Stability Of Surrounding Rock Research Articles

Plastic zone characteristics and rapid stability evaluation indexes of circular tunnels subjected to non-hydrostatic stress: A novel complex variable solution incorporating 3D rock mass strength

The morphological characteristics and distribution range of the plastic zone around tunnels, influenced by the true three-dimensional high geostress environment in deep engineering, constitute fundamental reference data for both tunnel design and the control of surrounding rock stability. Based on the GZZ three-dimensional rock mass strength criteria and the complex variable method, a novel semi-analytical method for solving the plastic zone of a circular tunnel subjected to non-hydrostatic stress is presented. The conformal mapping is employed to intricately transform the complex boundaries of plastic zones characterized by diverse shapes onto the unit circle boundary within the image plane. This framework proves invaluable for the precise analytical process of the complex plastic zone morphology and the plastic influence range within the surrounding rock under complex stress conditions. In contrast to traditional analytical methods, the efficacy and versatility of our proposed approach are substantiated. Notably, it demonstrates unique advantages, particularly in the context of non-hydrostatic stress fields and varied rock mass parameters, with respect to predicting both surrounding rock stability and plastic zone morphology. Through the analysis of numerous cases, the study reveals the systematic patterns of influence that in-situ stress and surrounding rock characteristic parameters have on the shape and maximum depth of the plastic zone. The results indicate that (1) there are notable disparities in the morphology and extent of the plastic zone between the GZZ and GHB criteria; (2) the transition of the plastic zone in surrounding rock from U-shaped to V-shaped is significantly influenced by the geostress-to-strength ratio Kσ; (3) there is a notable linear correlation observed between the maximum plastic zone thickness rmax and both Kσ and the stress concentration factor KSCF, importantly, this correlation is independent of far-field stress and the brittleness characteristics of the surrounding rock. These findings provide a novel discriminative method for the rapid analysis of surrounding rock stability in deep circular tunnels.

Controlled reconstruction and application research of lateral overlying strata structure in high-gas mines with thick-hard roofs for a fully-mechanized top-caving face

Due to the large mining area, the fully-mechanized top-caving mining with thick-hard roof is easy to form cantilever structure on the lateral roof of the working face, which on the one hand causes high stress level of adjacent roadway and serious deformation of roadway, on the other hand causes gas accumulation in corners, which brings severe challenges to safe and efficient mining of the mine. In this study, a mine facing such problems in Jincheng, China was taken as the research object. Based on the mechanical characteristics of coal and rock, the characteristics of overlying strata activity in the mining process of working face are mastered, and the dual effects of controlled transformation of lateral overlying strata structure on stress field and gas field were revealed. On this basis, roadway reinforcement and gas drainage schemes were put forward and applied. The results showed that the strength of the hard rock stratum was high in the triaxial stress environment, and it was not easily destroyed. However, once the strata exceed their strength threshold, they break down. In addition, the strength of coal is relatively low, and it is continuously deformed when the force exceeds its strength. The overlying strata structure after thick-hard roof fully-mechanized top-caving mining evolves in the following manner: “long cantilever length formed by the main roof being broken in the initial stage, voussoir beam formed by the upper hard roof being broken in the middle stage, and double cantilever beam formed by overlying strata compaction.” The stress carried by upper hard rock stratum is transferred to coal pillars, which is the main reason for the high stress environment of multi-purpose roadway with large coal pillars. The controlled transformation of lateral overlying strata structure by pre-splitting and roof cutting can realize the "transfer-unloading" of coal pillar stress and the "plugging and driving" of corner gas. Based on the hydraulic fracturing reconstruction of lateral overburden structure, the grouting reinforcement scheme of roadway and dynamic gas drainage scheme were put forward. The results demonstrated that after roof cutting, the maximum deformation of the surrounding rock in the multi-purpose roadway was reduced by approximately 90 %, and the maximum concentration of corner gas was decreased by 15.28 %. This approach successfully achieved a collaborative control effect on roadway surrounding rock stability and gas emission well within the safety limits.

