**3.2 Expanding the role of cooperatives and unions in community development**

There are two ways in which the cooperative organizational form holds promise for dealing with the local-level community challenges in the twenty first century. First, cooperatives have been able, over time, to adjust the services they provide to deal with a changing set of issues that local communities face. This is especially true with respect to their expanded influence in supporting infrastructure development in low population density rural communities. Today, for example, Electric Cooperatives are playing a major role in efforts to expand broadband service into rural areas [39, 40]. The U. S. Department of Agriculture's Community Development Programs, through the Cooperative Extension Service, offers assistance to local communities for a variety of services [41], including those to assist in mental health [42]. The Dairy Farmers of America Cooperative recently announced the introduction of a new service to provide 24/7 access to mental health services to their members [43].

Second, since cooperatives are, by definition, self-governed by their members, they play a critical role in promoting the values and skills that build civil society. This, in turn, provides an anti-dote to the feelings of powerlessness that plague disconnected individuals in a mass society, thereby reducing the appeal of populist authoritarian demagogues. This function, which Tocqueville [23] saw in American small town voluntary associations in the 1830s was recognized in *the post-genocide Rwandan government's decision to make cooperative development a central part of its economic development programs* [44].

Expansion of cooperatives, with the support of enabling legislation from state and national governments, can provide substantial support to many struggling communities. One of the most important developments in this respect has been the work

of USDA Extension in supporting increased linkages between rural food producers and communities through the Community Supported Agriculture (CSAs) program. This is especially helpful to small-scale fruit, vegetable, and meat producers, both in building sustainable collective linkages among themselves, markets, and consumers, as well as dealing with legislatures when decisions are made about licensing and other matters that affect their businesses [45, 46].

The cooperative organizational model also can be applied in ways that will expand the effectiveness of "upstream" interventions to promote health and mental health care in struggling communities, especially those with increasing rates of suicide, addiction, and preventable deaths from lack of early intervention. Researchers have found, for example, that important contributors to increasing health costs in rural communities is the lack of coordination between entities that deal with housing, access to healthy food and identification of vulnerable persons with symptoms indicating early stages of health or mental health problems. The increased interest in engaging local communities, especially in preventive public health programs has resulted in an upsurge of research on how best to understand local social networks and culture to implement programs that not only improve community health but also reduce costs to taxpayers [47–49].

Another collective organizational model that can be adapted to contribute to community sustainability in the twenty first century is the union. The conceptualization of the union during the post-World War II industrial boom years in the United States is articulated by John Kenneth Galbraith's [50], *American Capitalism: The Concept of Countervailing Power,* which was originally published in 1953 during the height of the post-World War II economic boom. His view was that the growth in size of mass production industries was matched by the growth in size of industrial unions, which, in turn, would bring overall benefits to workers, management and the public at large. This paradigm, however, has been seriously weakened by the increased mobility of capital and the internationalization of supply chains from the 1970s onward, and especially since the 1970s, by the increase in the application of robotics in industrial production [51]. This is reflected in the movement of significant portions of production overseas and the subsequent decline of union membership.

An alternative is to look at the German industrial organizational model in which unions and management play quite different roles than in the American case. In Germany union representatives sit on company boards and actively participate in day-to-day company policymaking. The impact of the 2007–2008 recession on workers in Germany versus the United States illustrates the practical outcome of the different organizational arrangements. When the recession hit mass production industries, like automobiles, in the United States, orders for new cars decreased and workers were laid off according to seniority. Alternatively, in Germany the boards, comprised of management and labor representatives, developed plans in which all workers would take a small cut in numbers of hours worked, with the government subsidizing the lost wages. This also reduced overall costs for unemployment benefits. The German industrial model, with the greater role for unions in day-to-day decision-making, is much more resilient than the American model in anticipating and adapting to external exigencies [52, 53]. It is important to emphasize that, as in the case of criminal justice reform, it is the *convergence of interests,* and the awareness of how working together can achieve their respective goals that provides an important incentive for both parties to support participation in the organization.


**1. Introduction**

This chapter presents the results of an entry into the 2015 Environmental Protection Agency (EPA) Campus RainWorks Challenge, Masterplan Category, employing the new Michigan Sate University (MSU) Medical Campus in Grand Rapids, Michigan as a case study. The plan employs

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

metrics to demonstrate the effects that the low-impact development can have upon urban sustainability issues. The metrics include the following: reduction in stormwater volume, increase in stormwater quality, increase in songbird habitat suitability, increase in vegetation biodiversity, reduction in water requirements by woody vegetation, increase in latent soil productivity, increase in vegetation adaptation to climate change, increase in visual quality, improvementinmicroclimatediversity,reductioninlandscapemaintenanceandenergyinputs, and walkability.

The plan blends green infrastructure, healthy urban environments, neighborhood entertain‐ ment opportunities, and sustainability together addressing fundamental issues. In the development of the project several best management practices (BMPs), tools are presented to improve water quality and the challenges brought by global climate changes. Some of the tools that are employed in the design include green roof, rain tanks and cisterns, permeable pavement, bioretention or rain gardens, dry and wet swale, and constructed wetlands. The project involved students, faculty, and administrators who influenced and directed the final product. The title for this project is "Vault of Heaven," an ancient Hebrew term for the sky, where the rainwater lands on the earth.


