, both ecological concrete slab and ordinary concrete slab can increase their ultimate bearing capacity and effectively control their horizontal displacement. The maximum horizontal displacement of ecological concrete slope and ordinary concrete slope is reduced by 29.3% and 51.6% respectively compared with unprotected variable slope.In terms of the control ability of slope horizontal displacement, eco-concrete slab is slightly lower than ordinary concrete slab, but with the growth of plant roots, the control ability of eco-concrete slab on slope horizontal displacement will be greatly improved [9, 10].

**Fig. 3.** The load displacement curve of bare slope test

**Fig. 4.** The load displacement curve of vegetation regenerated concrete test

**Fig. 5.** The load displacement curve of normal concrete slope test

**Table 2.** The ultimate load and maximum horizontal displacement of slopes on different slopes

# **4 Analysis of Influencing Factors on Deformation and Stability of Ecoconcrete**

### **4.1 The Influence of Soil Compaction Degree Change on Slope**

Figure 6 shows the distribution of horizontal displacements at different positions of the slope surface under the action of different soil compaction degrees of the slope. The horizontal displacement of the slope surface gradually decreases with the increase of the slope soil compaction. When the slope soil compaction degree increases from 85% to 95%, the maximum horizontal displacement of the slope surface decreases by 11.3% and 19.8%, which is a large reduction; therefore, the degree of compaction is an important factor affecting the horizontal displacement of the slope surface.

Figure 7 shows the maximum settlement of the top of the slope when the slope of the soil with different compaction degrees is damaged. From the analysis of the relationship between the degree of compaction and the maximum settlement of the top of the slope, the maximum settlement of the top of the slope increases with the degree of soil compaction of the slope. And quickly decrease. The compaction of the slope soil increased from 85% to 95%. When the slope is damaged, the maximum settlement of the slope top also decreases by 1.7% and 4.1%. From the analysis of the relationship between the degree of compaction and the ultimate load of the slope, the ultimate load gradually increases with the increase of the degree of compaction; the compaction of the slope soil increases from 85% to 95%, the ultimate load of the slope It also increases by 11.1% and 21.5%. The compaction of the soil is the key influencing factor of the ultimate load of the slope. In the design of vegetation concrete slope protection, the degree of soil compaction should be increased as much as possible. The increase of the degree of compaction is conducive to reducing the deformation of the slope and improving the stability of the slope.

**Fig. 6.** The influence of compactness on slope horizontal displacement

### **4.2 Influence of Soil Water Content Change on Slope**

Figure 8 shows the horizontal displacement distribution diagram of the slope soil under different water content conditions. The horizontal displacement of the slope gradually

**Fig. 7.** The influence of compaction degree on the maximum settlement of slope top

increases with the increase of the water content of the slope soil. When the water content of the slope soil increased from 12% to 18%, the maximum horizontal displacement of the slope increased by 4.6% and 8.5%, and the increase in the horizontal displacement of the slope gradually increased. Therefore, the water content of the slope soil is an important factor affecting the horizontal displacement of the slope.

Figure 9 shows the maximum settlement of the slope top under different moisture content conditions. Based on the analysis of the relationship between the water content and the maximum subsidence of the top of the slope, the maximum subsidence of the top of the slope gradually decreases with the increase of the water content. The moisture content of the soil has increased from 12% to 18%, and the maximum settlement of the top of the slope has also been reduced by 8.1% and 1.9%. From the analysis of the relationship between the moisture content and the ultimate load of the slope, the ultimate load of the slope gradually decreases with the increase of the moisture content. The moisture content of the soil increased from 12% to 18%, and the ultimate load of the slope was also reduced by 15% and 11.8%. The moisture content of the soil has a greater impact on the ultimate load of the slope. When vegetation concrete is used for slope protection, special attention needs to be paid to the possibility of slope damage when the soil moisture content changes due to precipitation, changes in underground runoff and other factors.

### **4.3 Influence of Different Slope Ratios on Slope**

Figure 10 shows the horizontal displacement distribution diagram of the slope under different slope ratios. As the slope ratio decreases, the horizontal displacement of the slope gradually decreases. When the slope ratio of the slope is reduced from 1:1 to 1:1.5, the maximum horizontal displacement of the slope is reduced by 7.8%. Therefore, the slope ratio of the slope has a certain influence on the horizontal displacement of the slope.