Investigation of surrounding rock stability during proximal coal seams mining process and feasibility of ground control technology

The goaf formation of upper seam stope in proximity coal seams mining would influence the stability of the surrounding rock mass due to mining stress redistribution, which will seriously threaten the subsequent mining process and even ground environmental protection. Therefore, developing safe and efficient mining techniques, robust support strategies, and comprehensive safety evaluation systems is crucial for ensuring the overall safety of the mining process. Drawing upon on-site data, this study conducted a detailed feasibility analysis of the mechanized caving method. We developed a simulation model using similar materials, tailored for scenarios with overlying goaf, to demonstrate how lower seam mining was affected by the caving zone of the upper seam, leading to the progressive evolution of fracture networks. Furthermore, we employed numerical simulation models to juxtapose the simulated deformation areas with the actual potential deformation zones in the mining area. The mine seismic prediction (MSP) technique was utilized for the precise identification of unfavorable geological formations ahead of the working face, thereby preempting potential fractures or irregularities due to the presence of overlying goaf. In addition, a comprehensive support strategy was designed and implemented to bolster the stability of the roadways, thereby reinforcing the safety measures within the mining process. This study presents an integrated approach to investigate mining activities in the lower layers during stratified extraction, particularly how the overlying goaf of the upper seam affects the mining of the lower seam, leading to the progressive evolution of fracture networks. The findings and methodologies outlined in this work hold substantial practical significance, offering a pathway to enhance the reliability and safety of the mining process.

Influence of advance direction on surrounding rock stability of main ramp under deep high ground stress

Due to the widespread use of trackless equipment in metal mines, the main ramp has become a major development roadway in large mines. Under deep high ground stress condition, the stability of the surrounding rock of the main ramp is subject to significant variability due to the change in the advance direction, leading to structural failure in different areas of the roadway. Because the support design scheme of surrounding rock of main ramp will not pay attention to the advance direction of roadway, leading to the key support area of the surrounding rock is not clear, resulting failure of the local supporting form occur frequently. Therefore, this paper adopts the combination of on-site investigation and numerical simulation to carry out the stability analysis of the surrounding rock under different advance directions of the roadway. Through on-site investigation, various failure modes of surrounding rock induced by the change of the advance direction of the roadway are summarized, and the key supporting area of surrounding rock of main ramp is determined according to the angle change between the roadway advance direction and the intermediate principal stress. The extent of the risk zone of the roadway surrounding rock is defined based on the Drucker-Prager criterion, which can be used as the new basis for the design of roadway support parameters. The results show that: As the angle between the advance direction and the intermediate principal stress increases, the degree of deformation of the surrounding rock decreases linearly, and the volume of the plastic and risk zones of the surrounding rock decreases nonlinearly. Based on the distribution of the strain energy density of the roadway surrounding rock, when the angle between the advance direction and the intermediate principal stress is small, the roadway surrounding rock is more prone to the floor heave phenomenon. When the angle between the advance direction and the intermediate principal stress is larger, the roadway surrounding rock is prone to the full-section failure phenomenon. Based on the block theory, when the advance direction is changed, the location and production of key blocks have significant variability, leading to the need for reasonable adjustment of the support parameters for the surrounding rock. The research results of this paper are of guiding significance for the optimization of the surrounding rock support scheme of the main ramp.

Optimization of inclined coal seam tunnel section angle and anchor angle based on response surface method

The mining of inclined coal seams is often accompanied by problems such as difficult to control deformation of the tunnel roof and failure of anchor bolts. Taking the transportation channel of Jinping Coal Industry 1071-1 in Shanxi Xiangkuang Mine as the background, FLAC3D numerical simulation software was used, and the method of response surface experimental design and data analysis was used to systematically study the effects of the anchor installation angle and the roof inclination angle of the tunnel section on different inclination angles. Influence of the surrounding rock stability of coal seam roadways. On this basis, a multi-index tunnel support design evaluation method based on the response surface method was proposed, and the actual support plan was optimized and industrial tests were carried out based on the actual on-site support plan. The research results show that: in terms of inclined coal seam support, the degree of influence on the tunnel stability is in the following order: anchor installation angle > tunnel section roof inclination angle > coal seam inclination angle; the optimized support design obtained through the proposed technology The method has good application effect and can improve the stability of the roadway during the mining of the working face. It also proves the effectiveness of this technology and provides new ideas for the design of anchor support of inclined coal seam roadways and the optimization of roadway sections.