*Article* **Stability Evaluation and Structural Parameters Optimization of Stope Based on Area Bearing Theory**

**Hao-Yu Qiu, Ming-Qing Huang \* and Ya-Jie Weng**

Zijin School of Geology and Mining, Fuzhou University, Fuzhou 350108, China<EMAIL_ADDRESS>(H.-Y.Q<EMAIL_ADDRESS>(Y.-J.W.)

**\*** Correspondence<EMAIL_ADDRESS>Tel.: +86-188-5010-1619

**Abstract:** A reasonable and stable stope structure is the premise of realizing safe mining of underground metal ore. To safely mine the gently inclined medium-thick ore body, stope stability in Bainiuchang Mine was analyzed based on the pillar area bearing theory, and stope stability with regard to nine groups of structural parameters was numerically simulated. The results show that the existing stope structural parameters failed to maintain stability requirements and tended to be exposed to the risk of stope collapse. The middle section of the pillar as well as stope roofs and floors are vulnerable due to tensile stress when mining by open stoping, and the compressive stress concentration is prone to occur at the junction of the pillars, stope side walls, roofs and floors. Shear stress contributes little to pillar failure. The reasonable stope structural parameters of open stoping for the gently inclined medium-thick ore body in Bainiuchang mine are optimized using ANSYS numerical simulation: stope height 4.5 m, pillar diameter 4 m, pillar spacing 7 m and pillar row spacing 8 m. The onsite trial shows that the ore recovery rate reaches 82% under these parameters, which also realizes the equilibrium of safety and economy.

**Keywords:** gently inclined medium-thick ore body; structural parameter optimization; stope stability; area bearing theory; numerical simulation

#### **1. Introduction**

Gently inclined medium-thick ore body is one of the most widely distributed types of underground metal deposits worldwide. The inclination angle of this type of ore body is mostly 5~30◦, which is not conducive to the normal operation of trackless mining equipment such as intelligent scrapers, nor to ore-drawing under gravity of blasted ore in the stope. It is internationally recognized as the most difficult type of ore body to mine [1–3]. Open stoping is commonly used in the world to mine gently inclined medium-thick ore bodies [4], and its mining structural parameters are the most important indicators for balancing safe, economic and efficient recovery. If pillars are too thin to resist ground pressure, it usually leads to safety accidents; in contrast, it will cause ore loss and reduce ore recovery rate and production profit. Structural parameters are the most influential factors for maintaining stope stability with open stoping. In 1973, Bieniawski proposed the RMR (Rock Mass Rating) rock mass classification method to evaluate the stability of various rock masses [5]. Bazaluk et al. [6] studied the stope stability of underground mining of iron ore by taking yuzhno-belozerskyi deposit as the research object. Wu et al. [7] used ANSYS and Flac3D to analyze the influence of mine room and pillar configuration on stope stability in highly fractured areas and preferred the stope structure configuration scheme based on the objective function and constraint function. Mikaeil et al. [8] used Flac2D to calculate the load cases such as axial forces, bending moments and shear forces in the vault, bottom and side walls of the underground roadway and analyzed the stability characteristics of the roadway support. Zhao et al. [9] used Flac3D to simulate the stope structure and design the safest stope exposure size based on the Mathews stability graphical solution method.

**Citation:** Qiu, H.-Y.; Huang, M.-Q.; Weng, Y.-J. Stability Evaluation and Structural Parameters Optimization of Stope Based on Area Bearing Theory. *Minerals* **2022**, *12*, 808. https://doi.org/10.3390/ min12070808

Academic Editor: Yosoon Choi

Received: 27 April 2022 Accepted: 21 June 2022 Published: 25 June 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Qin et al. [10] analyzed the stability characteristics of ore pillars with different thicknesses by numerical simulation in an iron mine, which provided a reference for the optimization of structural parameters. Lan et al. [11] constructed a second-order response surface model and realized the comprehensive optimization of the stope structural parameters through multi-objective optimization and multi-attribute decision making. Liu et al. [12] used Flac3D to establish a numerical calculation model of the fractured ore body and studied the relationship between the stope span parameters, roof displacement and plastic zone volume. However, the aforementioned studies were based on safety and technology for optimization, and less consideration was given to the best economic efficiency during mine recovery.

Bainiuchang Mine has a typical gently inclined medium-thick ore body, which is mainly mined using the room and pillar method. The width of ore block is generally 20~25 m, the length is 30~40 m, and a circular pillar with a side length of 2~4 m is reserved. With the increasing mining depth, the ground pressure management is becoming more and more complicated, and there is a serious risk of collapse. It is urgent to optimize the original stope structural parameters. Based on the area-bearing theory, the mining process before optimization of the Bainiuchang Mine was simulated through ANSYS, and the stope stability was evaluated through stress analysis. Nine different stope structural parameters optimization schemes were proposed through orthogonal design, and the stress conditions of pillar, roof and floor were analyzed based on numerical simulation, and safe and economic stope structural parameters were further optimized, so as to guide the mining of gently inclined medium-thick ore body.