Figure 11 shows the relationship between the slope ratio and the maximum settlement of the top of the slope. From the analysis of the relationship between the slope ratio and the maximum settlement at the top of the slope, the maximum settlement at the top of the slope gradually increases as the slope ratio decreases; the slope ratio decreases from 1:1 to 1:1.5, the slope top when the slope is damaged The maximum settlement increased

**Fig. 8.** The influence of water content on slope horizontal displacement of slope top

**Fig. 9.** The influence of water content on the maximum settlement of slope top

**Fig. 10.** The influence of slope on horizontal displacement of slope

**Fig. 11.** The influence of slope ratio on the maximum settlement of slope top

by 0.9%, and the slope ratio had little effect on the maximum settlement of the top of the slope when the slope was damaged. From the analysis of the relationship between the slope ratio and the ultimate load of the slope, the ultimate load of the slope gradually increases with the decrease of the slope ratio; the slope ratio is reduced from 1:1 to 1:1.5, the ultimate load of the slope failure This has increased by 15%. In the design of eco-concrete slopes, the slope ratio should be reduced as much as possible, which greatly improves the ultimate load of eco-concrete slopes.

# **5 Conclusion**

Under the action of slope top load, the deformation law of different slopes is basically the same, partial failure of slope occurs, slope protection structure is different, corresponding to the amplitude of each stage is also different.

Compared with the unguarded slope, the ecological concrete slope is significantly improved in ultimate bearing capacity and slope constraint capacity. In terms of ultimate load of slope, the ecological concrete slope and ordinary concrete slope are increased by 2.2 times and 2.4 times respectively. In terms of slope constraint capacity, the horizontal displacement of eco-concrete slope and ordinary concrete slope is reduced by 29.3% and 51.6%, respectively. Compared with the conventional concrete slope, there is still a gap in the protection effect of ecological concrete slope, but it has met the requirements of slope protection.

Slope in the case of ecological concrete protection, the deformation and stability of slope compaction, slope moisture content, slope ratio and other factors, in the design of ecological concrete slope, should consider the above factors on the deformation and stability of the slope.

Eco-concrete can restrain slope deformation and improve slope stability. By changing the above factors, the constraint ability of eco-concrete on slope deformation can be improved and the stability of slope can be improved, thus providing a certain reference for the application of eco-concrete in slope ecological restoration and reinforcement.

# **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Compressive Strength Performance of Additives for Cement-Based Grouting Material with Low Water-Binder Ratio by Response Surface Methodology**

Jiaxu Guo1(B) , Shaowei Hu1, Xuan Zhao2, Xiu Tao2, and Ying Nie2

1 School of Civil Engineering, Chongqing University, Chongqing 400030, China<EMAIL_ADDRESS>
2 CISDI Engineering Co., Ltd., Chongqing 401122, China

**Abstract.** In order to research the influence and the function mechanism of calcium formate and defoaming agent on the compressive strength of cement-based grouting material with low water-binder ratio at different ages, quadratic polynomial regression models were established by RSM, and the mix proportion was optimized. The function mechanism of additives was analysed by macroscopic mechanical properties and microstructure. The results indicated that the response surface method is scientific in optimizing the mix proportion of cement-based grouting material. The optimal mix proportion was obtained as fallow: the calcium formate was 0.64%, the water-binder ratio was 0.21 and the defoaming agent was 0.26%, with taking 1d, 3d, 28d compressive strength as the optimization objective. Calcium formate is highly significant for the early compressive strength of cement-based grouting materials with low water-binder ratio, while the waterbinder ratio and defoaming agent are highly significant for that of the middle and late period. Calcium formate promotes the formation of CSH gel and Ca*(*OH*)*2 crystallization in the early period, and the defoaming agent can effectively reduce macropores. The results can provide an optimization method for the mix proportion design of cement-based grouting material and a theoretical reference for its mechanical properties.

