**Fig. 2** Ground surface deformation of subway shield construction

$$S(\alpha) = \frac{V\_S}{\sqrt{2\pi}i} \cdot e^{\left(-\frac{(x-x\_c)^2}{2^2}\right)} \tag{3}$$

Among them, *xc* is the distance of the moving axis in the center of the settlement trough.

#### *3.1 The Variation Process of Settlement Trough Parameters with Shield Construction*

The curve fitting degree of settlement trough caused by subway and electric power tunnel construction is shown in Fig. 4. *adj-R2*reflects the curve fitting degree. The closer the value is, the higher the fitting degree is. It can be seen that the curve fitting

degree is low when the cutterhead is at a certain distance from the monitoring section (all less than 80%). This is because the maximum surface fitting settlement values of subway and electric power tunnel cutterhead in front of the monitoring fault are 4.63 and 1.62 mm respectively, and the disturbance degree of soil mass is low at this stage. At the same time, non-construction factors such as monitoring errors account for a small proportion of the monitoring data in this stage. Therefore, the corresponding fitting parameters may not accurately reflect the shape of the settlement trough. According to the monitoring data of electric power tunnel, compared with the Peck formula, the curve fitting degree of the modified Peck formula can be increased by about 1.5 times when the cutter head reaches the monitoring surface, and the curve fitting degree can be increased by about 1.1 times when the shield tail comes off the monitoring surface. It can be seen that the modified Peck formula is more suitable for the situation of different degree of soil disturbance on the left and right sides of the shield tunnel.

On the whole, the Peck formula is suitable for the upper sand and lower rock composite strata after karst cave reinforcement, and the fitting degree can basically reach 95%, which can meet the engineering requirements.

Since the Peck formula is based on the undrained assumption, we can refer to the method of Fang [17] to take the tail of the shield machine about 2–3 days after passing through the monitoring section as the boundary between drained and undrained soil. Therefore, for subway and electric power shield, it can be considered that the surface measuring points after the tail of the shield machine leaves the monitoring section of 10.94 and 15.09 m respectively are basically not affected by the disturbance of shield construction.

Based on this, the curve fitting parameters which are directly affected by the disturbance of shield construction and the degree of fitting is more than 95% are analyzed. The change of *K* during the construction of subway and electric power tunnels is shown in Fig. 5. It can be seen that *K* fluctuates near a certain value during normal construction and remains stable with the tunneling process. The linear fitting

equations are respectively.

$$K = -1.07 \times 10^{-4} \cdot x + 0.45\tag{4}$$

$$K = 1.05 \times 10^{-3} \cdot x + 0.33 \tag{5}$$

The fitting line is basically a horizontal line. Therefore, the *K* values of shield construction in the exposed rock layer and the single sand layer are 0.45 and 0.33 respectively.

It can be seen that *K* is affected by formation conditions, and can not be excluded from the influence of tunnel conditions. Therefore, when the strata and tunnel conditions are known, when the shield construction produces a certain degree of disturbance to the survey point, the *K* (or *i*) obtained by monitoring and fitting by Peck formula can be used to predict the surface lateral influence range in the whole process of shield construction, and can also be used to approximately calculate the surface lateral influence range caused by shield tunnel construction with similar strata and tunnel conditions. And assess the safety of important structures within the scope of influence.

The change of *VL* during subway and electric power tunnels construction is shown in Fig. 6. *VL* increases with shield construction, but the growth rate gradually decreases, and finally tends to remain the same. The *VL* caused by subway and electric power tunnels construction is about 1.1% and 1.6%.

In addition, there is an exponential relationship between *VL* and the monitoring section distance from the cutter head to the measuring point, and the fitting equations are respectively.

$$V\_L = 1.830 - 1.449 \cdot e^{(-0.032)} \tag{6}$$

$$V\_L = 1.821 - 2.060 \cdot e^{(-0.092)} \tag{7}$$

The corresponding adj-R2 is 98.9% and 98.8%, indicating that the index relationship can well reflect the changes of VL with the construction process. Therefore, the final stratum loss caused by shield construction under normal working conditions can be estimated by obtaining three data points through pre-monitoring.

#### *3.2 Settlement trough Moves with the Construction of Electric Power Tunnel*

Taking the monitoring data when the monitoring section is disturbed at the beginning of the electric power tunnel construction as the initial value, the translation of the center of the horizontal surface settlement trough during the construction is shown in Fig. 7. Combined with Fig. 4, Fig. 7 and Fig. 8, we can see that although the curve fitting degree of the settlement trough before the cutter head reaches the cross section is low, resulting in a certain discreteness of *xc*, from the overall change trend, taking the axis of the electric power tunnel as the center, the center of the settlement tank moves from the left side to the right side (that is, from side A to side B), and finally remains stable, and the moving process mainly occurs during the shield machine passing through the monitoring section. Taking the average *xc* of all the translation values after the tail of the shield machine is separated from the monitoring section, it can be known that the center of the surface settlement trough deviates from the axis about 0.5 m after the completion of the electric power tunnel construction.

As can be seen from Fig. 7 and Fig. 8, the center of the settlement trough is located on side A when the shield of the electric power tunnel is about to reach the monitoring section, because after the completion of the subway tunnel construction, the degree of disturbance of the soil is greater on the A side than on the B side. Subsequently, when the electric power tunnel gradually disturbs the monitoring point, the soil on

the A side is located in the superimposed area of the disturbance range of the subway and power shield construction, so that the center of the settlement trough is located on the A side at the beginning. After the subway construction, the subway tunnel construction grouting and karst cave grouting strengthen the soil layer, which makes the structure with high stiffness buried in the soil on the A side, and then the sand layer becomes denser after the disturbance of the electric power tunnel construction. The degree of disturbance of the soil is that the B side is greater than the A side, so that the center of the settlement trough gradually moves from side A to side B, after the tail of the shield machine leaves the monitoring section. The monitoring point is gradually out of the disturbance range, and the central position of the settlement trough remains stable. In addition, compared with the main construction parameters such as cutter head pressure and grouting pressure, the attitude parameters of shield machine have more influence on the center position of settlement trough.

#### *3.3 Settlement trough Shape Caused by Shield Construction of Two Tunnels Successively*

As mentioned earlier, after the tail of the shield machine leaves the monitoring Section 10.94 m, it is considered that the soil deformation is basically not affected by the shield disturbance, and the initial value of the shield monitoring of the electric power tunnel can be used to calculate the soil deformation value caused by the non-shield disturbance between the two monitoring. During this period, karst cave grouting treatment occurred near the monitoring section, because it only aims at the deep rock and soil, so the surface monitoring point mainly measures the consolidation deformation of the soil itself.

For double-line parallel tunnels, Liu Bo et al. [18] assume that the shield construction of two successive tunnels will not affect each other, and the surface settlement caused by the two tunnels is the same. With the help of superposition principle, two Peck formulas with the same parameters are used to calculate the final surface settlement. Ma Ke-Shuan [19] (Abbreviated as MKS) put forward the hypergeometric method, considering the influence of the later tunnel on the first tunnel, the Peck formula for superposition calculation has two different sets of calculation parameters, the calculation formula is as follows, but the parameters of the settlement trough of the latter tunnel are not specific.

$$\begin{split} S(\mathbf{x}) &= \frac{V\_{S1}}{\sqrt{2\pi} \cdot i\_1} \cdot e^{\left(-\frac{(\mathbf{x} + \mathbf{L}f \cdot \mathbf{2})^2}{2i\_1^2}\right)} \\ &+ \frac{V\_{S2}}{\sqrt{2\pi} \cdot i\_2} \cdot e^{\left(-\frac{(\mathbf{x} - \mathbf{L}f \cdot \mathbf{2})^2}{2i\_2^2}\right)} \end{split} \tag{8}$$

where *L* is the horizontal distance between the axes of the two tunnels.

Considering the translation of the center of the settlement trough caused by the rear tunnel shield, the MKS formula is modified as follows:

$$\begin{split} S(\boldsymbol{x}) &= \frac{V\_{S1}}{\sqrt{2\pi} \cdot i\_1} \cdot e^{\left(-\frac{(\boldsymbol{x} + \boldsymbol{L}/2)^2}{2i\_1^2}\right)} \\ &+ \frac{V\_{S2}}{\sqrt{2\pi} \cdot i\_2} \cdot e^{\left(-\frac{(\boldsymbol{x} - \boldsymbol{L}/2 - \boldsymbol{x}\_c)^2}{2i\_2^2}\right)} \end{split} \tag{9}$$

For this project, subscript 1 and 2 represent subway tunnel and electric power tunnel respectively.

Only consider the soil deformation caused by the shield construction of subway tunnel and electric power tunnel, and the total amount of surface settlement during the monitoring period. If the MKS formula and the modified MKS formula are used to fit the total settlement caused by successive shield construction, the unknown parameters are 4 and 5 respectively, and there are many possibilities of permutation and combination of parameters that satisfy a certain degree of fitting. and the physical meaning of the fitting parameters may not necessarily accord with the reality.

As mentioned earlier, the parameters *K* and *VL* can be obtained by fitting the surface subsidence with Peck formula. Therefore, it is known that the settlement trough parameters caused by single-line shield construction, *K* or *VL* in the MKS formula is artificially set (modified) to be equal to the single-line fitting value, the deviation degree between the other fitting parameters and the known values is observed, and the engineering practicability of (modified) MKS formula is evaluated.

For the modified MKS formula, the moving distance of the center of the settlement trough in the power tunnel is known, and the *xc* value is temporarily set to 0.44 m.

The *K* values of single and double lines are equal to the known values, and the *VL* values of subway tunnel and electric power tunnel and their standard deviation (degree of deviation) are obtained by fitting. The*VL* control value corresponding to subway tunnel and electric power tunnel construction is 1.09% and 1.55% respectively. Without considering different control conditions, the percentage of *VL* value deviated from the control value obtained by different formulas shows that there is little difference in the standard deviation of VL value between the two shield tunnels under different control conditions, and the VL fitted by the modified MKS formula is closer to the control value.

The *VL* value of the single line is equal to the known value, and the *K* value and its standard deviation of subway tunnel and electric power tunnel are obtained by fitting. The *K* control value for subway tunnel and electric power tunnel construction is 0.45 and 0.32 respectively. Without considering different control conditions, the percentage of *K* value deviated from the control value obtained by different formulas can be known. The standard deviation of *K* value caused by shield construction of subway tunnel and electric power tunnel is similar, the former is larger than the latter, and the *K* fitted by the modified MKS formula is closer to the control value.

From the analysis, it can be concluded that whether or not to control the *K* or *VL*  of single or double lines has little influence on the results of other fitting parameters, and the modified MKS formula is better to fit the total surface settlement caused by shield construction of two successive tunnels, but its use premise is that the center displacement of settlement trough caused by shield construction of the second tunnel is known. If the total surface settlement value and single-line settlement tank parameters caused by shield construction of two tunnels are known, the settlement trough parameters caused by another shield construction can be inverted by (modified) MKS formula.

The *K* or *VL* of the double line is set to a known value to evaluate the influence of different degrees of *xc* deviation on the fitting parameters. When the percentage of *xc* deviation is-100%, the modified MKS formula is changed into the MKS formula, that is, the center of the settlement trough is located above the axis of the electric power tunnel. Therefore, when it is not clear which side of the tunnel the center of the settlement trough is caused by the backward shield construction, the MKS formula can be used. Although the fitting parameter value deviates from the reality to a certain extent, it will not cause too much error.

**Fig. 9** Curve of transverse settlement trough caused by shield

The fitting curve of the (modified) MKS formula for controlling *VL1* is drawn as shown in Fig. 9, which shows that the two settlement curves are highly consistent with the measured data, but there are differences in the physical meanings of the two corresponding parameters. As shown in Fig. 9, when the surface settlement values caused by subway tunnel and electric power tunnel construction are known, they can be fitted by Peck formula and modified Peck formula respectively, and then the final surface settlement curve can be obtained according to the linear superposition principle. At this time, the superposition curve can also fit the measured values well, but its use premise is that the measured data of surface subsidence caused by the construction of two tunnels are known.