#### **2. Area Bearing Theory**

The area-bearing theory holds that the load on the pillar is the gravity of the overlying rock layer from the mining space it supports to the surface, and the area supported by the pillar is the sum of the mining area and the cross-sectional area of the pillar itself, from which the axial compressive stress of the pillar is approximated. It reveals the internal causes of pillar instability and failure (as shown in Figures 1 and 2). Its equilibrium equation is as follows Equation (1).

$$
\sigma\_{\rm p} \mathbb{W}\_{\rm p} = \left( \mathbb{W}\_{\rm o} + \mathbb{W}\_{\rm p} \right) p\_z \tag{1}
$$

where *σ*p is the axial compressive stress of the mine pillar; *pz* is the vertical positive stress component of the ground stress field before mining; *W*o is the width of the mine room; *W*p is the width of the mine pillar.

**Figure 1.** Schematic diagram of pillar stress.

The strip mine pillar and circular mine pillar are mainly arranged in Bainiuchang Mine. The calculation Equations (2) and (3) for the axial compressive stress of the two types of ore pillars can be derived from Equation (1).

$$\text{The strip minre pillar : } \sigma\_{\text{P}} = \gamma H \left( 1 + W\_{\text{o}} / W\_{\text{P}} \right) \tag{2}$$

**Figure 2.** Schematic diagram of pillar bearing calculation.

$$\text{The circular minre pillar : } \sigma\_{\text{P}} = \frac{4\gamma H}{\pi} \left( 1 + W\_{\text{o}} / W\_{\text{P}} \right)^{2} \tag{3}$$

where *γ* is the capacity of the overlying rock layer; *H* is the mining depth [13,14].

Based on the area bearing theory, the axial compressive stress of the ore pillar can be calculated. According to the area bearing theory, each pillar supports the ore rock in a certain area. The axial compressive stress of the ore pillar can be calculated by the gravity of the upper ore rock and the sectional area of the ore pillar. When the axial compressive stress exceeds the uniaxial compressive strength of the ore rock, the ore pillar will be crushed, resulting in fragmentation, deformation and even collapse. Then, cause the collapse of the stope roof. When the number of collapsed pillars reaches a certain amount, it will produce a chain effect, leading to the collapse of other pillars, and finally the overall collapse of the mine room. otherwise, it can be safely mined.

Combined with the area bearing theory (Equation (3)) and the Bieniawski pillar strength formula (Equation (4)), the safety factor calculation formula (Equation (5)) of the circular point pillar in Bainiuchang mine can be derived.

*S*p = *σ*c \* 0.64 + 0.36" *W*p/*h* #+ (4)

where *S*p is strength of ore pillar, MPa; *σ*c is strength parameter of ore and rock, MPa; *h* is the room height, m; *W*p is the width of the mine pillar.

$$K = \frac{\sigma\_{\text{c}} \left[ 0.64 + 0.36 \left( W\_{\text{P}} / h \right) \right]}{\frac{4 \gamma H}{\pi} \left( 1 + W\_{\text{O}} / W\_{\text{P}} \right)^{2}} \tag{5}$$

where *K* is the safety factor of circular point column. Other physical quantities are described above.

#### **3. Stope Stability Evaluation**

The existing stope stability of Bainiuchang mine is evaluated. The geological structure of the mining area is well developed, and the weathering is strong. The hydrogeological conditions of the deposit are complex, with strong karst aquifers filling with water. The roof of the ore body is a carbonate rock mixed with clastic rock karst fissure aquifer, and the inflow is 0.0025~1.52 L·s−1; The floor of the ore body is a karst fissure aquifer of clastic rock mixed with carbonate rock, and the inflow is 0.0109~2.69 L·s−1. The ore body is stratiform and lenticular in shape, with siltstone and mudstone on the roof and argillaceous limestone on the floor. The surrounding rock mass of the upper and lower walls of the ore body is of good quality, and the engineering geological conditions are simple. The physical and mechanical parameters of the main ore rocks of the Bainiuchang mine are shown in Table 1. In Table 1, *σc* represents uniaxial compressive strength, *σt* represents uniaxial tensile strength, *τ* represents shear strength, *c* represents cohesion, *ϕ* represents internal friction angle, *E* represents elastic modulus, *ρ* represents density, and *μ* represents Poisson's ratio. The pillar of Bainiuchang mine are shown in Figure 3.

**Table 1.** Physical and mechanical parameters of Bainiuchang's ore rocks.

**Figure 3.** Picture of pillar in Bainiuchang mine.

The structural geology of site: The fault structures in the mining area are developed, mainly NW trending faults, with NE trending faults interspersed between them, forming a structural framework. F2, F3, F6, F7 and F8 in the northwest direction are mainly exposed in the mining area. F2 fault strike NW-SE, dip direction SW, dip of 65◦. F3 fault is the most important ore controlling and hosting structure in Bainiuchang mine, with a total length of 5000~6000 m, strike NW-SE, dip direction of 200~230◦ to SW, and dip of 20~35◦. F6 fault is about 1.7 km, strike NW-SE, dip direction SW, dip of 30~35◦. F7 fault is about 3.5 km, strike NW-SE, dip direction SW, dip of 34~50◦. F8 fault is about 3.4 km, strike NW-SE, dip direction SW, dip of 60~75◦.

#### *3.1. Simulation Conditions and Process*

The onsite mining process of Bainiuchang mine (as shown in Figure 4): Strip rooms and strip pillars are arranged in intervals. Strip rooms are mined first. After strip rooms are mined, the strip pillars are mined, leaving round point pillars with a diameter of 3 m. The stope height is 3 m, stope length is 40 m and the width is 25 m. Next, a multi-step excavation finite element calculation model will be established according to the actual mining process by ANSYS 19.2.