**Keywords:** Cement-based grouting material · Response surface method · Compressive strength · Calcium formate · Defoaming agent · Mix proportion

# **1 Introduction**

Cement-based grouting material is a kind of building material prepared in a professional factory, which has the characteristics of early strength, high strength, self-levelling and micro-expansion after mixing with water in a prescribed proportion at using sites. With the rapid advance of infrastructure construction, cement-based grouting materials have been widely used in the fields of bolt anchorage, reinforcement and reconstruction of concrete, and prefabricated construction projects. At the same time, higher requirements are placed on the performance of cement-based grouting materials.

Cement-based grouting material should adopt low water-binder ratio to obtain excellent later strength, but it will lead to slow early hydration of cement and insufficient early strength [1]. Early strength agent is often added to dry powder system to satisfy the early strength requirements of cement-based grouting materials in practical engineering applications. Calcium formate has been widely used in dry powder system as early strength agent due to its excellent coagulation promotion ability and solubility. Calcium formate solution is weakly acidic, and it improves the hydration rates of C2*S* and C3*S*. And the ionized *Ca*2+ accelerate the crystallization of AFT owing to ion effect, it promotes the early strength development [2–4]. However, the incorporation of calcium formate will lead to the loss of fluidity, and it is harmful to working performance [5, 6]. As a surfactant, defoaming agent can promote the rupture of bubbles in slurry, reduce the porosity, and effectively improve the strength of cement-based grouting materials [7, 8].

Response surface methodology (RSM) is an analytical method to establish an accurate prediction model with limited experimental data which is obtained from standard tests. RSM uses second-order standard polynomial to fit the response value and different factors, and can draw response surfaces that intuitively reflects the influence of factors on the response value. RSM has been widely used in the process formulation design of grain, oil and food, chemical engineering, and biological engineering [9], but it is rarely used in the related fields of construction and civil engineering [10–12].

There are few reports on the influence of calcium formate and defoaming agent on the mechanical properties of cement-based grouting materials with low water binder ratio. In this paper, calcium formate content, water-binder ratio and defoaming agent content were selected as experimental factors, and the compressive strength of 1d, 3d and 28d were response values. Box-Behnken design (BBD) was used to design the compressive strength test of cement-based grouting materials with low water-binder ratio, and the functional relationships between the response values and the factors were established to analyse the influence of various factors and their interactions on the compressive strength, so as to optimize the mix proportion. And the mechanism of agents was analysed of action combined with macroscopic mechanical microscopic morphology.

# **2 Experiment**

### **2.1 Materials and Instruments**

P · II 52.5R portland cement (PC), II fly ash (FA) and S95 slag powder (SL) were used as cementitious materials, and the chemical composition is shown in Table 1.

**Table 1.** The chemical composition of cementitious materials

Concrete admixtures used in the experiment included industrial grade calcium formate (purity *>* 95%), P803 powder defoaming agent, low alkali u-type expansive agent, QH-100 plastic expansive agent, QS-8020 polycarboxylate superplasticizer. Other materials included water and ISO standard sand.

The compressive strength test adopted NELD-CH2000 electro-hydraulic servo pressure testing machine (Beijing Nierde Intelligent Technology Co., Ltd), structural equation model (SEM) analysis adopted Gemini300 scanning electron microscope (Carl Zeiss AG, German).

# **2.2 Compressive Strength Test Design**

According to preliminary test results, the basic mix proportion is shown in Table 2.

**Table 2.** The basic mix proportion

BBD method was used in the experimental design and data analysis would be completed. Calcium formate ratio, water-binder ratio and defoaming agent ratio were expressed as *x*1, *x*2 and *x*3, respectively. Each independent variables was set at low level, central point and high level, which were encoded as −1, 0 and +1, respectively. The level of each factor and the corresponding coding value are shown in the Table 3.

**Table 3.** Coding and level of independent variables

## **2.3 Specimen Forming and Test Method**

The dry powder was weighed according to the proportion during the molding process of the specimen. After mixing evenly, water was added in proportion and stirred at a low speed for 2 min, stopped for 15 s, and stirred at high speed for 2 min. The mortar was poured into the triple mold, demoulded after curing for 24 h, and maintained to the target age. The loading speed of compressive strength test was controlled at 2.4 ± 0.2 k N/s. The blocks with particle size less than 5 mm were taken on the new section in SEM analysis, and the microstructure of hydration products was observed after drying, spraying gold, fixing and vacuuming.