#### **4 Conclusions**

Through the field measurement method, this paper studied the deformation law of surface soil mass caused by the construction of two tunnels successively in the upper sand and lower rock composite strata, and drew the following conclusions:

#### **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.

### **Study on Soil Disturbance Caused by Shield Tunneling in Sandy Strata**

**Weiyu Zou, Shuyi Luo, Yingcheng Liu, and Hong Pan**

**Abstract** Shield tunneling and construction in sandy soil have great safety risks, so it is necessary to study the soil disturbance caused by tunneling in sandy soil. However, the law of soil disturbance is still relatively vague, so this paper relies on the actual tunnel project, through high-density, close monitoring; The settlement law of soil around shield tunnel is studied and analyzed. The research shows that the settlement of soil disturbance is basically stable after the shield tail leaves the monitoring section about twice the length of the shield machine; During shield tunneling in sandy strata, the sand on the upper part of the tunnel is very easy to collapse, thus forming a "collapse arch". The formation of this feature will be one of the reasons for the construction accidents of large diameter shield machines; The remarkable feature of soil disturbance around the tunnel in the water rich sand layer is that the maximum horizontal displacement of the measuring points at different locations occurs at the same depth, and does not develop from the tunnel center to the 45-ϕ/2 diffusion angle; The maximum horizontal deformation during tunnel construction is far less than the vertical deformation, so the horizontal displacement can be used to better analyze the actual impact of shield construction disturbance.

**Keywords** Shield Construction · Sandy Strata · Layered Settlement · Collapsed Arch

W. Zou · Y. Liu

S. Luo

#### H. Pan (B) South China University of Technology, Guangzhou 510641, Guangdong, China e-mail<EMAIL_ADDRESS>
China Southern Power Grid, Guangzhou 510660, Guangdong, China

Guangzhou Mass Transit Engineering Consultant Co., Ltd., Guangzhou 510660, Guangdong, China

#### **1 Introduction**

Nowadays, the scale of the city is increasing rapidly, and the development of underground space is also developing rapidly. with the improvement of the degree of development, the relationship between the projects of underground space is more complex, and the mutual influence can not be ignored. Shield construction as an important way of underground space development, it is very important to study the disturbance law of shield construction to the surrounding soil, so as to reduce stratum deformation and ensure the safety of the surrounding buildings and tunnels.

In the research on the disturbance of surrounding soil caused by tunnel shield construction, numerical simulation [1, 2] and theoretical analysis [3–6] are more common, in which the numerical simulation is generally based on the finite element calculation of continuum [7–9], while the theoretical analysis is basically aimed at saturated clay, and the undrained assumption [10, 11] is adopted at the same time, and there is little research on sand layer [12]. The research on the field measured data based on the actual project is less, and it is not systematic enough. At present, most of the existing studies on the displacement of the surrounding soil measured in the field only focus on a single deformation of the soil around the tunnel in the shield, such as surface settlement [13, 14], deep horizontal displacement [15, 16]. There is a lack of comprehensive research on the short-range and high-density soil displacement monitoring data for the same shield tunnel project.

Relying on the actual engineering, this paper carries out high-density monitoring of the surface settlement, layered settlement and the horizontal displacement of the deep soil around the shield tunnel, and studies the disturbance law of the surrounding soil caused by the shield construction in the upper soft and lower hard composite stratum. Combined with the synchronous grouting pressure, the fluctuation of the horizontal displacement of the deep soil when the tail of the shield machine leaves the monitoring section is discussed, and the disturbance law of the shield construction to the soil is studied.

#### **2 Background**

Shijing ~ Huanxi Power Tunnel (Xiwan Road ~ Shisha Road Section) is located in Liwan District and Baiyun District of Guangzhou City. The type of shield machine is mud-water balance shield, the length of shield machine is 9.62 m, the inner diameter of shield segment is 3.6 m, the thickness is 0.25 m, the outer diameter is 4.1 m, the diameter of cutter head is 4.35 m, and the buried depth is 415 m.

The monitoring section arranged in this project is located on the south side of Xiwan Road Crossing Zengpohe Highway Bridge in Guangzhou City. The strata of the tunnel are sand layer and silty clay layer. The buried depth of the tunnel axis is 14 m. The geological profile of monitoring section is shown in Fig. 1.

#### **Fig. 1** Geological Profile

The monitoring contents include surface subsidence, layered settlement and deep horizontal displacement. The distribution of each measuring point on the monitoring section is shown in Fig. 2. The surface subsidence measuring points are arranged perpendicular to the tunnel axis and are located on the same tunnel section. The layered settlement measuring points and deep horizontal displacement measuring points are basically symmetrically arranged along the tunnel axis. Due to the influence of the actual construction level and complex strata, the actual measuring points can not be strictly symmetrically arranged on both sides of the tunnel.

#### **3 Study on Disturbed Deformation of Soil Mass**

#### *3.1 Surface Subsidence*

The surface subsidence shows the surface subsidence of the monitoring section. There are six surface subsidence monitoring points in this project, numbered as CJ1, CJ2, CJ3, CJ4, CJ5 and CJ6,6. The measured surface subsidence is shown in Fig. 3. The Abscissa is the distance between the cutterhead and the monitoring section. The two red dotted lines in the Fig. divide the whole monitoring process into three stages. The dotted line on the left indicates that the cutterhead of the shield machine reaches the monitoring section. The dotted line on the right indicates that the tail of the shield machine is separated from the monitoring section.

As can be seen from Fig. 2. and Fig. 3, the settlement of the CJ4 measuring point with the smallest horizontal distance from the tunnel axis is the largest, and the settlement values of the other measuring points decrease with the increase of the horizontal distance between the location and the axis, which is consistent with the transverse surface subsidence curve proposed by Peck [17].

Before the cutterhead of the shield machine reaches the monitoring section, the surface settlement and settlement rate are very small, so it can be seen that the shield tunneling has little influence on the front surface subsidence; during the period when the shield machine passes through the monitoring section, the surface subsidence increases and the growth rate is larger, at this time, the surface is disturbed by construction; within 4 m from the monitoring section, the surface settlement value is still increasing rapidly, and then the growth rate slows down until it tends to be stable. The settlement rate of the tail of the shield machine is larger before 4 m away from the monitoring section, and then becomes smaller and more stable, the reason is mainly affected by tail grouting before 4 m, during this stage, a ring of segments forgot to

**Fig. 3** Surface Subsidence

grouting (see Fig. 8.), resulting in increased settlement; after grouting, the deformation is mainly consolidation settlement, so the performance is relatively stable. The overall performance of the soil disturbance is that the settlement is basically stable after the tail of the shield machine is separated from the monitoring section about 2 times the length of the shield. And Lei Huayang [18], Bian [19] and Jiang [20]have come to the same conclusion when the diameter of the cutter head is close to the buried depth of the shield machine and the soil conditions are quite different. It can be seen that this conclusion can be used as a reference for the research of relevant shield engineering and the construction of projects with similar buried depth and cutter head diameter.

As shown in Fig. 4, the settlement of each measuring point varies with the distance between the cutter head and the monitoring section. The settlement law of the stratified settlement measuring point on both sides of the tunnel axis is the same as the surface settlement law mentioned above, but the three layered settlement measuring points directly above the axis have undergone a large displacement, in which the FC3-3 measuring point, which is only 2.6 m away from the top of the tunnel, sinks 0.6 m when the cutter head reaches the monitoring section, and then the measuring point can not continue to work. The FC3-2 measuring point also has a large settlement when the cutter head reaches the monitoring section, and the settlement is 20.24 mm, and then the settlement develops slowly when the shield machine passes through the monitoring cross-section. when the tail of the shield machine leaves the monitoring section, FC3-2 changes greatly again, develops to 98.94 mm, and then continues to increase rapidly to about 140 mm before it is basically stable. The variation trend of FC3-1, which is located in the lower buried depth and farther from the tunnel, is close to that of FC3-2. Because of the distance, the settlement is relatively small, and the maximum settlement is 67.34 mm.

#### *3.2 Layered Settlement*

The three measuring points directly above the axis of the tunnel have a large displacement, because the upper part of the tunnel and FC3-2 and FC3-3 are located in the sand layer, the bonding between the soil particles in the sand layer is small, and the sand layer is easy to collapse in a small range in the process of tunnel excavation, so the settlement caused by construction is small and large, so the settlement increases sharply when the cutter head arrives and the tail of the shield machine detaches. This phenomenon should be paid attention to in shield construction in similar strata, especially when there are important buildings above the tunnel axis in the sand layer to avoid excessive settlement.

As shown in Fig. 5, the layered settlement monitoring point FC1 series and the surface settlement monitoring point CJ2 are on the same side of the tunnel and are almost the same horizontal distance from the tunnel axis. Similarly, the FC2 series and FC3 series correspond to the surface settlement monitoring points CJ3 and CJ4 respectively. The settlement difference ΔS is obtained by subtracting the measured

**Fig. 4** Layered Settlement Curve on Both Sides of Tunnel Axis

values of the upper and lower adjacent points in each settlement measuring point, as follows:

$$
\Delta \mathbf{S} = \mathbf{S}\_{\mathbf{D}} \mathbf{ - S}\_{\mathbf{S}},
$$

SD is the settlement of the deeper measuring points in the two adjacent measuring points, and SS is the settlement of the shallower measuring points in the adjacent two measuring points. A positive value of ΔS indicates that the soil between the two measuring points is compressed, while a negative value indicates that the distance between the two measuring points increases. Figure 5. shows the variation curve of the settlement difference between the upper and lower adjacent measuring points with the shield machine driving. Above the tunnel axis, the settlement difference of the CJ4 and FC3 series measuring points is relatively large. Therefore, the Y axis of the settlement difference curve of this series is the right axis. The Y axis of other curves is the left axis.

Because the settlement difference of CJ4 and FC3 series is larger than that of other measuring points above the tunnel axis, the Y axis of the settlement difference curve of this series is the right axis. The Y axis of other curves is the left axis. It can be seen from the diagram that most of the settlement differences of all measuring points occur in the interval between the arrival of the cutter head and the 3 m away from the monitoring section of the tail of the shield machine. The biggest difference

**Fig. 5** Settlement Difference Between Monitoring Points

in the Fig. is about-90 mm, which occurs between FC3-2 and FC3-1 above the axis of the tunnel. Because FC3-3 collapses when the cutter head arrives, resulting in about 600 mm settlement, it is inferred that the settlement difference between FC3-3 and FC3-2 is as high as-450 mm. The settlement difference of each measuring point above the axis of the tunnel is negative, indicating that the distance between the measuring points increases, forming a tensile loosening zone.

The final settlement difference distribution in the monitoring section is shown in Fig. 6. In the Fig., the red indicates that the vertical distance between the two connected measuring points increases, showing a stretched state, while the blue indicates that the vertical distance between the two connected measuring points decreases, showing a compressed state. The number at the segment represents the vertical displacement at the measuring point at both ends of the segment, " + " indicates compression, and "-" indicates tension. From this picture, it can be seen that the deformation of the upper soil caused by the tunnel shows obvious characteristics of "collapse arch": the settlement and settlement difference of each measuring point (including CJ4 and FC3 series measuring points) on the tunnel axis (vault) is the biggest, and the settlement of the measuring point closer to the top of the tunnel is larger, and the whole is in a state of tension. It is noted that the settlement difference between FC3-3 and FC3-2 is about 0.45 m, and it can be inferred that there is a collapse crack between the two measuring points. At the measuring points on both sides of the tunnel, with the increase of the distance from the tunnel, the difference between settlement and settlement becomes smaller, so the arch effect is formed. Moreover, it can be seen that the range of the arch increases with the increase of the distance from the tunnel, but the smaller the settlement difference between the adjacent measuring points is, it tends to decrease gradually. It can also be seen from Fig. 6. that the settlement and differential settlement of the measuring points below the tunnel axis are very small.

#### *3.3 Deep Horizontal Displacement*

The deep horizontal displacement of this project is the radial horizontal displacement relative to the tunnel. The deformation curve of each inclinometer tube in the process of shield machine tunneling is shown in Fig. 7. The swing amplitude of the curve is: CX2 > CX1. It can be seen from Fig. 7. that the horizontal displacement mainly moves towards the tunnel, and changes significantly when the distance between the cutter head and the monitoring section is (-0.8 m ~ 0.4 m) and (6.4 m ~ 7.6 m). Among them, -0.8 m and 0.4 m correspond to the arrival and passage of the cutter head, and 6.4 m and 7.6 m correspond to the ring at the end of the shield that is about to arrive and is not grouted.

**Fig. 7** Horizontal Displacement (CX1, CX2) Change Diagram of Deep Soil

**Fig. 8** Comparison of Horizontal Displacement of Characteristic Points and Changes of Shield Construction Parameters

The distance relationship between the two inclinometer tubes and the tunnel is: CX1 > CX2. The largest horizontal displacement occurs near -9.0 m, rather than 45 ϕ/2 angles upward from the center of the tunnel. The maximum horizontal displacement of CX2 is about 18 mm and the maximum horizontal displacement of CX1 is about 6 mm. There is a positive correlation between the distance between CX1 and CX2 from the axis of subway tunnel and the degree of disturbed deformation, that is, compared with CX2, the deformation degree of inclination curve of CX1 which is farther from the tunnel is smaller, which is consistent with the law of actual shield construction.

