Study on isolation pillar thickness optimization and slope stability control in hanging wall ore mining

Abstract

Aiming at the problems of easy disturbance to the overlying slope and difficulty in scientifically determining the thickness of the isolation pillar during the recovery of hanging-wall orebody under open-pit to underground mining conditions, this study takes Shizhuyuan Mine as the engineering background. FLAC3D numerical simulation and the strength reduction method (SRM) are adopted to conduct a comparative analysis of the stability response characteristics of the “slope-goaf-backfill” system under five working conditions with isolation pillar thicknesses ranging from 10 m to 50 m. The results show that although the safety factors of all working conditions meet the requirements for Grade I slope stability, the thickness of the isolation pillar exhibits a significant threshold effect on system deformation control: when the thickness increases to 30 m, the maximum system displacement is significantly reduced from the excessive level (> 80 mm) to approximately 34 mm, and the overall stability is obviously improved. However, the stability gain brought by further increasing the thickness gradually weakens. Under the recommended thickness, the stress distribution, displacement evolution, and plastic zone development of the goaf and backfill are all within the safe and controllable range. Considering both stability requirements and resource recovery rate, an isolation pillar thickness around 30 m can achieve a reasonable balance between safety and economy, which can provide a quantitative design reference for the safe recovery of hanging-wall orebodies under similar open-pit-underground coordinated mining conditions.

Introduction

With the continuous advancement of open-pit mines to deep levels, the gradual depletion of shallow resources, the rapid increase in stripping ratio, and the continuous rise in slope maintenance costs¹, have made the coordinated mining from open-pit to underground an important direction to improve resource utilization efficiency and ensure the sustainable production of mines. During this transition process, the hanging-wall orebodies occurring below the final open-pit slope have become key successive resources.

However, hanging-wall orebodies are usually located below the final open-pit slope and within the stress influence range of high and steep slopes. Their underground mining activities will inevitably disturb the original mechanical balance of the slope-goaf system. If the control measures are improper, the mining disturbance may extend upward along the pillars and surrounding rocks, leading to progressive slope deformation, local damage, or even overall instability risks. Existing studies have shown that slope stability under hanging-wall orebody mining conditions is significantly sensitive to underground mining methods, mining sequences, and support structures^2–5.

Focusing on the influence mechanism of hanging-wall orebody mining on slope stability, existing studies have systematically explored the mechanical response characteristics of the stope-slope system during mining and filling through numerical simulation and engineering case analysis^6–8. Therefore, during the transition stage from open-pit to underground mining, how to realize the safe and efficient recovery of hanging-wall orebodies under the premise of ensuring the long-term stability of the open-pit slope has become one of the key engineering problems faced by such mines.

Regarding the research on isolation pillars, the core lies in reasonably determining their reserved thickness to improve resource recovery rate while ensuring structural safety. An excessively thick isolation pillar will result in resource waste, while an insufficient reserved thickness may lead to instability risks. Therefore, in engineering practice, methods such as the limit span theory, empirical formula method, and limit equilibrium method are often used to determine the reasonable thickness⁹. On this basis, some studies have quantitatively analyzed the stability and safe thickness of isolation pillars through numerical simulation, comprehensive index evaluation, and mechanical criteria combined with specific engineering conditions^10–13.

In recent years, with the complexity of backfill mining technology and deep mining conditions, the research on isolation pillars has gradually developed towards multi-working conditions and refinement, such as the analysis of pillar stability under different filling conditions and stress environments^14–17. In general, existing studies have provided useful references for the design of isolation pillar thickness, but most focus on underground stopes or single working conditions, and few systematically study them within the overall framework of the coordinated action of open-pit slope and underground mining disturbance. Their applicability under open-pit to underground conditions still needs further exploration.

Focusing on slope stability evaluation and mining disturbance mechanism, scholars at home and abroad have carried out a lot of research. As a traditional analysis method, the limit equilibrium method calculates the safety factor by satisfying the force and moment balance conditions, and has formed mature calculation systems such as the simplified Bishop method, simplified Janbu method, Morgenstern-Price method, and Spencer method^18–20. However, such methods usually need to preset potential sliding surfaces, which are difficult to reflect the nonlinear mechanical behavior of rock mass materials and the progressive evolution process of slope failure, and have certain limitations under complex geological conditions and significant mining disturbance scenarios.

With the development of computational mechanics and numerical analysis technology, numerical methods such as the finite element method, finite difference method, and discrete element method have gradually become important means for slope stability research, which can simulate the goaf formation, surrounding rock deformation, and stress redistribution processes within the framework of continuous media or discrete structures.

Existing studies have combined numerical methods with SRM and widely applied them to slope stability evaluation in open-pit mines and complex geological conditions^21–23. SRM was first introduced into slope stability analysis by Zienkiewicz et al., and later scholars such as Matsui and San, Zheng et al., Cheng et al., and Yu systematically expanded and verified the method under different constitutive models, calculation dimensions, and engineering conditions.