Analysis of Surrounding Rock Stability and Supporting Structure Effect Based on a Hydropower Station Underground Cavern

The surrounding rock stability is a main difficult problem in the hydropower station construction and operation. Taking one hydropower station as object, FLAC 3D numerical simulation software was used to calculate the changes in surrounding rock failure zone distribution, surrounding rock strain, and block safety factor before and after supporting. The stability of the surrounding rock after excavation was analyzed and effect of the supporting structure was also evaluated. Finding that: the supporting structure can effectively improve the stability of surrounding rock. After supporting, the failure zone range, the deformation of surrounding rock, and the internal force of the supporting structure all reduced, while the safety factor of the block improved. Due to the effect of bolt, the deformation of the surrounding rock transformed from plastic to elastic, and the rebound zone of the surrounding rock increased, while the plastic and failure zone reduced. The depth of the failure zone on the downstream side is greater than that on the upstream side, and a large number of cracking zones are distributed on the downstream side. At the same time, due to the influence of cracks and geological fracture, the failure of surrounding rock around the main powerhouse is higher than that around the tailgate chamber higher than that in the main transformer chamber. The safety factor of the key blocks distributed around the main transformer chamber and the main power house improved, the sliding form of some blocks transformed from collapse to single-surface sliding.

Prediction of water inflow and analysis of surrounding rock stability in unfavorable geological mountain tunnel

During the construction of a mountain tunnel, water inflow and rock instability are common occurrences due to unfavorable geological conditions, posing serious threats to construction safety. This study focuses on a proposed mountain tunnel and employs multiple formulas to predict potential water inflow during excavation. Based on the amount of water inflow and deformation of surrounding rocks, comprehensive determinations are made for the thickness of grouting rings and permeability coefficients. The results demonstrate that: 1) Different formulas yield slightly varied outcomes but overall trends remain consistent; considering various calculations, the normal water inflow for this tunnel is approximately 115.5908×103 m3/d with a maximum at 210.9100×103 m3/d 2) Increasing grouting ring thickness or decreasing permeability coefficient can effectively reduce water inflow, but the reduction range is gradually narrowed. 3) Pre-grouting curtains have an evident effect in enhancing stability; however, their effectiveness decreases with increased thickness. 4) Taking into account both safety and economic factors, it is recommended that the grouting ring thickness be set at 8 m with a permeability coefficient equaling one 100th that of surrounding rocks for this tunnel project.

Damage evolution and failure characteristics of a cemented gangue backfill considering direct shear and dynamic tests

Backfill mining is an effective technique that can prevent and control the impact of dynamic disasters which can occur in deep underground coal mines. This technique allows to reduce the surface subsidence and achieve a greener mining. The backfill shear mechanical properties under mining disturbances, are of great significance for ensuring the surrounding rock stability in deep mining. Therefore, studying the shear mechanical properties of the cemented gangue backfill body (CGBB) under coupled dynamic and static loads actions in deep coal mining is of great importance. In this paper, shear mechanical tests and the acoustic emission (AE) technology were used to study the shear mechanical response characteristics of CGBB under low-frequency dynamic normal load conditions. The results show that a dynamic normal load with an amplitude of 5 kN improves the shear CGBB strength, while a dynamic load with an amplitude greater than 10 kN will cause a shear strength deterioration, and the degree of deterioration is positively correlated with the load amplitude. Under low-frequency dynamic normal load conditions, the shear CGBB stress-strain curve exhibits classical characteristics. AE indicate that the main CGBB damage changes from a nonlinear deformation to an elastic stage under low-frequency dynamic normal load conditions. During the shear failure process, the cumulative AE counts are positively correlated with the load amplitude. The crack type identification based on RA-AF shows that the low-frequency dynamic normal load affects the CGBB crack type. Under constant normal load (CNL) conditions, tensile or mixed cracks account for 63.95% and are the main fracture mode. Conversely, under low-frequency dynamic normal load conditions, shear cracks account for more than 60% and are the main failure mode. This research provides a reference for the CGBB stability analysis under complex stress conditions for the case of a deep underground coal mining.