The maximum horizontal displacement of the two measuring points occurs near-9.0 m, and the soil layer in this depth is a silt layer with poor stability, and up to the middle line of the tunnel is a sand layer, which shows that the horizontal deformation of this depth is mainly the horizontal loss of the sand layer to the tunnel direction. The maximum horizontal displacement does not occur in the range of tunnel depth, but in the sand layer above the top of the tunnel, and the maximum horizontal increment caused by secondary under pressure of cutter head and shield tail grouting, and the maximum horizontal displacement in the monitoring process all occur at the same depth. This shows that the horizontal deformation of the soil around the tunnel in the water-rich sand layer may be caused by the flow of groundwater to the shield caused by the under pressure of the cutter head mud water bunker and shield tail grouting, resulting in the horizontal loss of the sand layer with poor self-stability. Therefore, when the top of the shield is dug in the sand layer, it may not only produce a large vertical displacement in the sand layer, but also lead to abnormal horizontal displacement. On the one hand, this abnormal horizontal displacement may have an adverse impact on the facilities adjacent to the shield.

Figure 8. shows the relationship between the measured values of deep horizontal displacement at three elevations in CX1 and CX2 and shield construction parameters. The three elevations are the tunnel center elevation -14.0 m, the maximum displacement elevation -9.0 m and the silt soft soil center -5.0 m. The pressure and amount of shield tail grouting and the pressure of the slurry warehouse before the arrival of the cutter head are also given in the picture. It can be seen from the plane layout of the measuring points in Fig. 2. that the position of the inclinometer tube is 1.2 m in front of the monitoring section (the forward direction of the tunnel). Therefore, the cutter head arrives at the position of the measuring tube 1.2 m later than it arrives at the monitoring section.

In the process of shield machine tunneling, the deep horizontal displacement is roughly as follows: when the cutter head reaches 2 m in front of the inclinometer section, the displacement is basically zero, and then it deforms rapidly to the inside of the tunnel, and the displacement above the tunnel increases gradually when the shield machine passes through. The deformation of the tail of the shield machine gradually slows down and tends to be stable after it is separated from about 4 m. On the other hand, near the central side wall of the tunnel (|CX2|-14.0 m|), due to being squeezed by the cutter head, the deformation occurs to the outside of the tunnel, and the displacement increment is 4 mm. From the point of view of the displacement direction, whether it is horizontal displacement (Fig. 7.) or vertical displacement (Fig. 3 and Fig. 4), except for a small amount of outward extrusion deformation near the tunnel axis during the passage of the cutter head, the soil above the tunnel is displaced to the tunnel direction. This shows that the soil deformation in sandy stratum is mainly affected by slurry warehouse pressure or grouting pressure, and a large amount of grouting does not necessarily lead to soil uplift or compression. This may be related to the easy escape of grouting in sandy water-rich strata.

#### **4 Conclusions**

Based on the actual project, combined with the shield construction parameters, the surface settlement, layered settlement and deep horizontal displacement of the soil around the shield tunnel are analyzed and studied, and the following conclusions are drawn:

the formation of the collapsed arch does not have a great impact on the tunnel construction. Considering the large diameter tunnel engineering, this feature will be one of the causes of shield construction accidents.

#### **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.

### **Analysis of Blasting Vibration Signals at Different Initiation Positions of Tunnel Blastholes**

**Zhihao Yan, Genzhong Wang, Wenxue Gao, Min Zhou, Wangjing Hu, Jin Ye, Yanping Li, Yuelan Xie, Yu Hu, and Xiaojun Zhang**

**Abstract** In order to study the blasting vibration effect of different blasting points of the tunnel bore, the pilot tunnel in multi-arch tunnel was used to carry out the test of different blasting points of the bore. The results show that: 1) the peak velocity generated by blasting at different initiation points of the hole is different, and the magnitude of the peak velocity is reverse initiation > Intermediate initiation > Forward initiation; 2) The frequency distribution range of blasting vibration signal under the three initiation positions is: forward initiation > Reverse initiation > Intermediate initiation; At the same time, forward initiation is more conducive to the main frequency of blasting vibration signal moving to high frequency; 3) Compared with reverse initiation and intermediate initiation, forward initiation can better disperse energy, so that the energy is transferred from low frequency to high frequency, so that the blasting vibration is relatively small, which is more conducive to the safety of tunnel lining structure.

**Keywords** Multi-Arch Tunnel · Different Initiation Point of the Gun Hole · Wavelet Packet · Blasting Vibration · Signal Analysis

#### **1 Introduction**

In the construction process of tunnel drilling and blasting method, the change of different blasting positions of the hole will have a certain impact on the blasting vibration and blasting effect, mainly because the blasting position will determine the direction of the explosion energy propagation of the cylindrical charge pack and the time effect of the superposition of the blasting stress field of each charge pack [1, 2].

Z. Yan · W. Gao (B) · Y. Hu · X. Zhang

Faculty of Architecture, Civil and Transportation Engineering, Beijing University of Technology, Beijing 100124, China e-mail<EMAIL_ADDRESS>
G. Wang · M. Zhou · W. Hu · J. Ye · Y. Li · Y. Xie Zhejiang Lihua Blasting Engineering Co., Ltd., Suichang 323300, China

© The Author(s) 2023

G. Feng (ed.), *Proceedings of the 9th International Conference on Civil Engineering*, Lecture Notes in Civil Engineering 327, https://doi.org/10.1007/978-981-99-2532-2\_22

Therefore, it is necessary to study the blasting vibration effect caused by blasting at different blasting positions.

In view of blasting at different initiation positions of the gun hole, relevant scholars have carried out corresponding research from theoretical analysis, field test and numerical simulation. Based on the Heelan short column theory, Gao Qidong et al. [3] discussed the influence law of different blasting positions of the hole on blasting vibration, and obtained the calculation formula of blasting vibration field generated by blasting at different blasting positions. Leng Zhendong et al. [4] found that double point initiation was conducive to reducing rock size and improving blasting effect by comparing the experiments of double point initiation with hole bottom initiation. Liu Liang [5] and Wang Yapeng [6] simulated blasting at different initiation positions based on LS\_DYNA, and the research results showed that positive initiation was helpful to rock bottom fragmentation and reduce blasting vibration. At the same time, Gao Qidong [7] also used LS\_DYNA to study the impact of blasting at different initiation positions of cut holes on the tunnel support structure. The research results showed that the forward initiation was helpful to reduce the vibration of the structure, while the reverse initiation was helpful to rock fragmentation.

The above scholars conducted a detailed study on the blasting effect of different initiation points of the blasthole from theory and simulation experiments. However, what was relatively lacking was related research on different initiation points of the full-section blasthole on site, and the relationship between blasting vibration signal frequency and energy under different initiation positions of the blasthole on site. Therefore, based on the reconstruction project of G528 National Road Suichang Xinluwan to Shilian section, this paper conducts blasting test research on the fullsection blasting holes of the tunnel at different initiation positions in the guided tunnel, and studies the relationship between the frequency and energy of each signal.

#### **2 Field Blasting Test**

#### *2.1 Project Background*

This paper takes the dam tunnel in the reconstruction project of G528 National highway from Suichang Xinluwan to Shilian section as the background. The length of the tunnel is K4 + 928~K5 + 025, the total length is 97 m, and the maximum buried depth is 25 m. The surface of the tunnel is composed of residual slope silt clay containing gravel, the thickness is 1–2 m, and the underside is strongly to moderately weathered tuff, the rock mass is broken and the integrity is poor, which belongs to the IV grade surrounding rock. The whole section of the tunnel is excavated, and the area of the excavation section is 31.5 m2.

**Fig. 1** Schematic diagram of different initiation points of the hole

#### *2.2 Field Experiment Scheme*

In view of the factors such as broken surrounding rock and poor stability of the tunnel from the dam, and considering that the vibration generated by the blasting of the main tunnel is likely to have a greater impact on the middle partition wall, the blasting vibration reduction experiment is carried out in advance in the middle pilot tunnel of the tunnel, that is, reverse blasting, intermediate blasting and positive blasting are respectively adopted for all blasting holes in the full section. The blasting vibration effect under each blasting mode is obtained by conducting experiments on different blasting positions of the blast hole, which provides guidance for the subsequent main tunnel to select the appropriate blasting position of the blast hole. The schematic diagram of the positions of different initiation points of the blast hole is shown in Fig. 1 below. Detonation is conducted through the detonating tube, and the TC-6850 blasting vibration monitor is used to monitor the ground vibration. The measuring point is arranged 20 m from the ground to the working face.

#### *2.3 Blasting Parameter Design of Middle Guide Tunnel*

Based on the site engineering geological conditions and considering the use of the full-section method in the blasting construction of the guide tunnel, the layout of the shot holes in this experiment is designed, as shown in Fig. 2 below, with a total of 6 sections. Its hole parameters are shown in Table 1 below.

#### **3 Analysis of Blasting Vibration Signal at Different Positions of Blasting Holes**

#### *3.1 Time History Curve Analysis of Blasting Vibration Signal*

In the process of blasting vibration monitoring, the peak value of blasting vibration velocity collected in the X-axis direction (tunnel longitudinal direction) is the largest, so only wavelet packet decomposition of signals in this direction is carried out later

**Table 1** Charge amount of each section for each hole

in this paper to study the relationship between frequency and energy. The blasting vibration signals of three kinds of holes at different initiation positions measured in the field are shown in Fig. 3 below. It can also be seen from Fig. 3. that the three initiation modes all reach the maximum vibration velocity during the first cut hole blasting, in which the peak velocity of reverse initiation is 7.15 cm.s−1 and the occurrence time is 0.033 s. The peak velocity of intermediate initiation is 5.84 cm.s−1, and the occurrence time is 0.031 s. The peak velocity of forward initiation is 5.58 cm.s−1, and the occurrence time is 0.029 s, the peak vibration velocity: reverse initiation > intermediate initiation > forward initiation, and peak velocity time point: forward initiation < intermediate initiation < reverse initiation. Investigate its reason, mainly when columnar cartridge blasting, energy spread along the hole, priority of reverse initiation energy spread along the hole in the direction of constraints, initiation energy transmission along the hole to both sides, among which are initiating explosive energy along the gun Kong Chao spread of surrounding rock, which causes reverse initiation at the ground vibration caused by tunnel is the largest. Further observation of the waveforms in Fig. 3 shows that, with the increase of the detonator stage, the waveforms of reverse initiation and forward initiation are

**Fig. 3** Blasting vibration signals at different initiation positions of the hole

wide in MS9 and MS11 sections, while the waveforms of intermediate initiation are narrow in MS9 and MS11 sections, indicating that when the intermediate initiation of the detonator is in the middle of the hole, all the holes in the two sections of the detonator can easily achieve simultaneous initiation. However, the reverse and forward initiations are easy to cause separate initiation of each hole in the high stage detonators.

#### *3.2 Frequency Analysis of Blasting Vibration Signal*

In order to further analyze the frequency of blasting vibration signals under different initiation positions of the three holes, Fourier transform is carried out for the blasting vibration signals in Sect. 3.1 above and normalization is carried out to obtain the spectrum diagrams of different initiation positions of the three holes, as shown in Fig. 4 below. It can be found from Fig. 4 that the frequency distribution of forward initiation is wider than that of reverse initiation and intermediate initiation. The frequency of forward initiation is mainly distributed in the range of 0–400 Hz, the frequency of reverse initiation is mainly distributed in the range of 0–300 Hz, and the frequency of intermediate initiation is mainly distributed in the range of 0–200 Hz. At

**Fig. 4** Spectrum of blasting vibration signal at different initiation positions

the same time, the main frequency range of reverse initiation is 100–200 Hz, the main frequency of intermediate initiation is 50–150 Hz, and the main frequency of forward initiation has two peaks, one is 100–200 Hz, and the other is 300–400 Hz. This indicates that compared with reverse initiation and intermediate initiation, forward initiation is more conducive to energy transfer and high frequency dispersion.

#### **4 Wavelet Packet Analysis of Blasting Vibration Signal**

According to the blasting vibration signals at different initiation positions of the hole in Sect. 3.1 above, wavelet packet decomposition is carried out to study the energy distribution of each signal in different frequency bands. The wavelet basis function and the number of corresponding decomposition layers should be chosen reasonably when wavelet packet decomposition is carried out. The reasonable wavelet basis function can effectively remove the noise generated in the tunnel construction process and extract the real blasting vibration signal. However, the number of decomposition layers will directly affect the denoising effect of the signal. Too low decomposition layers will easily lead to mixed useful information in low frequency band, while too high decomposition layers will easily lead to deviation of the results. Therefore, this

paper adopts db8 basis function in db series, which is similar to the tunnel blasting vibration signal waveform, to decompose the blasting vibration signals at different initiation positions of the three holes in eight layers [8].