A large number of studies have shown that SRM does not need to preset sliding surfaces, can quantitatively solve the overall safety factor under heterogeneous rock masses, multi-stage disturbances, and complex boundary conditions, and has developed into one of the widely used slope overall stability evaluation methods in two-dimensional (2D) and three-dimensional (3D) numerical analysis^24–27.

In recent years, with the development of computing power and numerical modeling technology, 3D slope stability analysis methods have gradually attracted attention. Relevant studies have pointed out that under engineering conditions with significant topographic undulations, complex spatial distribution of structures, or asymmetric loads, 3D analysis can more truly reflect the mechanical response characteristics of slopes by comparing 2D and 3D analysis results^28–30.

However, due to the limitations of computational cost and modeling complexity, a large number of current studies are still carried out based on 2D assumptions, and directly applying 2D methods to 3D slope problems may lead to deviations in stability evaluation results. In addition, some so-called 3D analysis methods still rely on 2D analysis ideas in essence, and their ability to characterize real spatial effects is limited.

For open-pit mine engineering, existing studies have analyzed the impact of underground mining disturbance on open-pit slope response from 2D or 3D perspectives^31–34, but most focus on a single link or local effect. In general, for the engineering scenario of hanging-wall orebody mining under open-pit slopes, which has significant 3D structural characteristics and strong mining disturbance effects, the law of stability evolution still lacks systematic and in-depth research.

Although relevant studies have made certain progress in slope stability analysis, isolation pillar design, and numerical simulation methods, most of them focus on underground mining or adopt 2D simplified methods, and fail to conduct an integrated 3D coupling analysis of open-pit slope and underground mining disturbance. There are still several urgent problems to be solved for the specific engineering scenario of hanging-wall orebody mining under open-pit slopes:

(1) Most existing studies analyze open-pit slope stability and underground mining disturbance separately, lacking an integrated 3D coupling research framework of slope-goaf;

(2) The design of isolation pillar thickness still mainly relies on empirical methods or single working condition analysis, lacking quantitative optimization basis based on multi-working condition and multi-index comparison, making it difficult to balance safety and resource recovery rate;

(3) Insufficient attention is paid to the dynamic evolution characteristics of the bearing system during sequential mining and filling, especially the instability risk during the stage when the load-bearing is transferred from the original rock pillar to the backfill, which lacks systematic research;

(4) There is a lack of a coordinated trade-off mechanism between safety and resource recovery rate, and no thickness optimization criteria that can directly guide engineering design have been formed.

To address the above problems, this study takes Shizhuyuan open-pit mine as the engineering background, constructs a 3D numerical model under real geological conditions, and combines the “two-step sublevel open-stope subsequent filling” process to systematically analyze the mechanical response characteristics of the slope-goaf system under different isolation pillar thickness conditions.

The main work and innovations of the study are reflected in the following aspects:

(1) Establish a 3D slope-goaf coupling analysis framework for open-pit to underground conditions, and systematically characterize the coordinated evolution characteristics of slopes and underground mining processes;

(2) Construct a dynamic simulation system covering the entire mining-filling process, and identify the key stability control links during the load-bearing transition stage;

(3) Propose a comprehensive evaluation idea of isolation pillar thickness based on multi-index response, providing a quantitative basis for the coordinated optimization of safety and resource recovery rate.

This study clarifies the essential differences from existing research by constructing a 3D slope-goaf coupling model and multi-index quantitative evaluation method. Relevant research can provide engineering references for slope stability control and safe recovery of hanging-wall orebodies during the open-pit-underground coordinated mining stage.

Mine overview and research methods

Mine overview

This study takes the tungsten polymetallic open-pit stope of Hunan Shizhuyuan Nonferrous Metals Co., Ltd. as the engineering background. The mining area is located in Suxian District, Chenzhou City, Hunan Province, with a typical mountainous landform and relatively simple regional strata and structures. The orebody is mainly hosted in skarn, a typical contact metasomatic rock formed by the interaction between magmatic rocks and carbonate rocks. The hanging wall and footwall surrounding rocks of the orebody are marble and granite, respectively.

The data and conclusions of the on-site mine investigation are obtained from field survey and in-situ investigation of the study mine. Field investigations show that the rock mass has good overall integrity, dense structure, and thin weathered layer, belonging to hard rock mass with high stability, which has certain natural advantages for slope stability. The final area of the open-pit mine is about 616,200 m².

With the mining extending to the final boundary, a high and steep artificial slope with a height of hundreds of meters and a slope angle of 45°-65° will be formed. Its stability is not only related to the safety of mining operations in the pit but also has an important impact on regional public safety and traffic operation because it is adjacent to the Gangan River and the main transportation roads of the mining area below. Therefore, the stability control of the overlying slope is one of the core requirements for the safe production of the mine.

Below the determined open-pit mining boundary, exploration has revealed a considerable scale of hanging-wall orebodies. This part of the resources has important economic value, but due to factors such as mining right red lines, stripping ratio, ecological constraints, and green mine construction, it cannot be recovered by expanding the open-pit boundary, and must rely on underground mining methods to achieve safe and efficient utilization.