**Figure 4.** Arrangement and mining sequence of rooms and pillars.

Modeling: The finite element model is established according to the onsite geological conditions, and the mechanical model is established according to the influence range of 3~5 times the diameter of the excavation space. In order to balance the calculation speed and accuracy, a 500 m × 500 m × 625 m model is established (Figure 5). On the basis of not affecting the calculation results and considering the size coordination relationship of the model, the depth is taken to 1380 m above sea level. The model contains the ore body, and then contains the target ore block of numerical simulation calculation.

**Figure 5.** Finite element calculation model.

Mesh refinement analysis: If the mesh is sparse, the accuracy of calculation cannot meet the requirements. The finer the mesh, the higher the accuracy of calculation, but the amount of calculation will increase exponentially. In order to balance the calculation accuracy and efficiency, considering the regularity of the element, we established a material model based on the key points by using ANSYS. This work is according to the geological structure model and the distribution changes of the physical property parameters of each layer in the mining area. Using the tetrahedron (SOLID92) 10 node element type, we divided the finite element mesh of each volume element. The whole mesh was divided into 57,611 elements and 79,159 nodes (Figure 6).

**Figure 6.** Finite element model meshing.

Initial stress conditions: Calculated the distribution of in situ stress according to gravity, as shown in Figure 7.

Boundary condition: The outer four sides of the model are fixed along the *x*-axis and *y*-axis, respectively, and the bottom of the model is fixed along the *z*-axis as the boundary condition.

Multi-step excavation numerical simulation process: the internal loading model that releases the load along the excavation perimeter is used. In the first step, the inversion of original rock stress is revealed according to the boundary conditions and the load conditions (dead weight stress field). In order to get close to the actual results, the second step is to carry out multi-step excavation simulation calculation according to the onsite mining process of Bainiuchang mine.

Constitutive model: Three-dimensional elastic-plastic finite element calculation and analysis of the multi-step excavation was carried out using the Drucker–Prager plastic yielding criterion commonly used in geotechnical engineering [15,16]. This criterion is shown in Equation (6).

$$
\alpha l\_1 + l\_2^{1/2} = k \tag{6}
$$

where: *I*1 = *σ*1 + *σ*2 + *σ*3 is the first invariant of stress; *J*2 = 1 6 [(*σ*1 − *σ*2) 2 + (*σ*2 − *σ*3) 2 + (*σ*3 − *σ*1) 2 ] is the second invariant of stress deflection; α = √2 3 sin *φ* (3±*φ*), *k* = √6 3 *C*·cos *φ* (3±sin *φ*) are experimental constants related to the internal friction angle and cohesion of rock; *φ* is the internal friction angle of rock; *C* is the cohesion of rock; *σ*1, *σ*2, *σ*3 is the maximum, intermediate and minimum principal stress, respectively.

#### *3.2. Simulation Results*

Numerical simulations were performed according to the onsite mining process, and the numerical results of the maximum, intermediate and minimum principal stresses σ1, σ2, σ3 and three axial shear stresses within the stope and pillars can be obtained (Table 2). The main stress distribution cloud images are shown in Figures 8–13.

**Table 2.** Numerical simulation results of the recovery process before optimization.

According to the area bearing theory, when the current stope structural parameters are adopted, the axial compressive stress borne by the ore pillar is 135.5 MPa, which exceeds the uniaxial compressive strength of the ore rock (97.62 MPa). At the same time, the simulation results show that compressive and tensile stresses exist simultaneously during the mining process. Compared with that before mining, all stresses have increased by tens of times. The compressive stresses mainly exist in the junction part of the pillars, stope side walls, roofs and floors, while the tensile stresses mainly exist in stope side walls, roofs and floors. With the expansion of mining areas, the tensile stresses in the stope side walls and the roofs and floors gradually increase, and the compressive stresses in the ore pillars are also gradually concentrated, with the maximum compressive stress of 142.0 MPa in the pillar. This is much greater than the uniaxial compressive strength of the ore (97.62 MPa). The field observation also shows that under the existing stope structural parameters, the plastic yielding phenomenon of the ore pillars become more and more obvious as mining proceeds; after the end of the whole stope mining, all the pillars show yielding and the stope stability is poor. If the deep ore body continue to be mined according to the existing stope structural parameters, the risk of collapse is extremely high and safe and stable recovery cannot be guaranteed.

**Figure 8.** Maximum principal stress distribution in the ore block at 1480 mL before mining (parameters before optimization: stope height 3 m, pillar diameter 3 m, pillar spacing 7 m, pillar row spacing 9 m).

**Figure 9.** Minimum principal stress distribution in the block at 1480 mL before mining (parameters before optimization: stope height 3 m, pillar diameter 3 m, pillar spacing 7 m, pillar row spacing 9 m).

**Figure 10.** Maximum principal stress distribution in the ore block at 1480 mL after mining the strip room (parameters before optimization: stope height 3 m, pillar diameter 3 m, pillar spacing 7 m, pillar row spacing 9 m).

**Figure 11.** Minimum principal stress distribution in the ore block at 1480 mL after mining the strip room (parameters before optimization: stope height 3 m, pillar diameter 3 m, pillar spacing 7 m, pillar row spacing 9 m).