TC-6850 blasting vibration vibrometer produced by Chinese Academy of Sciences was used in this tunnel blasting test. The sampling frequency was set as 6400 Hz, and the Nyquist sampling frequency was 3200 Hz. A total of 256 frequency bands were generated after 8-layer decomposition of wavelet packet. The size of each frequency band is 12.5 Hz, that is, the minimum frequency band after decomposition is 0–12.5 Hz. The energy of each frequency band is obtained through the above wavelet packet decomposition, and the frequency band interval of the main frequency band is defined in this paper for each sub-band whose energy ratio exceeds 10% [8]. The energy proportion of each main frequency band of blasting vibration signals at different initiation positions of the three holes is statistically shown in Table 2 below.

As can be seen from Table 2, the blasting vibration energy of intermediate initiation is mainly concentrated at 100–125 Hz, accounting for 67.28% of the total energy, and the energy is relatively concentrated. Compared with intermediate initiation, the main frequency band of reverse initiation is below 100 Hz and above 125 Hz, and the energy ratio of the three main frequency bands is 38.6%, indicating that the energy is relatively scattered. However, the frequency range of the two main frequency bands for forward initiation is quite different, one of which is in 87.5–100 Hz and the other is in 287.5 Hz–300 Hz. The energy ratio of the two main frequency bands is not very different, occupying 20.9% of the total energy, indicating that forward initiation can better disperse energy compared with reverse initiation and intermediate initiation. And make the energy transfer from low frequency to high frequency, so that the blasting vibration is relatively small, more conducive to the safety of tunnel lining structure.

#### **5 Conclusions**

To study tunnel hole blasting vibration effect different detonation point, with national highway G528 local practice period of reconstruction engineering of the new road bay to stone dam to tunnel as the background, elaborated to carry out the whole section in tunnel hole, experimental study on different detonation position of hole respectively take the reverse initiation, intermediate initiation, forward initiation, the results show that the:

#### **References**

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### **DSM Based Optimization to the Design Process of Prefabricated Construction**

**Xinlong Yang**

**Abstract** The linear way of prefabricated construction (PC) design can induce extensive occurrence of reworks and increase costs and worktime. To optimize a reasonable and concurrent PC design workflow, a system of detailed PC design processes was built based on literature review and expert investigation. Based on graphic theory and DSM, the interdependent relationships between the processes were confirmed, and clusters of the coupled processes were identified. The paper proposed a model with an improved genetic algorithm to optimize the workflow to reduce rework costs and worktime. Then, a case study is used to estimate the model. The result shows that the optimization can reduce 12% costs and 12.43% worktime, and suggests that the cooperation between work of different design stages needs to be strengthened for a better product and less resource usage. The proposed model can effectively reduce the impact of rework. It improves the optimization methods of PC processes, and is valuable to PC planning and control.

**Keywords** Prefabricated Construction · Concurrent Engineering · Process Optimization · DSM · Genetic Algorithm

#### **1 Introduction**

China's construction industry is undergoing huge changes. Traditional construction methods in China consume high energy and produce large amounts of waste and carbon emissions. In 2020, the construction industry contributes 46.5% of total energy consumption and 51.3% of the total carbon emissions of the country [1], and the number is still rising as the housing demand grows. Considering the sustainable

X. Yang (B)

275

Department of Civil Engineering, Faculty of Civil Engineering, Taiyuan University of Technology, No. 79 West Street Yingze, Taiyuan, Shanxi, China e-mail<EMAIL_ADDRESS>
© The Author(s) 2023

G. Feng (ed.), *Proceedings of the 9th International Conference on Civil Engineering*, Lecture Notes in Civil Engineering 327, https://doi.org/10.1007/978-981-99-2532-2\_23

development of the country, China has announced its goal of cutting carbon emissions from construction and providing higher housing quality, which requires new construction methods for the industry.

Prefabricated construction (PC) differs from the traditional construction methods. It transfers a part of cast-in-situ work (mainly component manufacturing) into factories, which is known as off-site work. Therefore, the PC is more efficient, clean and has better quality. Compared with traditional construction methods, PC can reduce construction wastes, shorten project periods, reduce carbon emissions, save energy, and raise productivity [2–6].

Recently, China has introduced a series of policies including standards, initiatives, guidance and incentives to develop PC [7]. Yet the Chinese PC is still facing many challenges, including the immaturity of technology, the lack of experienced workers and the unfamiliarity of working process, etc. [8–10]. These problems can lead to reworks, which increases costs and worktime. Some other countries also faced the problems before, North America [11] once encountered the transportation issues of PC components; PC in Australia [12] development was hindered by unfriendly research environment, deficient planning and marketing; PC in South Korea [13] was subjected to the high construction costs, due to the immature design, workforce related problems and insufficient market size. China is still facing these problems in varying degrees.

Rework [14] (probably due to the errors or the nature of the process) is one of the major reasons for the high cost and prolonged working time in the Chinese practice of prefabricated construction. The ideal way of PC is closer to a concurrent process [15], but the common practice adopted in China is a linear process, which leads to reworks. DSM is an optimization method suitable for the manufacturing industry [16], and it mainly focuses on dealing with the coupled processes which cause wide ranges of reworks, and can make the linear process concurrent from a macro perspective. As PC has similar characteristics as manufacture in production methods, DSM can be applied to optimize PC process. Some researchers found that the design stage is a critical part, and it can cause a wide range of reworks when things go wrong in this phase [14].Therefore, it is necessary to confirm the design work and optimize the process through DSM. This paper proposes an optimization model with DSM to reduce costs and worktime, and the model can improve the optimization methods of PC processes, and be valuable to PC planning and control.

The structure of the contents is as follows: Sect. 2 briefly reviews the relevant research; Sect. 3 introduces DSM method and the DSM model building; Sect. 4 shows the optimization process and discusses the results of the work with a case study, and Sect. 5 summarizes the work.

**Fig. 1** The comparison of PC design process and traditional design process

#### **2 Literature Review**

#### *2.1 Concurrent Engineering*

Traditional Chinese building design is a linear process, while PC design is more suitable for a concurrent one [15, 17]. The comparison is shown in the Fig. 1.

The PC design needs to be integrated [18]. The PC component manufacturing and construction can be ideally implemented as early as in the design stage [19]. However, the PC design process now adopted in most projects in China is the linear type [17], which means that the work teams of different phases have little communication at early stages. The communication gap exists through the PC designing [15], causing increasing chance of errors. Hence, reworks can occur widely and increase costs and worktime.

Concurrent Engineering (CE) [20] is an idea proposed by IDA (Institute for Defense Analysis), widely adopted in manufacturing industry. CE emphasizes the idea of customer-oriented design (integrated design) and whole lifecycle design and communication through whole design stages [15]. It rearranges the process of product design and integrates the processes with strong interactions, in clusters [21]. The information exchanges can be intensive, but in smaller groups, because the information exchanges occur in different clusters concurrently [22]. This enhances the communication between different work teams within the clusters, which avoids a wide range of reworks. Therefore, it can provide higher working efficiency and better products. The current studies [23, 24] indicate that the concurrent way of construction integrates project teams, improves the quality of buildings and reduces time and costs of the projects, which gives the company competitive edge. Therefore, to reduce rework, optimization of design process needs to be carried out to make the process concurrent.

#### *2.2 Optimization Methods*

There are a lot of studies on the optimization methods of complex processes, e.g., Critical path method (CPM), IDEF method and DSM method.

CPM [25] is usually used in combination with PERT as evaluations. It optimizes the process by judging the critical path within the process system and optimizing the work on the path to minimize the overall worktime and resource usage. CPM is widely used in project management. Sroka, et al. [26] linearized CPM-Cost model for construction projects and tested it with an example. Mazlum, et al. [27] used the fuzzy CPM and PERT method to plan and improve a project of online internet branch. These studies show the utility and compatibility of CPM. However, CPM does not focus on the interactions between the work. Therefore, it is not an ideal way to solve the process coupling problems.

IDEF method [28] can represent the process systems by images. It is a comprehensive modeling method, including 16 sets of specific methods to represent the system in terms of functions, information exchanges and process obtaining, etc. In a product research, Li, et al. [29] used three methods of the IDEF to build the functional model, the message model and the model of its semantic relationships. However, IDEF method cannot show the interaction strength between processes in an explicit way. It is not an ideal way to deal with the coupling processes, either.

DSM method can show the interdependent strength between the processes in a matrix. It provides a simple but effective tool to model the interactions in a system and evaluate the coupling strength of the system. The DSM model is compatible with multiple approaches of optimization to improve the coupling relations. Therefore, it can be an ideal way to address the coupling problems. PEI, et al. [30] used DSM model and a genetic algorithm (GA) to cluster the process of complex product. The model can find the optimum results with the least coupling strength. It also can evolve with iterations to ensure the credibility of the optimal results. The DSM is often used in manufacturing industry [31] for project management and it is compatible with software simulation [32].The PC shares some similar features with manufacturing, which includes component production and shipment, and multiple involvers [14]. Unlike the traditional construction method, component production and erecting should also be considered. That means an integrated design [33] for PC is needed to coordinate different project teams to fulfill the needs of involvers and to manage this concurrent process. Therefore, DSM is suitable for PC processes, because the method has shown its utility in the integration of manufacturing projects and in the concurrent processes [34].

Some research used DSM for the PC process optimization in various degrees of depth. Chen [35], et al. built a model of QFD (Quality Function Deployment) to form the DSM matrix of the process in the PC component design, and an evaluation system was built. With the model, GA can be used to find the most reasonable working order. WANG [34], et al. and WANG [22] decomposed the PC design process, and set up a process system. These studies introduced the combination of DSM method and GAs to cluster process. Shen, et al. [14] proposed an optimizing model and an evaluation system of PC processes based on the DSM method, and built a risk management system for dealing with rework risks. In summary, the research shows the utility of the combination of the DSM optimization with the GA, and found that design stage is the most influential part of work [14, 33]. However, the current research only clusters the process, which is not practical for the PC design process. It is still necessary to optimize the sequence of the detailed design process considering rework impacts like costs and time.

#### **3 Methodology**

This paper aims at optimizing the ideal sequence of the design work. First, a questionnaire survey was implemented to verify the system of PC design processes, which was based on literature review [17, 33, 36, 37]. Then, a matrix representing the process system was built and the clustering was carried out based on graphic theory. A DSM model with an improved GA was used for process optimization. The optimization model considers the optimum sequence of work within the clusters and evaluates the optimization effects.

#### *3.1 DSM Model*

DSM (Design Structure Matrix) [38] is a method using matrices to optimize projects. There are two types of DSMs. One type is the Boolean type, or binary matrix, which contains only "0" and "1" as elements in the matrix. And the "0" indicates that the subjects do not have any relationships, while the "1" indicates that they do. The other is called Numeric Design Structure Matrix (NDSM), using numbers to show the strength of the relationships. Based on the directed graphs (digraphs) of the process chains, the DSM can be used to represent a complex system and show the interactions between the processes. The digraphs can be represented by binary DSM or NDSM, as in the Fig. 2. (digraph) and in the Fig. 3. (the DSM based on the digraph), since the DSM and the adjacency matrices of digraphs have the same structures [39].

**Fig. 2** Digraph

#### *3.2 Questionnaire Survey*

This study investigated some of the experienced experts in the PC industry to get a general evaluation of the relationships between the work for this optimization.

There are two questionnaires designed to identify the design processes and to build the DSM model of the PC design process. One questionnaire contains the background information of the experts and a five-point scale of recognition, and are sent to confirm the process system. The results of 11 questionnaires are shown in Fig. 4. The experts were from different cities such as Beijing, Shanghai, Chongqing, etc., and these cities can represent the development of PC in China. The scores of their recognition for the process system are shown in the Table 2. The average score of that is 4.27/5, which presents positive feedback for the process system. Some modifications were also mentioned in the questionnaires, including "The deepening design requires the complete involvement of the general contractor", "The component design will lag behind", "In the scheme stage, some contents were suggested should be advanced, and local product research can also be added". Then, the confirmed process system is shown in the Table 1. Another questionnaire used a four-point scale for the designers in the PC industry to determine the strength of relationships between the design processes. The scale looks into the information exchanges between the work, such as the frequency of communication between designers at different stages and the number of the transferred documents and files. The scores range from 0 to 3. Zero represents that there is no connection between the work, while 3 means a strong relationship between them, and 1 represents a mild relationship, and 2 represents a moderate relationship. Then, the NDSM was built based on the results of the fourpoint scale. A five-point scale was also used to evaluate the importance of the work as for rework impact.

#### *3.3 Optimization Model Building*

Two approaches were considered to optimize the process. One is based on graphic theory, the other is a simulation using GA. The first approach clusters the processes, so the work in different clusters can be done currently. The second approach finds the optimal workflow in the clusters.