Figure 1 shows the spatial relationship between the open-pit mine, the final slope, and the underlying hanging-wall orebody, intuitively presenting the “open-pit-underground” interaction characteristics concerned by the study.

Fig. 1.

Schematic diagram of the hanging-wall orebody (drawn with 3DMine Mining Engineering Software, Version:3DMine 2014.12, URL: https://www.3dmine-cn.com/). (a) Open-pit mine; (b) final slope; (c) underlying hanging-wall orebody.

To ensure the stability of the overlying slope during the recovery of the hanging-wall orebody, the study adopts the “two-step sublevel open-stope subsequent filling method” as the mining process, and its technological process is shown in Fig. 2.

Fig. 2.

Schematic diagram of the two-step sublevel open-stope subsequent filling method.

This method is one of the important technical approaches for the safe mining of deep orebodies under complex conditions. Its core lies in timely replacing the goaf area with artificial backfill to achieve effective support of the surrounding rock structure and regulation of stress redistribution, thereby significantly weakening the disturbance impact of mining activities on the overlying rock and slope. This provides a feasible and safe technical path for the recovery of underground resources in sensitive areas.

Research methods and objects

To systematically carry out the research on the optimization of isolation pillar thickness during the recovery of hanging-wall orebodies under open-pit to underground conditions, the study is carried out in accordance with the technical route of “engineering background-model construction-numerical simulation-stability evaluation-engineering conclusions”, and its overall research ideas and analysis process are shown in Fig. 3.

Fig. 3.

Overall research ideas and analysis flow chart (Model Construction Drawn with 3DMine Mining Engineering Software, Version:3DMine 2014.12, URL: https://www.3dmine-cn.com/; Numerical Simulation Drawn with FLAC3D, Version: FLAC3D 6.00, URL: https://itascasoftware.com/products/flac3d/).

Under this framework, first, the research objects and engineering conditions are clarified, and a 3D engineering geological model including open-pit slopes, goafs, and backfills is constructed; then, through the numerical simulation of the entire process of sequential mining and subsequent filling, key response indicators such as stress, displacement, plastic zone, and safety factor are extracted; on the basis of multi-working condition comparative analysis, the impact of different isolation pillar thicknesses on system stability is comprehensively evaluated, and the reasonable isolation pillar thickness is determined accordingly. The specific research methods and objects are explained below.

(1) Model Construction and Mesh Generation.

The study adopts CAD-Rhino-FLAC3D three-dimensional coupling modeling technology. First, the slope geological section is drawn in CAD based on geological exploration data to clarify the rock stratum interface and orebody boundary; then, the geometric model is imported into the Rhinoceros platform for solid modeling, and the Griddle plug-in is used to divide hexahedral meshes to generate calculation units with regular shape and uniform quality.

The final model dimensions are: length 800 m in the X direction; height 500 m in the Z direction; thickness 20 m in the Y direction (along the slope strike). The Y-direction thickness is set to 20 m to weaken the influence of lateral boundaries on the core analysis area, make the model meet the plane strain assumption, and improve the solution efficiency while ensuring the calculation accuracy.

(2) Selection of Research Objects

According to the engineering characteristics and geological structure of the slope of Shizhuyuan open-pit mine, the slope is generally divided into two categories: artificial slopes (Zones A-D) and natural slopes (Zones E-F), including 15 slope units R1-R11 and Z1-Z4. The slope zoning and monitoring point layout are shown in Fig. 4.

Fig. 4.

Schematic diagram of open-pit slope zoning and displacement monitoring point layout (Drawn with 3DMine Mining Engineering Software, Version:3DMine 2014.12, URL: https://www.3dmine-cn.com/). (a) Open-pit slope zoning; (b) displacement monitoring point layout.

For targeted stability evaluation, one most representative slope is selected from each zone. The selection principle is to comprehensively compare the slope height, hazard level, engineering safety level, and monitoring displacement, and prioritize those with relatively weak stability and more sensitive response to disturbance.

The classification criteria for safety and hazard levels are determined according to GB 16,423-2020 Safety Code for Metal and Nonmetal Mines³⁵ and GB 51,016-2014 Technical Code for Non-coal Open Pit Slope Engineering³⁶, combined with slope stability and rock mass characteristics. The classification of each slope is shown in Table 1.

Table 1.

Slope classification table.

Slope zone	Slope number	Slope height (m)		Height grade	Hazard level	Slope engineering safety class
Artificial slope	R1	328	High slope		II	I
	R2	290	Medium slope		III	III
	R3	448	High slope		II	I
	R4	410	High slope		II	I
	R5	407	High slope		II	I
	R6	231	Medium slope		III	III
	R7	168	Medium slope		III	III
	R8	240	Medium slope		III	III
	R9	231	Medium slope		III	III
	R10	171	Medium slope		III	III
	R11	228	Medium slope		III	III
Natural slope	Z1	220	Medium slope		II	II
	Z2	187	Medium slope		II	II
	Z3	120	Medium slope		III	III
	Z4	271	Medium slope		II	II

The displacement of each representative slope at the monitoring points is shown in Table 2.