**Figure 12.** Maximum principal stress distribution in the ore block at 1480 mL after mining of strip pillars (parameters before optimization: stope height 3 m, pillar diameter 3 m, pillar spacing 7 m, pillar row spacing 9 m).

**Figure 13.** Minimum principal stress distribution in the ore block at 1480 mL after mining of strip pillars (parameters before optimization: stope height 3 m, pillar diameter 3 m, pillar spacing 7 m, pillar row spacing 9 m).

#### **4. Optimization of Stope Structural Parameters**

The stope height in Bainiuchang Mine is generally between 2.5 and 4.5 m. Therefore, the optimization of stope structural parameters was conducted for the three stope heights of 2.5 m, 3.5 m and 4.5 m. The nine optimization schemes after conducting orthogonal design are shown in Table 3. The finite element calculation continues the method in Section 3.1, and the ore pillar arrangement is shown in Figure 14.

**Table 3.** Nine optimization schemes for orthogonal design.

#### *4.1. Stope Height 2.5 m*

The calculation results of schemes 1–3 are shown in Table 4, and the main stress distribution cloud images are shown in Figures 15–22. The results show that the maximum shear stress in the stope under the three schemes (36.3 MPa, 27.9 MPa, 28.0 MPa) does not exceed the shear strength of the ore rock (50.86 MPa). The tensile stresses mainly appear in the middle of the pillar, stope roof and floor, and the local tensile stresses of 5.83, 4.04 and 4.33 MPa is beyond the uniaxial tensile strength of ore by 2.07 MPa. It tends to result in a local rock fall in the stope roof. Pillars are mainly subjected to compressive stress, especially the junction area between the pillars and the roofs and floors is prone to stress concentration (Figures 17 and 21). In general, the maximum compressive stress values of 143.0, 118.0 and 123.0 MPa in the three schemes are much higher than the uniaxial compressive strength of the ore (97.62 MPa), and the ore pillar will be crushed by the overlying rock layer after the formation of mined-out areas. Hence, these three schemes are not advisable.

**Figure 14.** Nine schemes of room and pillar configurations (**a**) Scheme 1; (**b**) Scheme 2; (**c**) Scheme 3; (**d**) Scheme 4; (**e**) Scheme 5; (**f**) Scheme 6; (**g**) Scheme 7; (**h**) Scheme 8; (**i**) Scheme 9.

**Table 4.** Numerical calculation with stope height of 2.5 m.

**Figure 15.** Maximum principal stress distribution of scheme 1 pillars at 1480 mL (parameters of scheme 1: stope height 2.5 m, pillar diameter 2 m, pillar spacing 4 m, pillar row spacing 6 m).

#### *4.2. Stope Height 3.5 m*

The calculation results of schemes 4–6 are shown in Table 5, and the main stress distribution cloud images are shown in Figures 23–30. The results show that the maximum shear stress in the stope under the three schemes (39.9 MPa, 28.0 MPa, 19.6 MPa) does not exceed the shear strength of the ore rock (50.86 MPa). The tensile stress distribution law as mentioned in Section 4.1, and the local rock body of the roof is prone to fall. From Figures 25 and 29, the compressive stresses are mainly concentrated in the pillars, and the maximum compressive stress values of 155.0 and 123.0 MPa in the pillars of scheme 4 and scheme 5 are already much higher than the uniaxial compressive strength of the ore (97.62 MPa). The maximum compressive stress of 86.8 MPa in scheme 6 is relatively low, and all stress indexes are greater than those of schemes 4 and 5.

**Figure 16.** Maximum principal stress distribution in the middle of the pillar at 1480 mL of scheme 1 (parameters of scheme 1: stope height 2.5 m, pillar diameter 2 m, pillar spacing 4 m, pillar row spacing 6 m).

**Figure 17.** Minimum principal stress distribution of scheme 1 pillars at 1480 mL (parameters of scheme 1: stope height 2.5 m, pillar diameter 2 m, pillar spacing 4 m, pillar row spacing 6 m).

#### *4.3. Stope Height 4.5 m*

The calculation results of schemes 7–9 are shown in Table 6, and the main stress distribution cloud images are shown in Figures 31–38. The results show that the maximum shear stress in the stope under the three schemes (37.8 MPa, 28.3 MPa, 21.0 MPa) does not exceed the shear strength of the ore rock (50.86 MPa). The tensile stress distribution law as mentioned in Section 4.1, and the falling rock mass is prone to cause safety accidents. From Figures 33 and 37, the axes of the ore pillars suffer high compressive stresses, and the maximum compressive stress of 155.0 and 113.0 MPa in the pillars of scheme 7 and scheme 8 are much higher than the uniaxial compressive strength of the ore (97.62 MPa), and the pillars are susceptible to collapse by the pressure of the overlying rock after the formation of mined-out areas. In the perspective of safety, scheme 9 is greater than scheme 7 and 8.

**Figure 18.** Minimum principal stress distribution in the middle of the pillar at 1480 mL of scheme 1 (parameters of scheme 1: stope height 2.5 m, pillar diameter 2 m, pillar spacing 4 m, pillar row spacing 6 m).

**Figure 19.** Maximum principal stress distribution of scheme 2 pillars at 1480 mL (parameters of scheme 2: stope height 2.5 m, pillar diameter 3 m, pillar spacing 6 m, pillar row spacing 8 m).