**Optimization Based on the Graphic Theory.** In graphic theory, coupled processes have two-way links in digraph. Therefore, recognizing coupled processes can be done by finding the strongly connected paths in the digraph. As mentioned before, the digraph can be used to represent the DSM model of the designing process. Given that there is a path from work i to work j, and there is also a path from j to i, it is called a strongly connected path. The processes on the strongly connected paths are coupled processes (they have two-way links), as shown in Fig. 5.

An Accessibility Matrix (when there is a path from i to j, the element (i, j) is 1, otherwise it is 0) can be built from the digraph of the PC design process to find the

**Fig. 4** Back ground information of the participants

strongly connected paths. If work i strongly connects work j, the multiplication of the element (i, j) and the element (j, i) is 1. Therefore, the matrix *D* of the Eq. (1) can determine the strongly connected paths, and so the clusters of coupled work.

$$D = P.\*P^T\tag{l}$$

In the equation, the *P* is the accessibility matrix of the NDSM (Fig. 6.), and the *PT* is the transpose of the *P*.

**Optimization through GA.** Genetic algorithm [40] is an intelligent algorithm for solving multi-objective problems. Its idea originates from genic behaviors (inheritance, crossover, mutation) and the theory of "Survival of Fittest". It introduces the idea by coding the initial group, choosing the fittest groups by a function. And the winners inherit, crossover and mutate the codes. Then, it chooses the fittest and continues the operation again, until there is a final solution or it reaches the predetermined number of iterations. Yet, GA has the nature that it might premature and lead us to an unwanted result. An improved algorithm [14] can solve the problem, which changes the rate of crossover and mutation according to the convergence of the results. When the results of the offspring group are scattered, the crossover and mutation rate are low to accelerate the algorithm converging. When the results are highly converged, the rate goes high and the results can be better, as shown in the Eqs. (2) and (3). Then, the result of the GA can avoid the prematurity and the model can get the optimal result. The "roulette wheel selection" was used to select the fittest groups.

$$\mathcal{P}\_c = \begin{cases} \mathcal{P}c'(1/\beta), \alpha > a \text{ and } \beta > b \\\ \mathcal{P}c', \ else \end{cases} \tag{2}$$

**Table 1** The confirmed system of the PC design processes

**Table 2** Recognition scores for the system Recognition Scores

**Fig. 5** Strongly connected path between i and j

**Fig. 6** The strength of relationships between PC design work (NDSM)

$$\mathbf{P\_m} = \begin{cases} P m'(1/\beta), \alpha > a \text{ and } \beta > b \\\ p m', \text{ else} \end{cases} \tag{3}$$

Here, the *Pc* is the rate of the crossover, and the *Pm* is the rate of the mutation, in the improved algorithm. The *Pc'* and the *Pm'* are the presupposed values of the rate of the crossover and the mutation. The *α* equals the average of the fitness value divided by the greatest fitness value, in the groups, and the *β* equals the minimum fitness value divided by the greatest fitness value. The fitness value is the result of the Eq. (10) for every subject in the groups. The *a* and *b*, are presupposed numbers, ranging from 0.5 to 1 and 0 to 1 respectively. The lower of the value of the *a* and *b*, the easier the algorithm converges.

Based on DSM, real encoding is explicit to represent the sequence using sequential numbers. According to the project goals, the functions were designed to find results with lowest working time and costs. Based on the Iteration Risk matrix (**IR** matrix) [41, 42], the Rework Factor matrix (*RF* matrix), the Core Work evaluation (*CW(j)*)*,*  the functions are built for multi-objective optimization. Iteration Risk matrix (**IR**  matrix) [43] is built to show the impact of the sequence of the process on reworks (errors that happen in the latter part will cause more reworks). The elements in **IR**  matrix are calculated according to Eq. (4), in which the *i* and *j* represent the different processes and the *n* is the total number of the processes.

$$\text{IR}(i, j) = \exp(j/n - (i - j)/n) \tag{4}$$

Based on the research on rework propagation, a Rework Factor matrix (*RF* matrix) [44] shows the overall probability of the rework. In Eq. (5), the *m* represents the number of steps for every path available from process *i* to process *j*, in the digraph. Therefore, the value of "*m*" ranges from 1 to *i-j*-1. While the "*Cm*−1 *i*− *j*−1" is the total number of all the possible paths from *i* to *j*, and the "*k*" represents the specific path. The *PR (i, j)* is the elements from the Rework Probability matrices [42] and it shows the probability of the rework when the information is delivered from work *i* to *j*. The *PRk (m)* is the multiplication of all the *PR (i, j)* on the path "*k*".

$$RF(i,j) = 1 - \prod\_{m=1}^{i-j} \prod\_{k=1}^{C\_{i-j-1}^{m-1}} (1 - PR\_k^{(m)}(i,j)) \tag{5}$$

The Core Work (*CW*) considers the importance of each work as for the rework impact. In Eq. (6), the *Wj1* scores the probability of reworks, the *Wj2* scores the costs to solve the reworks, and the *Wj3* scores the extra worktime caused by rework.

$$w\_j = w\_{j1} \times \sum\_{k=2}^{3} w\_{jk} \tag{6}$$

$$CW(j) = \frac{w\_j}{\sum\_{j}^{n} wj} \tag{7}$$

Then, the multi-objective optimization model considers the minimum costs and time based on the aforementioned parameters and variables The main equation *f(x)*  and the relevant equations are shown as Eqs. (8), (9) and (10). Here, the *ωERC* and the *ωERT* are weight coefficients.

Main functions:

$$ERC = \sum\_{i=1}^{n} \sum\_{j=i+1}^{n} \left( RF(i,j) \times \sum\_{u=i}^{n} \left( \text{Cost}\_{u} \times RF(u,i) \right) \times CW(j) \times IR(i,j) \right) \tag{8}$$

$$ERT = \sum\_{i=1}^{n} \sum\_{j=i+1}^{n} (RF(i,j) \times \sum\_{u=i}^{n} (Time\_{u} \times RF(u,i)) \times CW(j) \times IR(i,j))\tag{9}$$

$$f(\mathbf{x}) = \min TEL = \omega\_{ERC} \times ERC + \omega\_{ERT} \times ERT \tag{10}$$

#### **4 Optimization Results and Discussion**

#### *4.1 Cluster Result with Graphic Theory*

A real case is used to estimate the model. According to the expert investigation, the NDSM of the design process is shown in the Fig. 6. Based on the graphic theory and the NDSM, the accessibility matrix is built, as in the Fig. 7, and the result of

#### **Fig. 7** Accessibility Matrix

**Fig. 8** The matrix *D*

the Eq. (1), which determine the clusters of the coupled processes, is shown in the Fig. 8.

The result *D* shows that the work in the PC design process is highly connected with each other. All the processes, except for the work No. 21 (PC molds design) and the work No.22 (Completion design), are coupled work and is put in a cluster.

#### *4.2 Optimization Model Based on GA*

By the given data of the time and costs of a practical case and the functions mentioned, we gained the optimal sequence of design processes through the GA. The result is shown in Fig. 9. The Fig. 11. shows that the maximum value of 1/TEL (minimum value of TEL) finally converged after 1200 times iterations, providing a credible answer. And the result also shows that the optimization reduces the cost (ERC) by 13.9% and the worktime (ERT) by 14.81%.

**Fig. 9** Sequence of PC design process after optimization

The optimal result shows that the optimization cut down the cost and worktime by sequencing. However, there is a logical error in the sequencing manipulation, probably due to the subjectivity of the data. The work of Structural calculation should start before the Design of structural components, because the latter work relies on the information provided by Structural calculation. Therefore, rectification has to be done to the optimization result, as in the Fig. 10. And the calculation shows that the final result accomplished 12% decrease on cost (ERC) and 12.43% on working time (ERT). In the optimized work sequence, some processes which originally tended to be in the later part were put ahead, such as Environment protection and energy saving design, Fire design and Collision detection, because they are strong information-output processes. Accordingly, the strong information-receiving processes were put behind, as "Civil air defense design" and "Prefabricated rate calculation". The information-outputting processes start first and then the information receiving processes start later. Therefore, the information flow is strong forward rather than backward, and reduces the occurrence of reworks. Generally, the optimized sequence of the work is more reasonable and has positive impacts on costs and worktime reduction. According to the scores on the importance, the process 1 (Prefabrication planning) and the process 2 (Building design) are the most important work, with the highest costs and worktime increase if reworks occur. The process 3 (Mechanical and electrical design) was rated to the process with the biggest probability of rework. Therefore, these processes have to be carefully implemented, and the corresponding involvers should closely communicate with each other.

**Fig. 10** The optimization result after rectification (final result)

#### **5 Conclusions**

The PC design is a critical part in the prefabrication process. Reworks occurring in the linear design process causes the increase of costs and time. Therefore, it is necessary to optimize the process. A system of detailed PC design processes was confirmed through literature review and expert investigation. A matrix of interactions between processes was constructed, and clusters of coupled processes were found based on DSM and graphic theory. A DSM model based on the GA was built to find the optimal sequence of the PC design processes in the concurrent way. Then, a case study was used to demonstrate the optimization effect. Besides positive outcomes, it is found that PC design has concurrent features, but the majority of the processes cannot be done in a separate way, as indicated by the matrix *D* (the result of the dot product). Therefore, the optimized PC design is concurrent between clusters, and the processes are linear in the clusters. In the logical sequence of the detailed work in the clusters, the information flow is strong forward, and the work of the different phases can be done concurrently. Therefore, the communication is enhanced and the probabilities of errors are reduced, which improves the impacts of reworks.

In summary, the optimization model provides a perspective to view the PC design, and the results and the findings can offer some new insights of the development of the PC in China. The model extends existing process optimization methods and has value for planning and controlling PC management. The main contributions are as follows:

This paper also needs further research. In the future, more practical information and objective data should be collected to identify more detailed processes and improve the model. Some other optimization methods, such as Particle swarm optimization, Discrete event system simulation method, and Euler net, can be used to compare the results and find an optimal one.

**Acknowledgements** The authors would like to thank all the experts investigated for their assistance in data collection. The authors also would like to thank Mr. Teng Chen in China Architecture Design & Research Group for his assistance in theoretical support and data collection.

#### **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 Vibration Signal Characteristics of Multilateral Boundary Deep Hole Blasting**

**Junkai Chen, Xiangjun Hao, Zheng Wei, Wenxue Gao, Xiaojun Zhang, and Zhaochen Liu**

**Abstract** The essence of blasting action is the interaction between explosive energy and medium, and the blasting effect depends on the characteristics of explosive energy, medium and interaction law. The multi-boundary comprehensive blasting theory of stonework establishes the functional relationship among boundary conditions, throwing rate and explosive quantity. In this paper, a formula for calculating the explosive charge of multi-boundary deep-hole blasting is put forward, and the experimental study is carried out based on HHT analysis technology. Research shows that: (1) Based on HHT analysis technology, the main frequency of blasting vibration signal energy is in 0–40 Hz, and mainly in low frequency band, while the energy contained in high frequency component gradually decays. (2) Multi-boundary deephole controlled blasting has evenly broken rock blocks and all collapsed within the design range, which has achieved good blasting effect.

**Keywords** Multi-boundary · HHT · Deep Hole Blasting · Signal Characteristics · Blasting Effect

#### **1 Introduction**

Wang [1] takes micro-topography as a main condition and directly introduces it into the theory of multilateral boundary rock blasting. Zhang et al. [2] analyzed and processed the blasting vibration signal by HHT method, and obtained that EMD can decompose the signal well according to different time scales, and the decomposed intrinsic mode function can reflect the intrinsic characteristics of the signal itself. Chen et al. [3] studied the control blasting design of rock mass structure, put

291

J. Chen · W. Gao (B) · X. Zhang · Z. Liu

College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China

e-mail<EMAIL_ADDRESS>
X. Hao · Z. Wei Inner Mongolia Kinergy Blasting Co., Ltd., Erdos 017000, China

forward the control theory of rock mass structure, and established the basic theory of rock mass blasting under geological boundary conditions. Guan et al. [4] uses the extreme point symmetric continuation method to eliminate the endpoint effect, which improves the computational efficiency and practicability of HHT. Zhang et al. [5] analyzed the empirical formula of blasting vibration prediction, and concluded that the nonlinear regression correction formula has the highest accuracy. Based on rock wave impedance and rock mass integrity coefficient, Hu et al. [6] constructs the expression of attenuation of peak vibration velocity of open pit bench blasting seismic wave with equivalent distance. Gao et al. [7] obtains the time-history relationship of seismic wave energy by wavelet transform, and deduces the calculation formula of vibration reduction delay of bench blasting interference. Zhang et al. [8] uses wavelet transform decomposition and response spectrum analysis to study the energy distribution characteristics of blasting vibration signal, and obtains that the main vibration frequency band of blasting vibration signal energy tends to low frequency band.