# **3 Results and Analysis of Compressive Strength Test**

### **3.1 Results and Fitting Models**

The test results of 1d, 3d, 28d compressive strength are shown in Table 4. A total of 17 groups were set up, of which 5 groups were at the central point of each factor values, repeated to evaluate the test deviation.

**Table 4.** Design and results of Box-behnken test

The second-order standard polynomials fitting of Table 4 test data were carried out by RSM. The simulation models of 1d compressive strength *(S*1*)*, 3d compressive strength *(S*2*)* and 28 d compressive strength *(S*3*)* are Eq. (1)–(3).

$$\rm S\_l = -2.77 + 15.46x\_l + 232.46x\_2 + 13.84x\_3 + 7.5x\_1x\_2 - 0.25x\_1x\_3 + 79.50x\_2x\_3$$

$$\Rightarrow -11.84x\_1^2 - 461.50x\_2^2 + 29.62x\_3^2$$

$$S\_2 = +0.38 + 12.08\mathbf{x}\_1 + 467.41\mathbf{x}\_2 + 47.14\mathbf{x}\_3 + 6.50\mathbf{x}\_1\mathbf{x}\_2 - 3.45\mathbf{x}\_1\mathbf{x}\_3 + 86.50\mathbf{x}\_2\mathbf{x}\_3$$

$$\approx -10.52\mathbf{x}\_1^2 - 1165.70\mathbf{x}\_2^2 - 133.42\mathbf{x}\_3^2$$

(2)

$$\begin{aligned} \mathbf{S}\_3 &= +41.35 + 6.05\mathbf{x}\_1 + 347.89\mathbf{x}\_2 + 25.05\mathbf{x}\_3 + 4.60\mathbf{x}\_1\mathbf{x}\_2 + 0.60\mathbf{x}\_1\mathbf{x}\_3 + 234.50\mathbf{x}\_2\mathbf{x}\_3 \\ &\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad -6.59\mathbf{x}\_1^2 - 1005.50\mathbf{x}\_2^2 - 159.38\mathbf{x}\_3^2 \end{aligned} \tag{3}$$

Table 5 shows variance analysis of regression models. F-value represents the test index of obviousness and P-value represents the probability, in which the smaller the P-value is, the stronger the significance of the model is and the higher the simulation accuracy is. The P-value of lack of fit reflects the significant degree that the experimental data is not related to the model. If the value is less than 0.05, the item is significant. and when the value is less than 0.05, the item is highly significant. The P-values of *S*1, *S*2 and *S*3 are 0.0004, 0.0005 and 0.0010, respectively, which are not greater than 0.01, indicating that the simulation models are highly significant. As for lack of fit, the P-values of each model are 0.2141, 0.2347 and 0.4019, which are greater than 0.05, indicating that the mismatch term is not significant and the errors of simulation models are small. The fitting equation is highly consistent with the actual.

**Table 5.** Variance analysis and of regression models

It can be seen from Table 6 that P*(x*1*) >* P*(x*2*) >* P*(x*3*)* for the 1d compressive strength model *S*1. It indicates that the water-binder ratio, the amount of calcium formate and the amount of defoaming agent all have a significant effect on the 1d compressive strength of the cement-based grouting material, and the main factor is calcium formate.

For the 3d compressive strength model *S*2,P*(x*2*) < P(x*1*) < P(x*3*) <* 0*.*01. The influence of water-binder ratio, calcium formate and defoaming agent on the 3d compressive strength of the cement-based grouting material is highly significant. The influence order is *x*2 *> x*1 *> x*3, and water-binder ratio is main factor.

The order of influence on the 28d compressive strength model *S*3 is *x*2 *> x*2 *> x*1, where the P-value of *x*1 is greater than 0.05. The influence of water-binder ratio and defoaming agent on 28d compressive strength of grouting material is highly significant, among which water-binder ratio is still the most important factor, but calcium formate will not have a significant impact.

In summary, the incorporation of calcium formate plays a significant role in the early strength development of low water-binder ratio cement-based grouting materials, but contributes less to the later strength. The effects of water-binder ratio and defoaming agent on the compressive strength of cement-based grouting materials with low waterbinder ratio at all ages cannot be ignored, especially for the strength contribution in the middle and late stages.