**Figure 20.** Maximum principal stress distribution in the middle of the pillar at 1480 mL of scheme 2 (parameters of scheme 2: stope height 2.5 m, pillar diameter 3 m, pillar spacing 6 m, pillar row spacing 8 m).

**Figure 21.** Minimum principal stress distribution of scheme 2 pillars at 1480 mL (parameters of scheme 2: stope height 2.5 m, pillar diameter 3 m, pillar spacing 6 m, pillar row spacing 8 m).

**Figure 22.** Minimum principal stress distribution in the middle of the pillar at 1480 mL of scheme 2 (parameters of scheme 2: stope height 2.5 m, pillar diameter 3 m, pillar spacing 6 m, pillar row spacing 8 m).

**Table 5.** Numerical calculation with stope height of 3.5 m.

**Figure 23.** Maximum principal stress distribution of scheme 4 pillars at 1480 mL (parameters of scheme 4: stope height 3.5 m, pillar diameter 2 m, pillar spacing 5 m, pillar row spacing 8 m).

**Figure 24.** Maximum principal stress distribution in the middle of the pillar at 1480 mL of scheme 4 (parameters of scheme 4: stope height 3.5 m, pillar diameter 2 m, pillar spacing 5 m, pillar row spacing 8 m).

**Figure 25.** Minimum principal stress distribution of scheme 4 pillars at 1480 mL (parameters of scheme 4: stope height 3.5 m, pillar diameter 2 m, pillar spacing 5 m, pillar row spacing 8 m).

**Figure 26.** Minimum principal stress distribution in the middle of the pillar at 1480 mL of scheme 4 (parameters of scheme 4: stope height 3.5 m, pillar diameter 2 m, pillar spacing 5 m, pillar row spacing 8 m).

**Figure 27.** Maximum principal stress distribution of scheme 6 pillars at 1480 mL (parameters of scheme 6: stope height 3.5 m, pillar diameter 4 m, pillar spacing 6 m, pillar row spacing 9 m).

**Figure 28.** Maximum principal stress distribution in the middle of the pillar at 1480 mL of scheme 6 (parameters of scheme 6: stope height 3.5 m, pillar diameter 4 m, pillar spacing 6 m, pillar row spacing 9 m).

**Figure 29.** Minimum principal stress distribution of scheme 6 pillars at 1480 mL (parameters of scheme 6: stope height 3.5 m, pillar diameter 4 m, pillar spacing 6 m, pillar row spacing 9 m).

**Figure 30.** Minimum principal stress distribution in the middle of the pillar at 1480 mL of scheme 6 (parameters of scheme 6: stope height 3.5 m, pillar diameter 4 m, pillar spacing 6 m, pillar row spacing 9 m).

**Table 6.** Numerical calculation with stope height of 4.5 m.

**Figure 31.** Maximum principal stress distribution of scheme 7 pillars at 1480 mL (parameters of scheme 7: stope height 4.5 m, pillar diameter 2 m, pillar spacing 6 m, pillar row spacing 7 m).

#### *4.4. Optimization Results*

In summary, the maximum shear stress in the ore pillar under the nine schemes is all lower than the shear strength of the ore rock of 50.86 MPa, and in the actual mining process, the occurrence state of the structural planes in the pillar can be disregarded, so the possibility of complete shear failure of the pillar is low. The maximum compressive stress of 86.8 and 92.5 MPa for schemes 6 and 9 are both lower than the uniaxial compressive strength of the ore (97.62 MPa) (Figure 39), which prevail over other schemes. Although stress values of scheme 6 are all low, scheme 9 has a lower ore loss than scheme 6 due to retained ore pillars, and the ore recovery rate of 84.92% is higher than that of 79.89% in scheme 6 (Figure 40). After comprehensive consideration, the stope structural parameters of scheme 9 are recommended.

**Figure 32.** Maximum principal stress distribution in the middle of the pillar at 1480 mL of scheme 7 (parameters of scheme 7: stope height 4.5 m, pillar diameter 2 m, pillar spacing 6 m, pillar row spacing 7 m).

**Figure 33.** Minimum principal stress distribution of scheme 7 pillars at 1480 mL (parameters of scheme 7: stope height 4.5 m, pillar diameter 2 m, pillar spacing 6 m, pillar row spacing 7 m).

**Figure 34.** Minimum principal stress distribution in the middle of the pillar at 1480 mL of scheme 7 (parameters of scheme 7: stope height 4.5 m, pillar diameter 2 m, pillar spacing 6 m, pillar row spacing 7 m).

**Figure 35.** Maximum principal stress distribution of scheme 9 pillars at 1480 mL (parameters of scheme 9: stope height 4.5 m, pillar diameter 4 m, pillar spacing 7 m, pillar row spacing 8 m).

**Figure 36.** Maximum principal stress distribution in the middle of the pillar at 1480 mL of scheme 9 (parameters of scheme 9: stope height 4.5 m, pillar diameter 4 m, pillar spacing 7 m, pillar row spacing 8 m).

**Figure 37.** Minimum principal stress distribution of scheme 9 pillars at 1480 mL (parameters of scheme 9: stope height 4.5 m, pillar diameter 4 m, pillar spacing 7 m, pillar row spacing 8 m).