Table 2.

Displacements of representative slopes in each zone at various monitoring points.

Slope number	Displacement at each monitoring point (10−2m)					Maximum value (10−2m)
	P1	P2	P3	P4	P5
R1	5.8	4.2	3.4	2.6	1.5	5.8
R3	12.6	10.6	8.6	4.0	2.6	12.6
R4	8.2	7.2	4.4	2.4	1.4	8.2
R8	0.8	0.7	0.4	0.6	0.5	0.8
Z1	0.8	0.4	0.5	0.7	0.8	0.8
Z4	0.6	0.5	0.3	0.2	0.1	0.6

It can be seen from the table that the displacement values of the R3 slope in Zone B at each monitoring point are significantly higher than those of other slopes, with a maximum displacement of 12.6 × 10⁻²m, showing obvious deformation characteristics. Based on its more sensitive response to mining disturbance, the study selects R3 as the key research object for the subsequent analysis of the influence of isolation pillar thickness to improve the typicality and identification ability of the result analysis.

(3) Rationality Check of Stress and Deformation of the Overall Model.

To comprehensively evaluate the rationality of the model configuration and boundary conditions, Fig. 5 shows the minimum principal stress, maximum principal stress, Z-direction displacement, and plastic zone distribution of the model under static load conditions.

Fig. 5.

Cloud diagrams of stress, displacement, and plastic zone distribution of the overall model (Drawn with FLAC3D, Version: FLAC3D 6.00, URL: https://itascasoftware.com/products/flac3d/). (a) Minimum principal stress cloud diagram of the overall model; (b) Maximum principal stress cloud diagram of the overall model; (c) Z-direction displacement cloud diagram of the overall model; (d) Plastic zone result of the overall model.

It can be seen from Fig. 5 that the principal stress field distribution is continuous, with no abnormal mutations or stress concentration areas, indicating that the model structure division and boundary constraint settings are reasonable; the displacement field changes gently with a small overall magnitude, indicating that the slope is dominated by elastic deformation under static load conditions; the plastic zone only appears locally and sporadically, and no through failure zone is formed, indicating that the rock mass has good overall integrity and no early evolution of instability mechanisms has occurred.

The above check results show that the model constructed in the study can reliably reflect the real mechanical response of the slope-goaf system, laying a solid foundation for the subsequent stability research under different isolation pillar thickness working conditions.

(4) Constitutive Model and Principle of SRM.

The Mohr-Coulomb elastoplastic constitutive model is adopted for the orebody, marble, granite, and backfill in the model. This model describes the shear strength through cohesion c and internal friction angle φ, and the tensile failure limit through tensile strength σₜ, which can effectively simulate the yield behavior of geotechnical materials under complex stress paths. Its parameters are shown in Table 3. The mechanical parameters listed in Table 3 are all obtained from field tests and in-situ measurements, which have been verified to ensure their representativeness and reliability in practical engineering.

Table 3.

Mechanical parameters of rock mass and backfill.

Rock type	Elastic modulus (GPa)	Tensile strength (MPa)	Poisson’s ratio	Density (kg m−3)	Cohesion (MPa)	Internal friction angle (°)
Orebody/skarn	45.42	9.76	0.22	3143	8.25	44.77
Surrounding rock/marble	28.68	3.56	0.27	2581	3.07	40.15
Surrounding rock/granite	37.67	7.04	0.24	2770	6.73	43.63
Backfill	0.23	0.41	0.25	1922	1.01	46.22

To quantitatively evaluate the slope stability, the study adopts SRM. SRM gradually reduces the shear strength parameters (cohesion and internal friction angle) of rock and soil mass until the slope reaches critical failure. The corresponding strength reduction factor is the safety factor. This method is widely adopted because it can intuitively reflect the overall stability and failure mode of the slope without prior assumption of the sliding surface. Its basic principle is to uniformly reduce the cohesion c and internal friction angle φ of the rock mass while keeping the external load and geometry unchanged:

When the calculation reaches non-convergence or obvious failure signs appear, the reduction factor F_s is the slope safety factor under the current working condition.

The model factor-of-safety function built in FLAC3D can automatically search for potential failure surfaces and determine the minimum safety factor, avoiding the subjectivity caused by artificially assuming sliding surfaces, and making the calculation results more objective and reliable.

Simulation scheme design

To ensure the effectiveness and practicality of the study, considering the complexity and variability of open-pit mining technology, the following simplified assumptions are formulated during the modeling process:

(1) The rock mass is assumed to be an ideal elastoplastic body, and its strength and volume remain unchanged once the yield point is reached.

(2) The orebody and surrounding rock are regarded as locally homogeneous and isotropic materials.