The closeness of R2 and Adj R2 can be used to verify the fitting degree of the simulation models, and the smaller the C.V is, the Adeq Precisior is greater than 4, indicating that the reliability and accuracy of the test are higher. It can be seen from Table 6 that the C.V of each model are 1.97%, 3.57% and 1.45%, respectively, and the Adeq Precisior of each model are 7.527, 9.524 and 6.199, respectively, indicating that the simulation models has high reliability and accuracy.

**Table 6.** Model reliability test analysis

### **3.2 Response Surface Interaction Analysis**

The response surface diagrams of 1d, 3d and 28d compressive strength were established as shown in Fig. 1, 2 and 3. The response surface reflects the effect of the interaction of two factors on the compressive strength of each age when the other factor is at the central point.

Figure 1 shows the 1d compressive strength had a process of first increasing and then decreasing with the increase of calcium formate ratio and water-binder ratio from −1 level and the increase of defoaming agent ratio promoted the continuous growth of 1d compressive strength, but the growth was limited under high ratio. Maximum 1d compressive strength was attained at around 0.72% calcium formate, 0.23 water-binder ratio and 0.30% defoaming agent. Table 6 shows that the P-values of the interaction of two factors in the 1d compressive strength model are 0.6572, 0.9762 and 0.3587, respectively, which are greater than 0.05. It indicates that the interaction of any two factors does not contribute significantly to the 1d compressive strength.

**Fig. 1.** Effect of two-factor interaction on 1d compressive strength

The compressive strength of 3d and 28d increased first and then decreased significantly with the increase of calcium formate ratio, water-binder ratio and defoaming agent ratio, as is shown in Fig. 2 and Fig. 3. Maximum 3d compressive strength was attained at around 0.60% calcium formate, 0.21 water-binder ratio and 0.24% defoaming agent, while Maximum 28d compressive strength was attained at around 0.54% calcium formate, 0.20 water-binder ratio and 0.23% defoaming agent. The compressive strength decreased slightly with the increase of the dosage, after the defoaming agent ratio reached the optimal solution, but the decrease was limited. Plot of Table 6 reveals the P-values of the interaction of the two factors in the 3d compressive strength model are 0.7128, 0.6961 and 0.3414, respectively, which are greater than 0.05, indicating that the interaction of any two factors has a low contribution to the 3d compressive strength. While, the P-value of the interaction of defoaming agent ratio and water-binder ratio in the 28d compressive strength model is 0.0427, which is less than 0.05, indicating that there is a strong dependence of 28d compressive strength on the interactive pattern between defoaming agent and water-binder ratio.

**Fig. 2.** Effect of two-factor interaction on 3d compressive strength

With the increase of calcium formate ratio, water-binder ratio and defoaming agent ratio, the compressive strength of each age generally had a process of first increasing and then decreasing. The proper calcium formate ratio promotes the hydration of *C*3*S*,

**Fig. 3.** Effect of two-factor interaction on 28d compressive strength

*C*2*S* and the formation of CSH gel, which is helpful for the early hydration of slurry. However, the high content leads to excessive loss of fluidity, which is not conducive to the formation of dense structure, and it causes the reduction of compressive strength [13]. Higher water consumption contributes to the early hydration reaction of cement particles, but the residual free water inside the slurry evaporates to form pores with the increase of age. The pores will increase with the increase of water-binder ratio, resulting in strength loss. With the increase of defoaming agent ratio, the compressive strength of 3d and 28d first increased and then decreased, and the compressive strength of 1d continued to increase, which was consistent with the early research [14]. The defoaming agent weakens the effect of water reducing agent, especially in the case of high dosage, resulting in the loss of fluidity. It is not conducive to the formation of dense structure, and it induce the decrease of strength.

### **3.3 Parameter Optimization and Verification**

Taking the compressive strength of each age as the optimization object, the mix proportion of cement-based grouting material was optimized, and the optimized mix proportion scheme was obtained as follows: 0.64% calcium formate, 0.21 water-binder ratio and 0.26% defoaming agent. The predicted values and test values of the regression model were compared, and the relative error was used for characterization. The results are shown in Table 7.

**Table 7.** Comparison of predicted value and test value after parameter optimization

The experimental results show that the compressive strength of cement-based grouting material prepared by optimized mix ratio is Relatively high, and the relative error between predicted value and test value is small. It is reliable and accurate to optimize the mix proportion of cement-based grouting materials by response surface method.