The above research results mainly focus on the horizontal boundary conditions, and it is not enough to consider the micro-topography change as an additional factor to the blasting theory and blasting method. Based on HHT analysis technique and multi-boundary rock comprehensive blasting theory, considering various terrain and geological conditions, a formula for calculating the charge of multi-boundary deephole blasting is put forward in this paper, which significantly improves the blasting effect.

#### **2 Basic Principle of HHT Analysis Method**

#### *2.1 EMD Decomposition Principle*

EMD decomposition is an important part of HHT transform, the core of which is to decompose vibration signal into a series of modal functions.

Assuming that the sampling sequence of slope blasting vibration signal is *S*(*t*), the EMD decomposition process can be expressed as:

$$S(t) = \sum\_{i=1}^{n} c\_i(t) + R\_n(t) \tag{1}$$

In Eq. (1), *n* is the order of signal decomposition. *ci*(*t*) is the *i*-order IMF component. *Rn*(*t*) is the residual component after *n*-order decomposition.

The remaining part *R*1(*t*) of the signal can be obtained by the first IMF component *c*1(*t*):

$$R\_1(t) = S(t) - c\_1(t) \tag{2}$$

By analogy, the *n*-order IMF component *cn*(*t*) and residual component *Rn*(*t*) of the original signal can be obtained. When both *cn*(*t*) and *Rn*(*t*) are less than the threshold, the EMD decomposition process ends.

EMD decomposition is based on the local characteristics of the signal, and the operation process of the algorithm is adaptive. IMF component is stable, linear and symmetrical, and is suitable for processing blasting vibration signals.

#### *2.2 Hilbert Transform and Spectrum*

The combination of several IMF components of the original signal is obtained by EMD decomposition, and the Hilbert spectrum can be obtained by combining the instantaneous spectra of all IMF components by Hilbert transform. Hilbert transform is a kind of linear transformation, which has intuitive physical meaning and emphasizes the local properties of signals.

Hilbert transformation of IMF components:

$$H[c(t)] = \frac{1}{\pi} PV \int\_{-\infty}^{\infty} \frac{c(t')}{t - t'} dt' \tag{3}$$

In Eq. (3), *PV* is Cauchy principal value. Constructing the analytic signal *z*(*t*):

$$z(t) = c(t) + jH[c(t)] = a(t)\mathbf{e}^{j\Phi(t)}\tag{4}$$

In Eq. (4), *a*(*t*) is the amplitude function.

$$a(t) = \sqrt{c^2(t) + H^2[S(t)]}\tag{5}$$

Φ(*t*) is the phase function:

$$\Phi(t) = \arctan \frac{H[c(t)]}{c(t)} \tag{6}$$

Define the instantaneous frequency as:

$$f(t) = \frac{d\Phi(t)}{dt} \tag{7}$$

The expression for the Hilbert instantaneous energy spectrum is:

$$H(\omega, t) = \text{Re}\sum\_{i=1}^{n} a\_i(t) \text{e}^{\int a\_i(t)dt} \tag{8}$$

*H*(ω,*t*) integrates time to get Hilbert marginal spectrum:

$$h(\omega) = \int\_0^t H(\omega, t)dt\tag{9}$$

Hilbert marginal spectrum expresses the amplitude of each frequency in the whole world.

Hilbert energy spectrum expression:

$$E(\omega) = \int\_0^t H^2(\omega, t)dt\tag{10}$$

Hilbert energy spectrum can express the energy accumulated at different frequencies in the whole time.

#### **3 Calculation Principle of Multi-boundary Blasting Charge**

#### *3.1 Principle of Charge Layout for Multi-face Empty Blasting*

#### *3.2 Calculation Formula of Multi-boundary Blasting Charge*

With the development and application of blasting technology, it is more and more important to study the relationship and interaction between boundary conditions and explosive explosion energy. Considering the interaction between blasting effect and topographic and geological boundary conditions, the formula for calculating the explosive charge of multi-boundary deep-hole blasting is obtained as follows:

$$\mathcal{Q} = K W^3 F(E, \alpha) = K F(E, \alpha) aWh \tag{11}$$

In Eq. (11), *a* is the hole distance (m). *h* is the drilling depth (m).

The multi-boundary blasting principle considers the stability and leakage of rock mass, the formation mechanism and development law of blasting cracks, and the formation mechanism of blasting engineering geological disasters. Combined with the classification of blasting rock mass, the classification of blasting rock mass structural plane and the design of controlled blasting of rock mass structure, the comprehensive blasting theory of medium potential energy and explosive blasting energy is put forward.

#### **4 Project Example**

#### *4.1 Engineering Geological Conditions*

Jinou Coal Mine is located in the west wing of Zhuozishan anticline, with scarce surface vegetation, fragile ecology, drought and little rain, and strong wind in winter and spring. The strata in the mining area and its vicinity are Carboniferous, Permian and Quaternary from old to new. Sinan, Cambrian and Ordovician limestone are distributed in turn from the axis of Zhuozishan anticline to the two wings, which constitute the sedimentary basement of coal-bearing strata and are in parallel and unintegrated contact with the overlying coal-bearing strata.

#### *4.2 Design of Multi-boundary Deep Hole Blasting*

Using hole packing or air interval charge to control explosive energy distribution. The millisecond delay reverse initiation technology in the hole is adopted to limit the maximum initiation charge in a single stage and control the blasting vibration and flying rocks. The anhydrous pore is made of ANFO explosive, and the water pore is made of emulsion explosive. Blasting design parameters are shown in Table 1.

#### *4.3 Design of Accurate Delay Initiation Network*

Based on the principle of stress wave superposition, free surface increase and rock block collision, the millisecond delay time is calculated by using the empirical formula of multi-boundary theory:

$$
\Delta t = K\_1 \cdot W(24 - f) \tag{12}
$$

In Eq. (12), Δ*t* is the millisecond delay interval (ms). *K*1 is the fracture coefficient of rocks, which is 0.5 for rocks with few fractures, 0.75 for rocks with medium fractures and 0.9 for rocks with developed fractures. *W* is the chassis resistance line (m). *f* is the rock firmness coefficient.

After calculation, the delay time is designed as 25 ms between holes and 60 ms between rows (Fig. 1).

**Fig. 1** Detonation network diagram of deep hole blasting

**Fig. 2** Time history curve of vibration velocity

#### **5 Characteristic Analysis of Blasting Vibration Signal**

#### *5.1 Vibration Velocity Analysis*

Measuring points are arranged at the horizontal distance of 110 m, 130 m, 150 m and 170 m from the blasting source to sample the blasting vibration velocity. In this paper, the blasting vibration velocity at a horizontal distance of 110 m from the blasting source is taken as an example to analyze the characteristics of blasting vibration signals, and the sampling time is 0.8 s.

According to Fig. 2, the blasting vibration velocity increases first and then decreases, and reaches the maximum at 0.171 s. Then, with the passage of blasting load time, the particle vibration velocity decays continuously, and gradually approaches 0 at about 0.5 s.

#### *5.2 HHT Analysis*

As can be seen from Fig. 3, the frequency components contained in the original signal are very rich, but most of them are below 60 Hz. The dominant frequency of the signal is mainly between 0 and 40 Hz, and the main frequency of vibration is 24.43 Hz. The energy contained in the high frequency components gradually decays.

**Fig. 3** Hilbert marginal spectrum

#### **6 Conclusions**

Multi-boundary blasting technology reduces the engineering cost, protects the rock mass outside the excavation boundary from damage as much as possible, accelerates the construction progress and improves the quality of blasting engineering.

#### **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.

### **Experimental Investigation on the Factors Influencing the Shear Strength of Loess-Mudstone Composite Layer**

#### **Xiaodong Zhou, Tienan Wang, and Bowen Xu**

**Abstract** Geological slopes are often disturbed by external engineering, leading changes of the upper moisture content and dry density in loess-mudstone composite layer. It directly affects the shear strength of the loess-mudstone composite layer interface. In order to explore the influence of the upper loess moisture content and dry density on the shear strength of the loess-mudstone composite layer, taking the cutting slope in a test base in Shaanxi Province as the engineering background, different loess moisture contents (10%, 13%, 16%, 19%) and dry densities (1.4, 1.45, 1.5, 1.55 g/cm3) are employed to investigate the shear strength of loess-mudstone composite layers. Scanning electron microscopy (SEM) is used to observe the failure interface of the loess-mudstone composite layer to analyze the failure mechanism of the samples. The results show that: (1) The shear strength of the loess-mudstone composite layer is lower than those of pure loess and mudstone samples. (2) The moisture content of loess will deteriorate the shear strength of the composite layer, and its effect is greater than that of homogeneous loess; but the dry density of loess will enhance the shear strength of the composite layer, and its effect is less than that of homogeneous loess (3) The moisture content and dry density of loess will affect the distribution of pores in the composite layer interface, changing the shear strength of the composite layer. The research can provide certain data and theoretical basis for the prevention and control of landslides at the loess-mudstone interface.

**Keywords** Loess-mudstone composite layer · Shear strength · Moisture content · Dry density · Microstructure

X. Zhou

T. Wang School of Civil Engineering, Southeast University, Nanjing 210000, China

B. Xu (B) Shaanxi Energy Vocational and Technical College, Xi'an 710054, China e-mail<EMAIL_ADDRESS>
School of Geological Engineering and Surveying, Chang'an University, Xi'an 710054, China

#### **1 Introduction**

Loess-mudstone interface landslide refers to the loess landslide sliding along the interface between the overlying loess and the underlying mudstone, which is one of the common types of loess landslide in the Loess Plateau [1–3]. At present, the research results of loess landslide mainly focus on the movement characteristics of loess landslide [4, 5], sliding failure mechanism [6, 7], landslide susceptibility and risk assessment [8–10], landslide types and spatial–temporal distribution [11, 12]. There is still a lack of in-depth research on the mechanical properties and influencing factors of loess-mudstone and other double heterogeneous soils.

The shear strength of the contact surface of double heterogeneous soil is one of the main aspects to characterize the mechanical properties of the contact surface. In engineering practice, the contact surface of double-layer heterogeneous rock and soil structures is often regarded as the weak surface, and has attracted great attention from some scholars. Potyondy [13] was the first to study the mechanical properties of the contact surface between a variety of construction materials and rock and soil mass with the aid of strain-controlled direct shear instrument, and concluded through experimental research that the moisture content of rock and soil mass, the roughness of the structure and the vertical stress would all affect the shear strength of the contact surface. Yoshimi and Kishida [14] introduced X-ray photography technology into shear test of sand-steel contact surface and found that the shear strength was significantly affected by steel surface roughness. Hu et al. [15] applied CCD digital camera technology to the direct shear test of sand-steel contact surface, and pointed out that there is a critical contact surface roughness, which can be divided into shear failure modes of low roughness surface and high roughness surface, and the ideal elastic–plastic failure and strain localized failure with strong strain softening and dilatation respectively. Zhang Ga et al. [16, 17], based on the direct shear and single shear tests on the contact surface of coarse-grained soil and steel plate, pointed out that the shear strength is greatly affected by the properties of rock and soil, vertical stress and the roughness of the contact surface, and is independent of the shear direction. Cheng Hao et al. [18], based on large-scale direct shear tests of red clayconcrete contact surface, found that with the increase of contact surface roughness, the shear failure mode of contact surface gradually evolved from contact surface slip to internal soil failure. Although a series of in-depth studies have been carried out on double-layer heterogeneous rock and soil structures, there are still few experimental studies on the influence of moisture content and dry density of loess on the shear strength of loess-mudstone composite layer.

Based on this, taking a road cut slope in a test base in Shaanxi Province as the engineering background, loess-mudstone composite samples with different loess moisture content and dry density were prepared according to relevant test standards, and direct shear tests were carried out. The influence of loess moisture content and dry density on the shear strength of loess-mudstone composite layer was analyzed. Finally, microscopic failure mode of loess-mudstone interface were observed by SEM to further reveal the mechanism of the influence of moisture content and dry density of loess on the shear strength of loess-mudstone composite layer.

#### **2 Experimental Design**

#### *2.1 Soil Sample Preparation*

The soil sample was taken from a road cut slope containing loess-mudstone contact surface in a test base in Shaanxi Province, as shown in Fig. 1. below. As can be seen from the Fig., the site loess-mudstone assemblage can be divided into three layers according to color. The uppermost layer is loess, the middle is mudstone with high moisture content, and the bottom is mudstone with low moisture content. The main reason for this phenomenon is that mudstone is more dense than loess, and it is difficult for rainwater to penetrate mudstone layer completely, resulting in the formation of aquifer between loess and mudstone layer.