Stability analysis and control countermeasures of surrounding rock of gob-side entry formed by roof-cutting in inclined coal seams

The stability of the surrounding rock in the inclined coal seam stope is crucial for the safety of the gob-side entry. In this article, we systematically analyze the surrounding rock stability of the gob-side entry formed by roof-cutting (GEFR) in an inclined coal seam. We identify three forms of roof structure evolution in the formation process of GEFR and analyze the two main modules affecting the deformation of the surrounding rock structure. We determine the critical elements of surrounding rock deformation in different stages of the GEFR retaining process. Further, we propose a classification of the deformation of the surrounding rock structure of GEFR into stress and structural types during stabilization. We analyze the length of the gangue side's bearing area and calculate the lateral gangue's impact energy. We establish three instability modes of the roof based on the fractured state of the roof structure of the GEFR and provide a mechanical criterion of instability. Finally, based on the results of our theoretical analysis, we propose a control principle for the surrounding rock deformation of GEFR and establish countermeasures for controlling the roof-cutting angle and an asymmetric coupling support system. A field case study was conducted under conditions involving an inclined thick coal seam to investigate the surrounding rock deformation and overburden stress evolution using field monitoring data. The field test results confirm that the control measures of the control roof-cutting angle and the asymmetric coupling support system positively impact the stability of the surrounding rock of the roof-cutting entry in an inclined coal seam.

Risk prediction of water inrush in karst tunnels and analysis of surrounding rock stability

Karst tunnel construction has always been an important and difficult point in tunnel engineering. Based on the Yilai Expressway Wantan Tunnel Project, this paper analyzes the water-bearing lithofacies of the surrounding rock of the Wantan Tunnel and the karst hydrogeological conditions of the tunnel site area, and predicts the risk of tunnel water inrush disaster. Through monitoring and measurement, the existing construction technology was analyzed and the following conclusions were drawn: The surrounding rock of the Wantan Tunnel is a typical carbonate phase stratum, with a large amount of water inflow during the rainy season. There are local caves and karst pipes, and the comprehensive water inrush assessment level is III (medium risk); According to the monitoring, the displacement and deformation of each monitoring section in the tunnel changes normally, and the cumulative deformation value is less than 1/3 of the limit value. The stability of the surrounding rock is good, and the construction safety is high.

Strengthening Device for Improving Shear Performance of Anchor Cable in Rock Support.

Many designs of anchor cables are currently in use for rock support in civil and mining operations. Because of the exposed surface and weak shear performance of the cable bolt's free section (CBFS) in end-anchored structures, breaking failure frequently occurs. Numerical simulations and laboratory experiments were performed in this study to develop measures to improve CBFS resistance to shear failure. Analysis of shear characteristics of the CBFS showed that higher axial tension weakens the cable bolt's shear resistance, and that shear damage on the cable surface and uneven distribution of shear stress aggravate CBFS tensile-shear failure. A high-strength steel pipe is proposed to protect the shear cable bolt, and the preliminary design of a CBFS-strengthening device (CFSD) is presented. Numerical simulation revealed that the CFSD effectively improved CBFS shear resistance and provided protection from harmful shear damage. The optimal performance of a Q-type (slotted steel pipe) CFSD was confirmed. The mechanism of improvement of the cable's shear resistance to surrounding rock by employing the CFSD was analyzed. Double-shear tests were carried out on a bare cable bolt and a cable bolt with a Q-CFSD. The results revealed that the CFSD increased the peak shear force on the joint plane, cable peak axial force, and ultimate shear displacement by 31%, 18%, and 11%, respectively. The proposed device is effective in improving the shear performance of end-anchored cable bolts and enhancing surrounding rock stability.

Stress–Structural Failure of a 610 m Crushing Station Left-Side Tunnel Section in Jinchuan II Mine: A Numerical Simulation Study

To address the stress–structural failure phenomenon that can be induced by the excavation of a left-side tunnel section of a 610 m crushing station, an unmanned aerial vehicle was used in this study to collect the geological conditions and rock mass information of the working face, and important geometric information such as the attitude and spacing of rock mass were extracted. Based on the identified attitude and spacing information, a three-dimensional rock mass structure and numerical simulation model of the 610 m crushing station left-side tunnel section were constructed using discrete element numerical simulation software (3DEC) (version 5.0). The results show that the surrounding rock instability of the left-side tunnel section of the 610 m crushing station is controlled by both the stress field in the contact zone between reddish-brown granite stratum and the gray-black-gray gneiss stratum. The cause of stress–structural failure is that the joint sets (JSet #2 and JSet #3) are most likely to form unfavorable blocks with the excavation surface due to unloading triggered by the excavation. Therefore, stress–structural failure disasters in jointed strata sections are one of the key issues for surrounding rock stability during crushing station excavation. It is suggested to adopt ‘optimized excavation parameters + combined support forms’ to systematically control stress–structural failure after unloading due to the excavation from three levels: surface, shallow, and deep. The stress–structural failure mechanism of deep rock mass is generally applicable to a large extent, so the results of this research have reference value for engineering projects facing similar problems around the world.