(3) Considering the limitations of the finite element program, it is assumed that the site is not affected by tectonic activities, the in-situ stress is of the geostatic field type, the contact between various rock strata is conformable, and the interior of the rock strata is regarded as a continuous medium.

(4) The model does not consider the influence of groundwater activities, nor the influence of structural planes, fractures, and weak layers that may exist in the rock strata and orebody on stability.

(5) In the calculation, the selected load remains unchanged, does not change with the direction of the element, and always maintains the initial direction. The surface load is equal to the weight of the overlying rock stratum or backfill layer.

These simplified assumptions help optimize the efficiency of analysis and calculation, ensure that the study can be carried out efficiently under relatively simplified conditions, and at the same time ensure the reliability and applicability of the results.

Based on the above assumptions, the study designs five comparative schemes for isolation pillar thickness, namely 10 m, 20 m, 30 m, 40 m, and 50 m. The only variable is the thickness of the isolation pillar near the open-pit slope, and its geometric layout is shown in Fig. 6. The selected thickness range covers the common pillar sizes in engineering practice, which helps to reveal the influence of different thickness changes on the mechanical response and identify possible threshold effects.

Fig. 6.

Boundary pillar and stope division. (a) Slope section containing hanging-wall orebody; (b) Mining scheme planning diagram.

Among these five schemes, the 30 m thickness is considered to have high engineering feasibility. Therefore, after completing the overall stability comparison, a special analysis is further carried out on the mechanical evolution of the goaf and backfill system under this scheme to ensure that the recommended thickness has sufficient safety reserves under sequential mining and filling conditions.

All schemes adopt the same sequential mining method, and combined with the evolution curve of the safety factor, representative key mining stages are selected for key research on stress, displacement, and plastic zone, so as to comprehensively evaluate the impact of isolation pillar thickness on the overall process stability.

Results and analysis

Slope stability analysis

To quantitatively reveal the control law of isolation pillar thickness on the stability of open-pit slopes, the study conducts numerical simulations of the entire dynamic mining process of hanging-wall orebodies based on five thickness schemes: 10 m, 20 m, 30 m, 40 m, and 50 m. The slope safety factors and monitoring point displacements of each scheme under different mining steps are summarized in Table 4.

Table 4.

Summary of simulation results.

Mining Step	Scheme 1 (10 m)		Scheme 2 (20 m)		Scheme 3 (30 m)		Scheme 4 (40 m)		Scheme 5 (50 m)
	Safety factor	Monitoring point displacement (m)	Safety factor	Monitoring point displacement (m)	Safety factor	Monitoring point displacement (m)	Safety factor	Monitoring point displacement (m)	Safety factor	Monitoring point displacement (m)
1	5.27	0.0120	5.70	0.0120	5.58	0.0113	5.55	0.0119	5.83	0.0118
2	4.44	0.0124	4.92	0.0124	5.16	0.0141	5.20	0.0101	5.53	0.0121
3	5.08	0.0131	5.42	0.0126	5.20	0.0125	5.17	0.0126	5.40	0.0127
4	3.77	0.0184	4.28	0.0139	4.56	0.0172	4.81	0.0084	4.90	0.0069
5	5.58	0.0285	5.69	0.0284	5.69	0.0161	5.66	0.0165	5.78	0.0149
6	5.02	0.0335	5.23	0.0288	5.20	0.0184	5.40	0.0152	5.44	0.0140
7	5.66	0.0552	5.83	0.0658	5.81	0.0290	5.86	0.0240	5.89	0.0218
8	5.44	0.0583	5.67	0.0820	5.72	0.0302	5.81	0.0292	5.86	0.0220
9	5.33	0.0852	5.73	0.0811	5.77	0.0344	5.83	0.0288	–	–
10	5.36	0.0750	–	–	–	–	–	–	–	–
Average	5.10	0.0392	5.39	0.0374	5.41	0.0204	5.48	0.0174	5.58	0.0145

Based on the data in the table, this section systematically analyzes the influence law of isolation pillar thickness from two core indicators: safety factor and displacement response, and demonstrates the theoretical basis for the optimal thickness accordingly.

Safety factor analysis based on SRM

The safety factor is a key indicator for evaluating the overall anti-sliding capacity of the slope, and its change with the mining process can reflect the disturbance and recovery process caused by underground mining and filling. The evolution law of the safety factor under different isolation pillar thickness schemes is shown in Fig. 7, and the typical characteristic values are shown in Table 4.

Fig. 7.

Evolution curves of slope safety factors under different isolation pillar thickness schemes.

The simulation results show that with the isolation pillar set, the minimum safety factors of all schemes are in the range of 3.77–4.90, which are significantly higher than the design standard of 1.20–1.25 for Grade I slopes specified in the “Technical Code for Slope Engineering of Non-Coal Open-Pit Mines” (GB51016-2014)³⁶. This indicates that the five thickness schemes all have sufficient safety reserves in terms of strength, and the overall anti-sliding stability meets the long-term service requirements.