According to the Standard of Geotechnical Test Method (GB/T 50,123–2019), the basic physical property parameters of the test soil samples were determined respectively. In view of the high heterogeneity of the soil, four sites were selected to collect soil, and three groups of samples were prepared at each location for repeated measurement and the average value was obtained, as shown in Table 1.

The remolded loess and fully weathered mudstone samples retrieved from the site after air drying were put into the grinding dish for moderate grinding. In order to obtain well-graded test soil samples, the screening method was used to pass the

**Fig. 1** Distribution of soil layers in the cutting slope

**Table 1** Basic physical parameters of samples

**Fig. 2** Particle size gradation of loess and mudstone for testing

loess and mudstone through sieves with pore sizes of 2, 1.18, 0.6, 0.425, 0.3, 0.212 and 0.15 mm successively. The gradation composition of loess with fully weathered mudstone with particle size <0.15 mm was analyzed by laser particle size analyzer. Finally, the gradation parameters of the test loess and mudstone are shown in Fig. 2. In order to keep the basic physical property parameters of the control test soil samples unchanged, each group of soil samples was prepared according to this grading method.

Considering that the influence of rainfall and engineering disturbance on slope soil mostly stays in the loess layer. This experiment kept the physical parameters of the underlying mudstone unchanged, and mainly explored the influence of the loess moisture content and dry density on the shear strength of the loess-mudstone interface. The field loess moisture content ranges from 10.31% to 19.80% and the dry density ranges from 1.38 to 1.56 g/cm3. Therefore, the design of the loess soil moisture content of 10, 13, 16 and 19% (at this time the dry density of loess is 1.5 g/cm3), and the dry density of 1.4, 1.45, 1.5 and 1.55 g/cm3 (at this time the moisture content of loess is 13%). Then, mudstone with moisture content of 15% and dry density of 1.7 g/cm3 is configured as loess-mudstone composite layer. The vertical stress of 100, 200, 300 and 400 kPa is applied respectively, and the fast shear without consolidation and drainage is carried out. A total of 64 kinds of composite layer conditions are obtained. Meanwhile, parallel control tests of pure loess sample and mudstone group under vertical stress are designed. The shear rate of 0.8 mm/min and shear displacement of 6 mm were used in all tests. The test was repeated 3 times for each condition, and the results were averaged.

Mudstone compresses when vertical stress is applied. In order to avoid the actual shear position deviating from the preset contact surface, the loading mass of mudstone should be calculated according to the predetermined moisture content and dry density (accurate to 0.01 g when weighing). The pure mudstone ring cutter samples were prepared, and the consolidation and compression tests of the soil samples were Experimental Investigation on the Factors Influencing... 305

**Table 2** Compression of mudstone samples under different normal pressures

conducted under normal pressures of 100, 200, 300 and 400 kPa respectively. The compression amounts of the pure mudstone samples under different normal pressures were recorded, and the density of the compressed samples was calculated according to the compression amounts. That is, the actual mudstone sample density when the sample with predetermined moisture content and dry density is prepared under the corresponding vertical stress. The test results are shown in Table 2.

#### *2.2 Direct Shear Test Scheme*

The direct shear test of loess-mudstone contact surface adopts strain direct shear instrument, whose upper and lower shear boxes have the same size and can accommodate samples with a cross-sectional area of 30 cm2 and a height of 2 cm (as shown in Fig. 3.). The loess is located in the upper shear box, and the mudstone is located in the lower shear box. By applying horizontal shear stress to the lower shear box, the sample is shear at the contact point of the upper shear box, that is, the loess-mudstone contact surface.

**Fig. 3** Strain-controlled direct shearing instrument

The direct shear instrument can apply shear forces under different normal pressure loads (100, 200, 300 and 400 kPa) and shear four samples simultaneously. However, in order to reduce instrument error, only one sample is placed at a fixed position for each shear. The shear displacement value of the display screen (accuracy 0.001 mm) and the deformation of the measuring ring measured by the electric dial indicator (accuracy 0.01 mm) were recorded by the software dynamometer system 3.9A, and the horizontal shear stress was obtained according to the coefficient of the measuring ring.

As the shear area gradually decreases during the test, the test result is smaller than the vertical stress applied by the actual instrument. In addition, if the set shear displacement and the actual shear displacement are not distinguished, the measured shear strength will be less than the actual shear strength of the soil. In this paper, the results of direct shear tests are modified from the aspects of effective shear area and effective vertical stress.

Due to the symmetry of the shear plane, 1/2 of the shear area is taken for area correction. The initial shear area A0 is regarded as invalid parts A1 and A2, as shown in Fig. 4.

According to the geometric relation in Fig. 4., the expression of A2 can be obtained:

$$\mathbf{A}\_2 = \mathbf{2(S\_{\text{sector}\bullet AB} - S\_{\triangle O\prime AB})} = \frac{\mathbf{D^2 \cos^{-1}(\frac{\mathbf{x}}{D})}}{2} - \mathbf{x}\sqrt{\frac{\mathbf{D^2}}{4} - \frac{\mathbf{x}^2}{4}} \tag{1}$$

where, D is the diameter of the sample, which is 6.18 cm here. x is the shear displacement (cm). When x = 0, the initial shear area A0 is 30 cm2, and when x = 6 mm, the initial shear area A2 is 26.29 cm2. Let the area correction factor α satisfy:

Experimental Investigation on the Factors Influencing... 307

$$
\alpha = \frac{\mathbf{A}\_0}{\mathbf{A}\_2} \tag{2}
$$

there is:

$$
\pi\_1 = \alpha \pi\_0 \tag{3}
$$

where,τ1 is the shear strength of the modified sample (kPa); τ0 is the shear strength of sample without area correction (kPa).

The vertical stress on the effective shear area was corrected, and the force analysis of the upper shear soil sample was shown in Fig. 5. In Fig. 5, σ1 is the uniform vertical stress (kPa) applied to the non-effective shear area A1, σ0 is the uniform vertical stress (kPa) applied to the top of the shear soil sample, σ2 is the uniform vertical stress applied to the effective shear area A2, and P is the applied shear force.

According to the moment equilibrium MyQ = 0 of each stress component in the y direction of the central point Q of the effective shear area in Fig. 5, it satisfies [19]:

$$\mathbf{M}\_{\sigma 1} = \mathbf{M}\_{\sigma 0} + \mathbf{M}\_{\pi 1} \tag{4}$$

According to the geometric relationship in Fig. 4. and Fig. 5, it can be obtained:

$$
\sigma\_2 = \sigma\_0 - \frac{\mathbf{r}\_{\rm l}}{\pi \chi} [\pi - 2\theta + \sin(2\theta)] \tag{5}
$$

where, I is the height of the soil sample in the upper shear box, which is 10 mm. Let the normal correction coefficient β satisfy:

$$
\beta = \frac{\sigma\_2}{\sigma\_0} \tag{6}
$$

The shear strength of the comprehensively modified sample τ2 can be obtained:

**Fig. 5** The force diagram of the soil sample in the upper shear box after shear dislocation

τ2 = βτ1 (7)

#### **3 Shear Test Results and Analysis of Sample**

#### *3.1 Effect of Moisture Content on Shear Strength of Sample*

The relationship between shear strength and vertical stress of loess, loess-mudstone composite layer and mudstone under different moisture content is shown in Fig. 6. As can be seen from the Fig. 6, under the same vertical stress, the loess-mudstone composite sample with double heterostructure has the lowest shear strength, followed by the loess sample on the upper layer, and the mudstone sample has the highest shear strength. This indicates that the contact surface is the weak strength of loessmudstone composite layer. When the vertical stress was the same and the vertical stress was 400 MPa, for example, when the moisture content increased from 10 to 19%, the shear strength of loess continued to decrease by 3.71, 6.93 and 12.08% to 10.02, 18.72 and 32.62 kPa, respectively. The shear strength of loess-mudstone composite layer decreases by 11.67, 22.26 and 37.51 kPa, respectively, by 4.87, 9.29 and 15.65%. This indicates that moisture content has a more significant effect on the deterioration of shear strength at the loess-mudstone interface.

In to the pressure, the upper loess pore structure are pressure, saturation increases, the soil particles between weakly bound water and free moisture content increases, and the lower mudstone is more dense loess, poor permeability and a relative impermeable layer, makes the bottom of the north part of the water accumulation in the loess-mudstone contact area, contact area of soil In the overwatering soft plasticsaturated state, Thus, the shear strength of the contact surface is significantly reduced. This conclusion is consistent with the conclusion proposed by Xing Lin et al. [20] that the loess shear strength decreases with the increase of saturation, that is, the higher the moisture content of the upper loess, the more water accumulated at the loess-mudstone interface, and the higher the deterioration degree of the shear strength of the interface.

#### *3.2 Influence of Dry Density on Shear Strength of Sample*

The relationship between the shear strength of loess and loess-mudstone composite layer and the dry density of loess is shown in Fig. 7. It can be seen from the Fig. 7 that, under the same vertical stress, the loess-mudstone composite layer has the lowest shear strength in various working conditions that only change the dry density of loess, that is, the contact surface is still the weak strength surface of the whole loessmudstone double-layer heterogeneous structure. However, when the vertical stress

**Fig. 6** Variation of shear strength of loess and composite layers with moisture content of loess

was the same and the vertical stress was 400 kPa for example, with the dry density of loess increasing from 1.4 g/cm3 to 1.55 g/cm3, the shear strength of loess increased by 14.92, 22.81 and 39.35 kPa, respectively, by 6.29, 9.61 and 16.58%. The shear strength of loess-mudstone composite layer increases by 11.70, 15.16, 24.99 kPa, 5.50, 7.12, 11.74%, respectively. It can be seen that the dry density of loess has greater influence on the shear strength of homogeneous loess than that of composite loess.

The relationship between the shear strength of loess and loess-mudstone composite layer and the dry density of loess is shown in Fig. 7. It can be seen from the Fig. 7 that, under the same vertical stress, the loess-mudstone composite layer has the lowest shear strength in various working conditions that only change the dry density of loess, that is, the contact surface is still the weak strength surface of the whole loess-mudstone double-layer heterogeneous structure. However, when the vertical stress was the same and the vertical stress was 400 kPa for example, with the dry density of loess increasing from 1.4 to 1.55 g/cm3, the shear strength of loess increased by 14.92, 22.81 and 39.35 kPa, respectively, by 6.29, 9.61 and 16.58%. The shear strength of loess-mudstone composite layer increases by 11.70, 15.16, 24.99 kPa, 5.50, 7.12, 11.74%, respectively. It can be seen that the dry density of loess has greater influence on the shear strength of homogeneous loess than that of composite loess.

**Fig. 7** Variation of shear strength of loess and composite layers on dry density of loess

#### **4 Microstructure of Loess-Mudstone Interface after Shear Failure**

In order to further reveal the influence of different loess moisture content and dry density on the shear strength of loess-mudstone composite layer, it is necessary to observe the structural changes of soil samples at the interface of the composite layer under different working conditions by microscopic means. The damaged loessiemudstone interface block was observed by FEI Quanta 400 FEG environmental scanning electron microscope (SEM), State Key Laboratory of Continental Dynamics, Northwest University.

The microstructure of contact surface after shear failure of composite layers with different loess moisture content is shown in Fig. 8. As can be seen from the Fig. 8, when the moisture content is low, the soil particles are larger on the whole, with looser arrangement and more pores. In addition, it can be seen that small clay groups fill between the larger structural units and play an internal cementation role. Under this condition, the contact particles mainly have mechanical friction under shear. With the increase of moisture content, the amount of water accumulated on the contact surface increases, the amount of clastic material and clay material on the contact surface increases, and some large particles are aggregated into a whole state under the connection of clay particles, and the pore area decreases continuously. When the moisture content increased to 19%, the cement inside the clay mass was softened, dismembered into small clay particles and filled in the pores, and there were no obvious large pores in the visual field. The shear strength of the contact surface decreases due to the thicker bonded water film adsorbed by the disintegrated slime.

Figure 9. shows the microstructure scanning of the interface of composite layer with different dry density of loess after shear failure. Furthermore, PCAS software was used to binarize the image, and the results showed that the porosity of 1.4, 1.45, 1.5 and 1.55 (g/cm3) loess under dry density conditions were 8.52, 7.33, 6.17 and 5.31%, respectively. The average pore area is 228.88, 231.88, 185.94, and 183.65 (pixel). Therefore, it can be seen that with the increase of the dry density of the upper loess, the microscopic characteristics of the pores on the contact surface have a great change, and the pore number and average pore area on the whole decrease, while the porosity decreases. This is mainly because when the dry density of the upper loess increases, more soil particles will be embedded and adhered to the contact surface, filling the original pore structure on the contact surface. The large pores in the overhead are transformed into small and micro pores, and the particles are arranged from loose to tight, and the degree of occlusion is enhanced. Macroscopically, the shear strength and parameters of the contact surface increase to a certain extent with the increase of the dry density of the upper loess.