# **4 Analysis of the Action Mechanism of Additives**

Calcium formate and defoaming agent are additives widely used in cement-based grouting materials. In order to analyse the mechanism of action of the two, five groups of samples were taken to observe the type, morphology and quantity of hydration products of cement-based grouting materials by scanning electron microscope. The typical morphology diagrams are shown in Fig. 4.

Figure 4a shows that a large number of needle-like AFT crystals were formed on the surface of cement, mineral powder and fly ash particles after hydration for 1 day, and the network structure was constructed by alternating AFT, with 1% calcium formate and 0.3% defoaming agent. Increased magnification factor from 10k to 30k, Fig. 4b shows that there was a small amount of CSH gel in the network structure, forming a relatively stable hydration structure, but the overall hydration degree of the slurry was low and the structure was loose. It can be seen from Fig. 4c that when the slurry was hydrated to 3 days, the AFT crystallization was more robust, and the constructed network structure was obviously filled with a large number of flocculent CSH gels. The lamellar Ca*(OH)*2 crystals were obviously observed on the surface of cement, mineral powder and fly ash particles, and the hydration degree was significantly improved. The overall structure was more stable than that of 1 day, forming a relatively dense hydration structure. When the slurry is hydrated to 28 days, the microstructure is shown in Fig. 4f. The network structure constructed by AFT crystallization was basically filled and compacted by hydration products, and a stable structure formed between cement, mineral powder and fly ash particles. At this time, the hydration reaction has been basically completed and the microstructure was dense.

Comparing Fig. 4c (3d, 0.1% calcium formate) with Fig. 4d (3d, 0% calcium formate), the sample without calcium formate still had a network structure formed by alternating overlap of AFT, but the CSH gel was significantly reduced compared with the calcium formate group. There are no lamellar Ca*(OH)*2 crystals were observed, and the hydration structure was loose. The above phenomenon shows that the incorporation of calcium formate into cement-based grouting materials helps the slurry to form.

Ca*(OH)*2 crystallization and CSH gel in the early stage, thereby improving the early compressive strength.

It can be seen from Fig. 4c (3d, 0.3% defoaming agent) and Fig. 4e (3d, 0.1% defoaming agent), that when the ratio of defoaming agent decreased from 0.3% to 0.1%, a large number of flocculent CSH gels are still filled into the network structure constructed by AFT crystallization, and a large number of flake **Ca***(OH)*2 crystals are precipitated as well, and there was no obvious increase in the gap between particles. Therefore, it indicated that the significant influence of defoaming agent is not based on changing the microstructure of hydration products to improve compressive strength. Compared with Fig. 5a (3d, 0.3% defoaming agent) and Fig. 5b (3d, 0.1% defoaming agent), when the dosage of defoaming agent ratio was 0.1%, there were a large number of visible pores on the cross section of the sample. With the increase of the dosage to 0.3%, the pores on the

**Fig. 4.** SEM diagrams of hydration products

**Fig. 5.** Section of test block

cross section decreased significantly and the structure was denser. The above phenomena show that the defoaming agent can improve the compressive strength of cement-based grouting materials, because it can promote the bubble rupture in the slurry and reduce the macro pores, rather than having no significant influence on the microstructure of hydration products.

# **5 Conclusion**

The effects of calcium formate and defoamer on the mechanical properties of cementbased grouting materials were studied through compressive strength test and microstructure analysis. The results show that:

**Acknowledgments.** This work was financially supported by Technology Innovation and Application Development Special Key Program of Chongqing, China (Grant No. cstc2019jscxgksbX0013) and Innovation Group Science Foundation of the Natural Science Foundation of Chongqing, China (Grant No. cstc2020jcyj-cxttX0003).