It should be noted that all schemes have a common “safety factor trough” in Step 4. It can be found that the valley value of the safety factor appears at Step 4 in all schemes, which is a universal phenomenon. This stage corresponds to the complete formation of the first set of permanent pillars composed of low-strength backfill, which begins to replace the original rock pillars to bear the main supporting role. This characteristic is closely related to backfill stiffness, backfill strength, interface contact conditions, and filling timing.

Since the elastic modulus of the backfill is only about 0.23GPa, much lower than that of the surrounding rock (greater than 28GPa), the sudden drop in stiffness leads to obvious adjustment of the bearing system, stress redistribution to the surrounding rock mass, and a temporary weakening of the slope anti-sliding potential.

The low stiffness of backfill leads to temporary stress redistribution at the early stage of filling, resulting in a short-term drop in the safety factor. As the bearing structure stabilizes, the safety factor gradually recovers, which explains why this valley stage exists in all schemes.

Although the safety factor is still much higher than the lower limit of the specification at this time, from the perspective of the entire process, this stage is the most sensitive risk inflection point, and it is advisable to strengthen monitoring and early warning in engineering practice.

The isolation pillar thickness has an obvious interval characteristic for the improvement of system stability. In the range of 10–30 m, the minimum safety factor increases from 3.77 to 4.56, with an increase of about 21%, indicating that the pillar stiffness and bearing capacity increase significantly with the thickness at this stage, which is the main controlling factor for improving slope stability. When the thickness is further increased to 40 m and 50 m, the minimum safety factor only increases to 4.81 and 4.90, with an overall increase of less than 7.5%, showing a typical characteristic of diminishing marginal benefits.

From the mechanical mechanism, the thickening of the isolation pillar changes the stress flow path of the overlying rock mass of the goaf.

When the thickness is insufficient (≤ 20 m), the pillar is difficult to form a stable stress arch structure, and the goaf disturbance can penetrate the pillar and spread to the overlying slope, resulting in high sensitivity of the system stability.

when the thickness increases to 30 m, the cross-sectional stiffness of the pillar approaches the critical level, the stress arch structure is effectively developed, and the stress forms a relatively stable bypass channel between the pillar and the surrounding rock, which significantly weakens the mechanical coupling between the goaf and the slope; after further thickening to 40 m and 50 m, the stress arch structure is basically stable, and the further improvement of the bearing path is limited, so the gain of the safety factor slows down.

In summary, based on the comprehensive judgment of the evolution law of the safety factor and the reconstruction mechanism of the bearing system, 30 m can be regarded as the “safety efficiency critical point” of the isolation pillar thickness.

Deformation control analysis of surface displacement

The surface displacement of the slope is an important indicator reflecting the controllability of system deformation, and its evolution mode and final residual value are closely related to the long-term stability of the slope. The evolution law of the maximum displacement of the monitoring points under different isolation pillar thickness schemes is shown in Fig. 8, and its key indicators and engineering discrimination results are shown in Table 5.

Fig. 8.

Evolution curves of maximum displacements of slope monitoring points under different schemes.

Table 5.

Slope displacement response and engineering compliance evaluation table of each scheme.

Scheme number	Isolation pillar thickness (m)	Maximum displacement (mm)	Final displacement (mm)	Compliance with engineering control standards
1	10	85.2	75.0	No
2	20	82.0	81.1	No
3	30	34.4	34.4	Yes
4	40	29.2	28.8	Yes
5	50	22.0	22.0	Yes

The results show that the isolation pillar thickness has a significant threshold effect on displacement control. The maximum displacements of the 10 m and 20 m schemes reach 85.2 mm and 82.0 mm respectively, and the final residual displacements are still 75.0 mm and 81.1 mm. Moreover, the displacement curves have not converged at the end of mining, indicating that the system is difficult to establish a new stable balance, and there are risks of cumulative deformation and delayed failure.

When the thickness increases to 30 m, the maximum displacement drops sharply to 34.4 mm, a decrease of about 58% compared with the 20 m scheme, and the displacement achieves stable convergence in the later stage of mining, indicating that the system enters a stable state. When the thickness is further increased to 40 m and 50 m, the maximum displacements decrease to 29.2 mm and 22.0 mm respectively. Although there is a further improvement, the gain is limited compared with the 30 m scheme.

From the perspective of the displacement evolution mode, the 10 m and 20 m schemes show a “continuous growth type”, and the system cannot form a stable balance during the disturbance process; while the schemes with thickness of 30 m and above show a “rapid growth-platform convergence type”, indicating that the pillar and surrounding rock can effectively coordinate deformation, enabling the system to reach a new balance state in a timely manner in the middle and later stages of mining.

The displacement evolution curves in Fig. 8 show obvious differences among different schemes. For the 10 m and 20 m isolation pillar schemes, the displacement continues to increase without convergence, mainly because the pillar thickness is too small to form an effective stress-bearing structure. The low stiffness and weak disturbance resistance lead to continuous stress adjustment and large-scale deformation development.