**Figure 38.** Minimum principal stress distribution in the middle of the pillar at 1480 mL of scheme 9 (parameters of scheme 9: stope height 4.5 m, pillar diameter 4 m, pillar spacing 7 m, pillar row spacing 8 m).

**Figure 39.** Maximum compressive stress in the ore pillars of schemes 1 to 9 (compared with the uniaxial compressive strength of the ore (97.62 MPa)).

**Figure 40.** Designed ore recovery rate of schemes 1 to 9.

The optimal structural parameters of the room and pillar method are: stope height 4.5 m, ore pillar diameter 4 m, ore pillar spacing 7 m, and ore pillar row spacing 8 m. Based on the area-bearing theory, the axial compressive stress of the pillar under this parameter is 67.75 MPa, which is lower than the uniaxial compressive strength of the ore rock (97.62 MPa). The onsite trial is carried out in S3 stope at 1480 m using the recommended stope structural parameters, where all the stresses of the ore pillars meet the strength requirements of the ore rock, and the pillars ensures safety and stability after the ore room is mined. Additionally, the ore recovery rate of optimized stope reaches 82%, which also realizes the equilibrium of safety and economy.

#### **5. Conclusions**

**Author Contributions:** Writing—original draft preparation and editing, investigation, software, H.-Y.Q.; funding acquisition, writing—review, M.-Q.H.; translation, Y.-J.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Key Research and Development Program of China (Grant No. 2017YFC0602900), The National Natural Science Foundation of China (Grant No. 51804079) and National College Students' innovation and entrepreneurship training program (Grant No.<PHONE_NUMBER>22).

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**7. Experimental results**

We provide solutions for a standard evaluation set without detection and description. Then, we discuss the solutions obtained during when applying the algorithm to apply the real object. All detectors and descriptions are based on comparison with the original application of the authorizer. In standard evaluation, we test our detectors and describe the applied sequence of images and software tests. The test set included images of actual, narrow, and structured scenes. Given the limited page count of this manuscript, we cannot provide the results of all sequences. To compare the performances of the detectors, we selected images with changes in perspective (Graffiti and Wall), magnification and rotation (Boats), and illumination (Leuven). Test notes for all sequences are presented in addition to the base sequence. We applied the degree of repetition, as described in [10], to detect the number of points of interest in two images relative to the indicator of interest (which is only the visible part of both images). The performance of the detection algorithm was compared with that of the Gaussian (DOG) [2], Harris, and Hessian Laplace [12] algorithms. All algorithms provided similar number of points of interest. This finding applies to all images, including the database used in the object recognition experiment (see **Table 1** for an example). In addition,

**Table 1.** Threshold element, numbers of points detected, and computational time (the first image of the graffiti sequence, 900 × 640).

the computational speed of our Quick Hessian detector was more than three times faster than that of DOG and five times quicker than that of Hessian Laplace. At certain timepoints, the repetitions of our detector approximated (Graffiti, Leuven, Boat) or exceeded (Walls) that of the competition. The Graffiti and Walls sequences contained out-of-play gyration, and solutions in affine contortions when the detection compared only gyration and were scaled invariantly. Therefore, distortions must be addressed through the overall durability of features. The descriptors were evaluated by the applied call diagrams (1 precisely) in [3, 9]. In each evaluation, we applied the first and fourth images of the sequence, except for the Graffiti image and the Walls scenario. The corresponding perspective change was 30 and 50 points., we compared our SURF signifier (GLOH0, SIFT, and PCA-SIFT) with our "Quick Hessian" detector. SURF outperformed the other signifiers in almost all tests. In **Figure 4**, we equated the solutions applied to two different corresponding techniques one established on the same threshold element and one founded on the closest neighbor proportion (see [9] for a discussion of this technique). This phenomenon affected the order of descriptors but SURF performance is better in both events because of limited spacing. However, the only solutions on likeness similar to the similarity threshold are shown in **Figure 7** because this technique is most appropriate for representing the runner distribution in its advantage spacing [9] and used more routinely. SURF descriptor is systematically and extensively superior to other descriptors and exhibited 11% improvement. Its computational time is rapid (**Table 2**). The microprocessor (Surf-126) seems to be slightly superior to the general SURF system. However, its matching process was slow. Thus, it may be unsuitable for applications that require speed. Object recognition was performed under a similar set of standards and threshold element (**Table 1**). The moment was evaluated on a standard Unix computer (Pentium IV, 2.5GHZ). The objects are recognized because we experienced new

performance. In addition, SURF has excellent performance that surpasses that of the latest state-of-the-art algorithm. To provide an index of the pairing phase, Laplacian signs (i.e., the Hessian matrix effect) are included for the basic point of interest. Typically, the points of interest are in plug-type structures. The label marks luminous points on the darker background of the reversed situation. This functionality is available at an additional price, which has already been calculated throughout the detecting process. During matching, we compare the feature only if they have the similar contrast types. Thus, this minimum data speeds up matching and

We provide solutions for a standard evaluation set without detection and description. Then, we discuss the solutions obtained during when applying the algorithm to apply the real object. All detectors and descriptions are based on comparison with the original application of the authorizer. In standard evaluation, we test our detectors and describe the applied sequence of images and software tests. The test set included images of actual, narrow, and structured scenes. Given the limited page count of this manuscript, we cannot provide the results of all sequences. To compare the performances of the detectors, we selected images with changes in perspective (Graffiti and Wall), magnification and rotation (Boats), and illumination (Leuven). Test notes for all sequences are presented in addition to the base sequence. We applied the degree of repetition, as described in [10], to detect the number of points of interest in two images relative to the indicator of interest (which is only the visible part of both images). The performance of the detection algorithm was compared with that of the Gaussian (DOG) [2], Harris, and Hessian Laplace [12] algorithms. All algorithms provided similar number of points of interest. This finding applies to all images, including the database used in the object recognition experiment (see **Table 1** for an example). In addition,

improves performance.