# **References**

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# **Study on Seismic Performance of Integrated Support of Steel Arch and Anchor in Loose Surrounding Rock of Highway Tunnel**

Zhigang Zhang1, Xiyuan Liu2(B) , Chong Zhang2, Jing Zhang2, and Dongqiang Xu2

1 Hebei Provincial Expressway Yan Chong Construction Office, Zhangjiakou, China 2 School of Civil Engineering and Transport, Hebei University of Technology, Tianjin, China<EMAIL_ADDRESS>
**Abstract.** In order to study the seismic performance of the new support structure with the integration of steel arch and anchor rod under the bulk surrounding rock of highway tunnel, this paper takes Xinglinpu tunnel of Yanchong expressway as the engineering background and conducts the dynamic time-history analysis of the deformation, stress and plastic zone distribution of the tunnel second lining structure under the original support and the new support according to the specification and with the help of FLAC3D finite difference software. It is concluded that the seismic performance of the original support and the new support structure is basically the same. The new support structure reduces the number of anchors, the disturbance to the surrounding rock and the cost, so the new support structure is worth promoting.

**Keywords:** Highway tunnel · Scattered surrounding rock · Seismic performance · Dynamic response · Numerical simulation

# **1 Introduction**

After the 21st century, the average annual growth rate of road tunnels in China was 20% [1]. With the increase in tunnel mileage, the number of tunnels built in mountain ranges in high-intensity seismic zones had reached a significant percentage. In 2008, 33 of the 56 tunnels near the earthquake area of the Wenchuan earthquake (magnitude 8.0) were damaged. The tunnel structure in the fault fracture zone and lining defect section was the most damaged, and it was difficult to repair after tunnel failure [2]. Therefore, it is necessary to carry out a systematic study of the seismic performance of road tunnels.

Qiangqiang Sun [3] carried out a dynamic non-linear time course numerical simulation of tunnel construction to investigate the effect of the construction-induced initial stress state on the seismic response of the tunnel. Longqi Yan [4] applied a twodimensional transient dynamic finite element simulation technique to investigate the seismic response of a soil-structure interaction system under the oblique incidence of P- and SV-waves. Wang Mingnian [5] and Cui Guangyao [6] pointed out that the seismic damping of underground structures in high-intensity seismic zones can be done by changing their structural properties or by installing a damping layer. By conducting a large shaking table model test study on the cavern section of the Galongla tunnel, Jiang Shuping [7] concluded that attention should be paid to the prevention and control of surrounding rock instability during the earthquake process to reduce the damage produced by the surrounding rock to the tunnel. Wang Qjuyi [8] proposed a comprehensive seismic measure of adding a damping layer between the initial support and the second lining and appropriately increasing the reinforcement of the second lining. Liang Bo [9] analyzed the dynamic response of road tunnel lining in mega-section and pointed out that the second lining could play a major role as a safety reserve during earthquakes. By analyzing different grouting schemes for highway tunnels, Based on the concrete plastic damage model, He Zegan [10] established a three-dimensional nonlinear finite element model of the tunnel-surrounding rock system and pointed out that the arch shoulder and arch waist of the lining structure are the weak parts of its seismic resistance. By performing dynamic time-history analysis of road tunnels, Liu Liyu [11] concluded that the acceleration response of the tunnel structure decreases when located on soft ground and poor surrounding rock, but larger stresses are generated.

The seismic performance of tunnels based on the new practical patent technology "Integrated support structure of steel arch and prestressed anchor rod for highway tunnel" invented by Xu Dongqiang [12] has not been studied in the above-mentioned existing tunnel seismic studies. This new support structure optimizes the arrangement of anchor rods (pipes), so that the steel arch, anchor rods (pipes), shotcrete and surrounding rock form an integrated structure, thus greatly improving the stability of the surrounding rock and support structure.

Therefore, this paper presents a dynamic time-history analysis of the deformation, stress and plastic zone distribution of the tunnel second lining structure under the original support and the new support.

# **2 Project Overview**

The Xinglinpu tunnel is a highway separated long tunnel, located in the north of Xinglinbao, Huailai County, Zhangjiakou, which is one of the more difficult tunnels to construct with poor surrounding rock conditions in Yanchong expressway. The left and right sides of the Hebei section of the tunnel are both 1520 m. The average proportion of grade V surrounding rock is 44.5%, and the average proportion of grade IV surrounding rock is 43.8%. The broken bulk surrounding rock occupies 90% of the total length of the tunnel. The maximum burial depth of the tunnel is 480 m. The area to which the Xinglinpu tunnel belongs is a temperate subarid zone in the continental monsoon climate. The groundwater is localized by bedrock fracture water and dominated by pore diving. It is located in the middle mountainous area of igneous rocks. The stratigraphic rocks are mainly andesite and coarse andesite with developed joints and fissures, and quartz sandstone is locally present.