In contrast, the displacement curves of schemes with a thickness of 30 m and above gradually tend to be stable and convergent. This is attributed to the reasonable stiffness matching between the isolation pillar and surrounding rock, which can effectively restrain the propagation of mining disturbance and form a stable stress path. With the increase of pillar thickness, the overall bearing system is gradually improved, and the deformation tends to converge under the action of self-stability and stress redistribution.

The above differences are closely related to stress paths, stiffness matching, and disturbance propagation mechanisms.

The above threshold characteristics can be attributed to the “stiffness matching mechanism” between the isolation pillar and the surrounding rock. When the pillar thickness is insufficient, its overall stiffness is low, and its ability to constrain the subsidence and lateral expansion of the goaf is limited. Mining disturbance cannot be effectively attenuated and is easily transmitted upward to the slope along the pillar, leading to continuous stress adjustment and persistent displacement amplification.

when the thickness reaches about 30 m, the pillar stiffness and surrounding rock strength achieve relative matching, forming a stable stress transmission path, and the disturbance is mainly dissipated and attenuated in the near field of the goaf, thereby significantly weakening the impact on the slope, making the displacement process controlled and finally converged; further thickening is still helpful to reduce displacement, but the improvement range has been significantly reduced, showing a “performance saturation” characteristic.

The comprehensive comparative analysis results of safety factor and displacement response show that: although the 10 m and 20 m isolation pillar thickness schemes meet the specification requirements in terms of safety factor, the deformation development of the slope and goaf is relatively significant, the overall deformation control ability is insufficient, and the stability safety reserve is limited, so they should be eliminated; the 40 m and 50 m thickness schemes are better in terms of stability and deformation control, but they lead to higher ore loss rate and lower resource recovery, obviously increasing resource waste and mining economy loss. Compared with the 30 m scheme, the stability improvement shows an obvious characteristic of diminishing marginal benefits.

Therefore, the determination of isolation pillar thickness can be regarded as a dual-objective trade-off between safety and resource economy. Under the engineering conditions of this study, the 30 m scheme not only satisfies stability and deformation control requirements, but also maintains higher resource recovery rate and lower ore loss rate, achieving the optimal balance between safety, deformation control and resource utilization efficiency. Thus, 30 m is recommended as the comprehensive optimal thickness of the isolation pillar.

Stability evaluation of underlying goaf and backfill

On the basis of determining the optimal isolation pillar thickness as 30 m in Sect.  3.1, to further reveal the mechanical response characteristics of the open-pit slope-goaf-backfill system during the dynamic mining process, four representative stages (Steps 1, 4, 6, and 9) are selected for analysis.

Step 1 corresponds to the initial stress state; Step 4 corresponds to the sensitive period when the bearing system is transformed from the original rock pillar to the backfill pillar; Step 6 is the stage of large-scale mining with the strongest disturbance; Step 9 is the final stable stage after the completion of mining and filling. The analysis is carried out from three aspects: stress field, displacement field, and plastic zone to reveal the evolution process of the system bearing mechanism and the overall stability.

Stress field distribution and strength check

The maximum and minimum principal stress cloud diagrams of Scheme 3 at each key stage are shown in Figs. 9 and 10 respectively.

Fig. 9.

Maximum principal stress cloud diagrams of Scheme 3 (Drawn with FLAC3D, Version: FLAC3D 6.00, URL: https://itascasoftware.com/products/flac3d/). (a) Step 1; (b) Step 4; (c) Step 6; (d) Step 9.

Fig. 10.

Minimum principal stress cloud diagrams of Scheme 3(Drawn with FLAC3D, Version: FLAC3D 6.00, URL: https://itascasoftware.com/products/flac3d/). (a) Step 1; (b) Step 4; (c) Step 6; (d) Step 9.

From the distribution of the maximum principal stress (tensile stress), the mining disturbance mainly acts on the middle part of the goaf roof and the local backfill pillar area, which is consistent with the tensile characteristics of the cantilever roof and the engineering understanding of local stress concentration in the backfill. The maximum tensile stress in the four stages appears in Step 9, which is about 2.37 MPa, significantly lower than the tensile strengths of skarn (9.76 MPa), granite (7.04 MPa), and marble (3.56 MPa).

Although this value is greater than the tensile strength of the backfill (0.41 MPa), the peak tensile stress is located inside the surrounding rock, and the tensile stress borne by the backfill itself is generally less than 0.5 MPa, which does not reach its tensile strength limit, so the system has no risk of tensile failure.

The minimum principal stress (compressive stress) is stable during the entire mining process, and its peak value always appears in the deep intact surrounding rock, with a maximum value of 15.86 MPa, much lower than the compressive strengths of granite (102.59 MPa) and marble (72.45 MPa); the compressive stress level in the backfill pillar is 0.5-2.0 MPa, which is also less than its compressive strength (2.48 MPa), indicating no risk of crushing failure.