**7. Experimental results**

**Figure 9.** Line graphs for different methods.

42 Evolving BCI Therapy - Engaging Brain State Dynamics

The threshold element is adjusted to detect the same number of indicators of interest for all methods. The relatively shorter calculation time also represents the other image.

**Table 2.** Calculation time for common detectors—descriptive applications, testing on the first image of the Graffiti sequence.

functionalities on the practical application, aiming to identify the art object in the museum. The data consisted of 216 images of 22 objects. The test group images comprised 116 images. Under different conditions, including extreme illumination changes, object reflections in glass cabinetry, changes in perspective, magnification, and differences in camera quality, images are small (319 × 240) and difficult to recognize because they lose detail. To identify the objects in the database management, we proceed as follows: The images of the test group are compared with all the images of the reference group by associating their respective indicators of interest. The object represented on the reference image is selected with the greatest amount of correspondence with respect to the test image as a recognized object. Correspondence is performed as follows: A perspective of interest in the test image is compared with a perspective of interest in the referenced image by computing the value of Euclidean space between the vector and its descriptors. A corresponding pair is detected if the vision distance is closer by 0.6 times than that from the closest neighbor to the second. It is the closest strategy that corresponds to the ratio of the neighbors [2, 8, 27]. Extra engineering restrictions reduced the impact of false-positive matching, and this can be performed over any situation. For comparative reasoning, this does not make sense because it may be hiding the lack of the basic tables. On average, the rating reflection of the solutions of our performed appraisal is established. The leaders are SURF-126 with a recognizability rate of 85.7%, followed by U-SURF (84.8%), and SURF (83.7%). The other descriptors were 78.4% for GLOH, 78.2% for SIFT, and 72.3% for

Rotation Invariant on Harris Interest Points for Exposing Image Region Duplication Forgery

http://dx.doi.org/10.5772/intechopen.76332

45

A brain-computer interface (BCI) is a direct interface between the human brain and an artifi-

Many researchers have proposed modern algorithms to solve the problem of image authentication. This study explored and compared the application of different algorithms that detect common types of image forgery. The characteristics of the algorithms are shown in **Table 2**. The algorithms we examined in this study are undoubtedly important for the detection of image counterfeiting. Previous researchers have attempted to improve the reliability of image fraud detection algorithms. They have achieved this objective by (1) reducing algorithm complexity and computational time. This objective was achieved by using small vector dimensions, as shown in Refs. [18, 37–41] increasing the robustness of the algorithms. This aim was achieved by adopting a powerful feature that is consistent for a wide range of image processes, as shown in Refs. [42–48]. The algorithm based on fixed key indicators and fixed instances exhibits remarkable performance, as shown in **Table 2**. However, several barriers and challenges remain. We summarize the defects of available algorithms in **Tables 1** and **2**: (1) the algorithms cannot handle all possible types of image processing that can be applied to forge images; (2) some algorithms rely heavily on several threshold elements or initial value, and the identification of these threshold elements and values require experimentation and improvements; and (3)

PCA-SIFT (**Figures 10** and **11**).

**8. Discussion and conclusions**

cial system. Its purpose is to control the actuation of a device.

**Figure 10.** Example images of the reference group (left) and the test group (right). Note the difference in perspective and colors.

**Figure 11.** Left to right and from top to bottom: Frequency of Walls-Graffiti (perspective change), Leuven (illumination change), and Boats (magnification and rotation).

functionalities on the practical application, aiming to identify the art object in the museum. The data consisted of 216 images of 22 objects. The test group images comprised 116 images.

Under different conditions, including extreme illumination changes, object reflections in glass cabinetry, changes in perspective, magnification, and differences in camera quality, images are small (319 × 240) and difficult to recognize because they lose detail. To identify the objects in the database management, we proceed as follows: The images of the test group are compared with all the images of the reference group by associating their respective indicators of interest. The object represented on the reference image is selected with the greatest amount of correspondence with respect to the test image as a recognized object. Correspondence is performed as follows: A perspective of interest in the test image is compared with a perspective of interest in the referenced image by computing the value of Euclidean space between the vector and its descriptors. A corresponding pair is detected if the vision distance is closer by 0.6 times than that from the closest neighbor to the second. It is the closest strategy that corresponds to the ratio of the neighbors [2, 8, 27]. Extra engineering restrictions reduced the impact of false-positive matching, and this can be performed over any situation. For comparative reasoning, this does not make sense because it may be hiding the lack of the basic tables. On average, the rating reflection of the solutions of our performed appraisal is established. The leaders are SURF-126 with a recognizability rate of 85.7%, followed by U-SURF (84.8%), and SURF (83.7%). The other descriptors were 78.4% for GLOH, 78.2% for SIFT, and 72.3% for PCA-SIFT (**Figures 10** and **11**).