Retracted: Image Recognition about Stability of Soft Surrounding Rock in Tunnel Based on ILBP Algorithm

Retracted: Image Recognition about Stability of Soft Surrounding Rock in Tunnel Based on ILBP Algorithm

Microstructural and thermal properties of coal measure sandstone subjected to high temperatures

To study the microscopic structure, thermal and mechanical properties of sandstones under the influence of temperature, coal measure sandstones from Southwest China are adopted as the research object to carry out high-temperature tests at 25 °C–1000 °C. The microscopic images of sandstone after thermal treatment are obtained by means of polarizing microscopy and scanning electron microscopy (SEM). Based on thermogravimetric (TG) analysis and differential scanning calorimetric (DSC) analysis, the model function of coal measure sandstone is explored through thermal analysis kinetics (TAK) theory, and the kinetic parameters of thermal decomposition and the thermal decomposition reaction rate of rock are studied. Through the uniaxial compression experiments, the stress‒strain curves and strength characteristics of sandstone under the influence of temperature are obtained. The results show that the temperature has a significant effect on the microstructure, mineral composition and mechanical properties of sandstone. In particular, when the temperature exceeds 400 °C, the thermal fracture phenomenon of rock is obvious, the activity of activated molecules is significantly enhanced, and the kinetic phenomenon of the thermal decomposition reaction of rock appears rapidly. The mechanical properties of rock are weakened under the influence of rock thermal fracture and mineral thermal decomposition. These research results can provide a reference for the analysis of surrounding rock stability and the control of disasters caused by thermal damage in areas such as underground coal gasification (UCG) channels and rock masses subjected to mine fires.

Study on correlation between TBM tailings gradation and granitic gneiss surrounding rock stability

In the process of double-shield TBM excavation, it is difficult to directly observe and test the characteristics of the surrounding rock. In this paper, the screening test of the different type tailings in the wet state was carried out to obtain the gradation curve and curve evaluation index. Combining with the excavation parameters and the surrounding rock characteristics of the tailings, a comprehensive analysis was carried out to establish the evaluation system among with the tailings gradation characteristics, lithology characteristics and excavation parameters. The results showed that: Sparsely fissured rock: the tailings are extensional fractures, the tailings gradation curve is inverse “S” type and gentle, and the evaluation index value: (1.50 > lg(Cu) > 1.35), (1.90 > Cc > 1.10). Broken surrounding rock: the curve is “L” type and steep, the content of coarse particles is much more than that of fine particles and (1.10 > lg(Cu) > 1.00), (2.60 > Cc > 2.40). Fractured rock: the curve is “Step” type, the tailings particles lack the middle particle size, the minerals are mostly weathered, (2.15 > lg(Cu )> 1.95), (0.09 > Cc > 0.07). The research results have good applicability to the surrounding rock stability evaluation of the example tunnel, which verifies the feasibility of the method.

Theoretical analysis of anchorage-seepage coupling effect of the surrounding rock stability in deep buried abandoned chambers

How to ensure the safety of abandoned mine resources, scientifically develop and utilize abandoned mine resources, and promote the transformation of resource-exhausted mining areas have become an important issue in the field of energy and environment in the world today. Aiming at the stability of the surrounding rock in deep closed/abandoned mine chamber, the mechanical model of the surrounding rock under the coupling effect of anchorage and seepage field was proposed. Considering the elastic brittleness degradation and plastic dilatancy effect of rock mass, the analytical solutions of stress and displacement of rockbolt-seepage-surrounding rock coupling system were respectively deduced, and the accuracy of the results were verified. Based on the analytical results, the evolution law of stress and displacement of the surrounding rock under the combined action of seepage field and anchorage effect were further revealed, and a new quantitative design method of rockbolt parameters was proposed. Results show that the influence of rockbolt spacing and rod diameter on the mechanical field is obvious, while the rockbolt length and pre-tension load is small. Dense, short rockbolt with larger diameter should be used in the surrounding rock of deep chamber. The influence of seepage on the displacement of the surrounding rock is very significant. The more serious the seepage is, the more obvious the control effect of rockbolt on the displacement is. Appropriately increasing the density and diameter of rockbolt can effectively reduce the displacement of the surrounding rock.