According to the *Seismic ground motion parameters zonation map of China* (GB18306–2015) [13] issued by the National Seismological Bureau, the area is a Class II site, with a 50-year exceedance probability of 10%, a seismic intensity of 8 degrees, a design basic ground vibration peak acceleration of 0.20 g and a characteristic period of 0.40 s for the ground vibration response spectrum.

# **3 Simulation Support Scheme**

The original support structure scheme (hereinafter referred to as the original scheme) under grade V surrounding rocks is 28 hollow grouting system anchors per bay of steel arch, 2 hollow grouting 1ocking foot anchors on each 1eft and right arch waist, and grouting small conduits within 120° of the arch roof, with a grouting reinforcement radius of 1 m, as shown in Fig. 1(a).

The new support structure scheme for the tunnel under grade V surrounding rock is 2 rows of hollow grouting locking foot anchors per steel arch at the left and right arch shoulders of the tunnel, 1 row of hollow grouting foot locking anchors at the left and right arch waist and arch foot, two of them in each row. The grouting small conduit is laid at 120° at the top of the arch, and the radius of grouting reinforcement is 1m. Due to the poor condition of the surrounding rock, reinforced support is required at the top of the arch crown, so two different reinforced support schemes are used. As shown in Fig. 1(b), the new support structure scheme 1 (hereinafter referred to as new scheme 1) has 8 additional anchors of the hollow grouting system within 60° of the arch crown. As shown in Fig. 1(c), the new support structure scheme 2 (hereinafter referred to as new scheme 2) has 14 additional anchors of the hollow grouting system within 120 of the arch crown.

**Fig. 1.** Support structure scheme

# **4 Establishment of Tunnel Model and Selection of Parameters**

### **4.1 Establishment of Calculation Model**

The simulations were carried out using FLAC3D for the dynamic time-history analysis of the tunnel. The model boundary is 50 m from the center point of the tunnel section to the bottom and left and right boundaries respectively, and the distance to the top surface is taken to the surface, with a tunnel depth of 200 m. The inner contour of the tunnel calculation model section adopts the form of three center circles. The vertical effective height of the tunnel structure is 9.85 m, and the structural width is 12.1 m. As the longitudinal structure of the tunnel is continuous and regular, the cross-sectional configuration remains unchanged and the tunnel longitudinal direction is taken to be 6 m. Only the seismic checking calculation in the cross-sectional direction of the tunnel was performed.

After the tunnel excavation, initial support and second lining have been completed, seismic waves were applied to the tunnel structure as a whole to assess the seismic performance of the tunnel support structure by analyzing the deformation, stress and plastic zone distribution of the tunnel second lining structure.

### **4.2 Unit Type and Parameter Setting**

Taking into account the preliminary geological survey report, construction conditions, advanced geological forecasts and the graded determination parameters of the surrounding rocks on site, and referring to the physical and mechanical parameters of the surrounding rocks at all levels specified in the specification [14], the specific parameters selected are shown in Table 1. In the actual project, the test section of the tunnel has about 24 m thick gravel soil layer at the surface, and below the gravel soil layer are all grade V surrounding rocks.

According to the relevant literature [15], the elastic modulus of the surrounding rock in the anchor grouting area increases by 50%, the Poisson's ratio decreases by 9%, the cohesion increases by 65% and the angle of internal friction increases by 3%. The modulus of elasticity of the surrounding rock in the small conduit reinforcement circle of grade V surrounding rock is increased by 2.6 times, Poisson's ratio is unchanged, internal friction angle is increased by 1.2 times, cohesion is increased by 2 times and density is increased by 10%. The surrounding rock is simulated in solid units, using an elastoplastic principal structure model and satisfying the Mohr-Coulomb yielding criterion.

**Table 1.** Enclosure rock and structural parameters

The initial support for all three support schemes consists of reinforcement mesh, I18 I-beam steel arches (75 cm longitudinal spacing) and 24 cm thick C25 shotcrete. The second lining is C35 molded reinforced concrete with a thickness of 45 cm. Both system anchors and locking foot anchors are hollow grouted anchors.