**Fig. 8** Scanning images of the contact surface microstructure in the composite layers with different loess moisture contents

**Fig. 9** Scanning images of the contact surface microstructure in the composite layers with different loess dry density

#### **5 Conclusion**

This paper conducted an experimental study on the shear strength of loess-mudstone composite layer with different loess moisture content and dry density, and observed the microstructure of the composite layer after shear failure with scanning electron microscopy. It can be concluded that:

loess moisture content will reduce the pore area of the contact surface of the composite layer, resulting in the accumulation of water at the contact surface, and reduce the shear strength of the loess-mudstone composite layer.

#### **References**

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### **Compaction Effect Due to Single Pile Driving in PHC Pile Treated Soft Clayey Deposit**

**Guowei Li, Ruyi Liu, Chao Zhao, Yang Zhou, and Li Xiong**

**Abstract** The compaction effect of extra-long prestressed high-strength concrete (PHC) piles in deep soft soil foundation was studied by field test. The pore water pressure gauge, inclinometer were embedded in different plane positions or different depths of the foundation to monitor the pore pressure and deformation of the foundation when driving pile. The research shows that the magnitude of excess pore water pressure caused by single pile installation is mainly related to buried depth of the measuring point and the linear distance between the pile tip and the measuring point. The shorter the distance or the deeper the depth is, the greater the excess pore pressure caused by pile installation. The horizontal influence radius of pile compacting on the pore water pressure is about 10.7 m. The excess pore pressure induced by pile installation increases with depth, and is obviously affected by stratum properties. In the vicinity of soil with high permeability coefficient, such as thin sand layer or silty fine sand layer, the excess pore pressure cannot be accumulated in a large amount. The existing subgrade obviously restricts the lateral deformation of soil between piles and PHC piles. The pile deformation is small at the top and bottom, and large in the middle. The inflection point of the deformation curve appears at the pile connection position. The relationship the excess pore pressure of the measuring point with the depth and distance of the measuring point is given.

**Keywords** PHC pile · Compaction effect · Pore water pressure · Lateral displacement

G. Li · R. Liu · L. Xiong

C. Zhao

Guangdong Road and Bridge Construction Development Co., Ltd, Guangzhou 510510, China

Y. Zhou (B) Henan University of Technology, Civil Engineering School, Zhengzhou 450001, China e-mail<EMAIL_ADDRESS>
315

Hohai University, Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Nanjing 210024, China

#### **1 Introduction**

PHC pile has reliable quality and is widely used in soft foundation treatment. And the compaction effect of PHC pile during installation is significant. The pile penetration makes the soil around the pile compact which will induce lateral extrusion and vertical uplift of the soil and in turn causes tilting or floating of the adjacent pile, even crack and overturning of the adjacent buildings [1–3] (a. Zhang et al.2006 b. Liu et al. and c. Wang et al.). In addition, compaction effect leads to the increase of excess pore pressure, and the dissipation of the induced excess pore pressure, i.e., consolidation, results in considerable soil settlement and negative surface friction around the pile. Field test is a commonly used research method by many scholars because of its authenticity and reflecting the engineering practice. Li et al. (2011) [4] and Liu et al. (2012) [5] studied the influence of pile installation process on foundation deformation, excess pore pressure and plugging effect through field tests. Xing et al. (2009) [6] found that the lateral displacement of the soil mass at the distance of 16 *d* (*d* is the pile diameter) from the edge of the pile group edge was the largest, equal to15 mm. Wei et al. (2020) [7] investigated the effect of the pre-drilled hole and isolation effect in PHC pile installation; Wan et al. (2020) [8] studied the effect of soil properties and pile driving speed on soil compaction during pile installation. In summary, the PHC piles has been widely researched and lots of useful results were obtained.

However, the existing research on PHC pile driving is basically within 10 m long, lacking of research on the extra-long PHC pile which usually exceeds 40 m and requires pile extensions more than three times. For extra-long PHC pile, the pile installation process has a more s13ignificant impact on the lateral deformation than the normal pile [9–12]. In the southeast regions of China, the thickness of the soft foundation often reaches tens of meters, even nearly 100 m which acquires longer pile length. The existing research showed that the excess pore pressure is positively related to the penetration depth. Thus, it is necessary to study the compaction effect of extra-long PHC piles. In addition, previous studies mostly focused on the excess pore pressure and lateral deformation of soil caused by driving piles, and there has no research about the compaction effect on the lateral deformation of adjacent piles.

In this paper, field test was conducted to study the compaction effect of extra-long PHC piles. Thorough this test, excess pore pressure changes, lateral displacements of the soil and pile shaft during the pile installation were monitored. And the compaction effect caused by the penetration of extra-long PHC piles was analyzed assisted with the measured data.

Compaction Effect Due to Single Pile Driving... 317

**Table 1** Physical–mechanical indexes of soil

#### **2 Field Test**

#### *2.1 Test Site*

The field test was carried out in an expansion project of express way in Guangdong province in China. The test site is relatively flat but with very deep soft clay deposits. At the top, there is a layer of sand filling with a thickness of 2.5 m, and the followed by 34 m – thick clay layer, including silty clay, a shell layer and a layer of silty, the bottom of a 8 m silty sand located on the moderately weathered rock stratum. The main physical parameters are shown in Table 1.

#### *2.2 Tested Program*

The moderately weathered rock stratum below the fine sand was designed as the bearing stratum of the piles. The design length of the pile is ranging from 45 to 150 m, the pile has an outer diameter of 400 mm and an inner diameter of 310 mm, thus the thickness of the annular of the PHC pile is 90 mm. The material of the pile was C80 concrete. A total of 79 piles were installed. The piles were installed in a rectangular shape. The pile space is 3 × 2 m along the longitudinal and transversal direction. The pile location layout and installation route procedure are illustrated in Fig. 1. The PHC pile installation in the test area started on A-1 (5 May) and ended on V-16 (4 June), and lasted for 31 days. The layout of the test instruments is shown in Fig. 1. Two inclinometer tubes were installed, designed as CX1 and CX2 with a depth of 42 m and 44 m, respectively. CX1 was used for lateral deformation measurement of the soil within piles. And CX2 was used for the pile shaft and placed inside the hollow of the pile I-5. In addition two of the piezometers were set at K1 points with a buried depth of 12 m and 18 m respectively. As shown in Fig. 1, K1 has an equal radial distance of 3.5 m from the surrounding 4 piles.

**Fig. 1** Instrument layout and construction sequence diagram

#### **3 Test Results and Analysis from Single Pile Driving**

#### *3.1 Pore Water Pressure*

In the section, the compaction effect of three piles with different radial distance on the target pile I-5 was investigated. In this paper, pile II-4, pile III-4 and pile VI-4 are selected and these piles are representative of the pile installation at close distance, middle distance and far distance. The excess pore pressure variation with pile installation time was shown in Fig. 2(a)–(c) for the above three piles, respectively. Note the excess pore pressure plotted in Fig. 2. are the incremental pressure induced by the penetration from an initial time. Figure 2(a) shows the relationship between the excess pore water pressure in K1 and the driving time of pile II-4. It can be seen that when the pile tip depth is less than 13 m, the pore water pressure of K1–12 increases rapidly. When the pile depth exceeded 13 m, the excess pore water pressure of K1-12 basically remains unchanged, keeps at 6 kPa. For K1-18, the excess pore pressure is zero when the pile depth is within 13 m. When the pile depth ranges within 13 –37 m, the excess pore pressure rises rapidly, with the maximum value of 15.8 kPa. It is interesting to find that the excess pore water pressure starts to slowly decrease as the pile tip depth is beyond 37 m, and the excess pore water pressure of K1-18 is 13.3 kPa after pile installation.

Figure 2. (b) shows the relationship between the excess pore pressure and the driving time for pile III-4. The total penetration depth of the PHC pile is 45 m. Basically, the trend of pore pressure with time is consistent with pile II-4. For both piles, i.e., II-4 and III-4, the excess pore pressure rises rapidly when the pile tip reaches near the measuring point. And the induced excess pore pressure measured at the deep point (18 m) is larger than that at the shallow point (12 m). For K1-12, the

**Fig. 2** Curve of excess pore water pressure generated by single pile installation

peak value of the induced excess pore pressure is 2.0 kPa, and the residual value after installation is 0.6 kPa. For K1-18, the peak value is 8.5 kPa, and the residual value is 8.5 kPa. Figure 2. (c) shows relationship between the excess pore water pressure and the driving time for pile VI-4. The total penetration depth is 38 m with a peak excess pore pressure 1.4 kPa and a residual value of 0.9 kPa at K1-12, and a peak value of 1.6 kPa and a residual value of 1.54 kPa at K1-18. Clearly, as the distance of increasing between the PHC pile and the measuring point, the excess pore water pressure caused by the single pile installation decreases gradually. For example, the excess pore water pressure during the penetration of pile VI-4 is very small generally indicating no significant compaction effect due to pile driving at farther distance. Therefore, the horizontal distance between pile VI-4 and the measuring point, e.g., K1, can be taken as the impacting radius, which is 10.7 m in this study.

#### *3.2 Lateral Displacement of Soil*

The pile II-6 and II-8 were selected to study the impact of penetration on the lateral deformation of soil between piles. Figure 3. shows the lateral displacement with depth in X and Y directions after each pile's installation. The lateral displacement were obtained from the inclinometer at CX1. In general, the pile installation pushing the soil mass away results in positive displacement in Y direction and negative displacement in X direction. In Y direction, the maximum lateral displacement of pile II-6 is 3.8 mm at the depth of about 24 m and the value induced by pile II-8 is basically close to 0. And the maximum lateral displacement caused by pile II-6 and II-8 in X direction is 4.8 mm and 2.5 mm, respectively. Definitely, the lateral displacement of soil induced by the PHC pile installation decreases with the distance of the driven pile. It also can be seen from Fig. 3. that the lateral displacement of soil in the Y direction is significantly smaller than that in the X direction. Due to the existence of the in-service expressway, there is a constraint effect on soil deformation induced by pile installation in the Y direction. In addition, the lateral displacement at the upper and lower parts in Y direction are small, while the displacement in middle height is relatively larger. Contrast to Y direction, the soil displacement in X direction shows a continuous increase from bottom to the top. As mentioned above, the existing embankment has significant resistant effect on the soil deformation in Y direction, but it is not true in X direction.

#### *3.3 Lateral Deformation of PHC Pile*

The influence of pile installation on the lateral deformation of adjacent piles mostly researched by numerical simulation or model test [13–16] (a. Yao et al. b. Zhan et al. and c. Wei et al. d Luo et al.) at present. Rare reports about field tests on this topic were found up to date. In this paper, by setting inclinometer in the pile the lateral deformation of the pile was directly measured. Thus the impact of the compaction effect of subsequent pile installation on the existing pile can be directly estimated. As shown in Fig. 1, pile I-5 is selected to be the target pile with a 44 m-long inclinometer. First, four consecutive piles (II-5, III-5, IV-5 and V-5) are selected as the research object along the Y direction. Figure 4. shows the curve of lateral displacement of pile I-5 with depth as the four piles (II-5, III-5, IV-5 and V-5) were penetrated. Among

**Fig. 3** Lateral displacement curve of soil caused by single pile installation

them, the penetration of the nearest PHC pile II-5 has the greatest impact on the lateral displacement of the pile shaft, and the maximum lateral displacement is 4.3 mm at the depth of 22 m. In addition, the pile's displacement mainly occurs at 1/3–2/3 of the pile length. Considering the connection position of the prefabricated pile shaft, the lateral displacement turning points (1/3 and 2/3 depth) exists consistent with the connection points. It is possible that the joint of the pile shaft is a relatively weak point resulting in the bending and deformation of the whole pile due to installation of near pile. Therefore, special attention should be paid to the joint of shaft of a PHC pile during driving. The results also show that the influence of driving for pile V-5 on the deformation of pile I-5 can be ignored. The influence range of pile installation on the deformation of adjacent piles is about 4 times the pile spacing, generally equal to 10.7 m.

#### *3.4 Influencing Radius*

Figure 5. shows excess pore pressure with horizontal distance from pile-center to the K1. Note that the excess pore water pressure in Fig. 5. (a) is the maximum value after penetration of each pile. It can be seen from Fig. 5. (a) that the maximum excess pore water pressure caused by single pile installation at a depth of 12 m is 26 kPa, and the value at 18 m is 80 kPa at horizontal distance of 1.8 m. As mentioned above, deeper soil yields larger pore water pressure. As the horizontal distance increases, the pile driving induced excess pore water pressure caused by