Surrounding Rocks Deformation Mechanism and Roof Cutting-Grouting Joint Control Technology for Soft and Thick Coal Seam Roadway

High-efficiency maintenance and control of the deep coal roadway surrounding rock stability is a reliable guarantee for the sustainable development of a coal mine. However, it is difficult to control the stability of a roadway in soft and thick coal beds. To maintain the roadway with soft and thick coal beds under strong mining effect, the novel technology of “anchor bolt (cable) support-presplitting-grouting” is proposed. In this technique, the surface of the surrounding rock was supported by high-strength anchor bolts (cables) and metal mesh to prevent the rocks from falling off; pre-splitting roof cutting was adopted to improve the stress state of deep-part surrounding rocks, and the grouting reinforcement technology was used to reduce fractures and improve lithology. To investigate the deformation characteristics of surrounding rocks under this special condition, the equivalent load calculation model of stress distribution in roadway surrounding rocks was established, and the key area of roadway deformation and instability was defined. According to the theoretical model, the UDEC 7.0 software was employed to analyze the impacts of roof cutting depth, angle, and distance of presplitting kerf on the surrounding rock deformation. Based on the data analysis for simulation results with the Response Surface Method (RSM), the influences of single factors and multi-factor horizontal interactions on the stability of surrounding rocks and the internal causes were analyzed, and the optimal cutting parameters were ultimately defined. The in situ application of this technology shows that the fractures on the coal pillar side and the shear failure of surrounding rocks in the bed were effectively controlled, which provides a reference for roadway control under similar conditions.

Experimental and Numerical Study of Water–Rock Coupling Creep under Uniaxial Compression

In order to study the influence of the long-term strength of the rock surrounding deep roadways under the action of groundwater on surrounding rock stability, taking the rock surrounding the deep roadway of the Wanfu Coal Mine as the main research object, uniaxial compression and uniaxial creep tests were carried out on sandstone samples under different water-content states. It was found that the water content had an obvious softening effect on short-term and long-term strength, and both strengths showed a negative exponentially declining relationship. The viscosity modulus (E¯v) was put forward to describe viscoelastic creep deformation. And damage variables corresponding to E (the instantaneous elastic modulus) and E¯v were proposed. A sticky element that can describe the accelerated creep behavior was also established to improve the Nishihara model, based on the experimental results and damage theory. A comparison of the identified parameters and the experimental curves showed that the model can describe the mechanical behavior of various creep stages well. The model was developed using the ABAQUS user subroutine function, and the uniaxial compression creep experiment was simulated. The simulation results were basically consistent with the experimental results, which provide a basis for the further long-term stable use of roadway and creep failure simulation and have important practical and guiding significance.

Crop Cultivation in Abandoned Mines

Expounds the current status of the rising number of abandoned mines, sums up some mainstream of abandoned mine reuse idea, put forward the idea of cultivation of crops in the shaft, through the analysis of roadway surrounding rock stability, residual gas extraction and various key factors needed to make crops grow, and so on, this is a feasible and environmentally friendly concept.

Evaluating construction parameters of HB and CD methods for super large section tunnel: a case study

The double sidewall guide pit and centre cross diagram (CRD) methods are often used for the construction of large-section tunnels through water-rich fault fracture zones due to their long construction time and high construction cost. To shorten the construction period and save costs, the top heading and benching method (HB) and centre diaphragm (CD) can be chosen for construction. The construction parameters of the step and CD methods are optimized to ensure the surrounding rock stability and tunnel safety. By relying on the Tongzi Tunnel, we simulate the excavation of different step heights in the construction of the top heading and benching method (HB) and CD methods through numerical simulation, the laws of tunnel vault settlement, and changes in the surrounding rock stress, initial support axial force, bending moment and safety factor. The study shows that as the height of the upper step increases, the settlement of the vault and the convergence of the periphery increase, the initial support safety factor decreases, and the plastic zone of the surrounding rock increases at 30 m from the target face. The step height for the top heading and benching method (HB) of construction is optimized as follows. The ratios of the upper, middle and lower step heights are 0.45H, 0.35H and 0.2H, respectively. The CD method construction step height is optimized to the left (right) upper and left (right) lower step height ratios of 0.5H and 0.5H, respectively.