The evolution process of the stress field reflects the gradual transition of the bearing system from “original rock pillar main bearing” to “backfill-surrounding rock cooperative bearing” and then to “stable bearing structure”. At Step 4, due to the low stiffness of the backfill, local stress accumulates temporarily; as the backfill fully participates in bearing at Step 6, the stress gradually transfers to it and tends to be uniform; by Step 9, the stress field is overall stable, and the bearing system has formed a new stable structure.

In summary, the stress analysis shows that the system always meets the material strength conditions during the entire mining cycle, and there is no risk of strength failure.

Displacement field evolution analysis

The displacement cloud diagrams of Scheme 3 at each stage are shown in Fig. 11.

Fig. 11.

Displacement cloud diagrams of Scheme 3 (Drawn with FLAC3D, Version: FLAC3D 6.00, URL: https://itascasoftware.com/products/flac3d/). (a) Step 1; (b) Step 4; (c) Step 6; (d) Step 9.

The displacement evolution has obvious phased characteristics. At Step 1, the displacement is mainly concentrated on the top and bottom plates of the newly formed goaf, with a maximum displacement of about 1.18 cm, which is the local deformation caused by initial disturbance. At Steps 4 and 6, as the backfill pillar gradually undertakes the main bearing function and new goafs are formed, the high displacement area shifts from the roof area to the backfill pillar and its adjacent surrounding rock. The maximum displacement at Step 6 reaches 11.13 cm, which is the peak value during the entire mining process, reflecting the compressive deformation of the backfill under load and its traction effect on the surrounding rock.

At Step 9, the maximum system displacement decreases to 5.05 cm, and the distribution of displacement contour lines is more gentle, indicating that after the completion of all mining and filling, the overall deformation gradually converges, and the mechanical system reaches a new balance state.

Mechanically, the displacement evolution reflects the combined effect of the “bearing conversion effect” and the “disturbance absorption mechanism”: on the one hand, the original rock pillars are gradually mined out and replaced by backfill, making the backfill bear greater deformation in a short time; on the other hand, as the backfill and surrounding rock form a stable support system, the mining disturbance is gradually absorbed and attenuated locally, and the system transitions from the deformation amplification stage to the stable convergence stage. The overall process conforms to the typical evolution mode of “local disturbance-bearing transfer-deformation peak-stable recovery” in complex mine mining.

Plastic zone development and penetrability evaluation

The plastic zone distribution of Scheme 3 is shown in Fig. 12.

Fig. 12.

Plastic zone simulation results of Scheme 3 (drawn with FLAC3D, Version: FLAC3D 6.00, URL: https://itascasoftware.com/products/flac3d/). (a) Step 1; (b) Step 4; (c) Step 6; (d) Step 9.

The plastic zone mainly appears in the shallow part of the goaf roof, the end of the backfill pillar, and the local surrounding rock corner, distributed in patchy or thin-layered forms. Quantitative statistics show that the plastic zone volume is relatively small and the maximum penetration length is limited throughout the mining process.

At Steps 4 and 6, with the backfill starting to bear the main stress and the formation of new goafs, the scope of the plastic zone expands, but the increased plastic zone volume and penetration length still do not lead to through failure, and it is always limited to local areas. During the entire mining process, there is no through plastic zone from the roof through the pillar to the floor, indicating that the potential sliding surface cannot be formed, and the system does not undergo macroscopic instability.

By Step 9, the scope of the plastic zone shrinks significantly, with the plastic zone volume further reduced and the maximum penetration length basically unchanged, and only a small range of plastic zones remains at the contact interface between the backfill and the surrounding rock, indicating that after the completion of all mining and filling, the plastic evolution of the system has tended to be stable, and the structural integrity has been maintained.

Mechanically, on the one hand, the 30 m-thick isolation pillar has sufficient stiffness, which can form a stable stress arch structure together with the surrounding rock, so that the disturbance is effectively dispersed in the near field; on the other hand, the backfill plays a more “buffering-energy dissipation” role in the later stage, which is conducive to inhibiting the further expansion of the plastic zone.

The comprehensive analysis results of the evolution characteristics of the stress field, displacement field, and plastic zone show that under the working condition of the isolation pillar thickness of 30 m, the “slope-goaf-backfill” system maintains good overall stability during the entire mining process.

The bearing system has undergone a reasonable evolution process from “original rock main bearing” to “backfill-surrounding rock cooperative bearing” and then to “stable arch structure control”. The stress distribution is continuous, the plastic zone does not have through failure, and the system deformation development is controlled. The above analysis results verify the rationality of the system stability under the condition of the 30 m isolation pillar thickness from the perspective of mechanical response and failure mechanism, and provide mechanism-level support for the aforementioned thickness optimization conclusion.

Discussion

Focusing on the optimization of isolation pillar thickness under open-pit-underground coordinated mining conditions, the results of multi-scheme numerical simulation show that the influence of isolation pillar thickness on the stability of the “slope-goaf-backfill” system has significant nonlinear characteristics. Its action mechanism is not simply linearly enhanced with the increase of thickness, but controls the mechanical response mode of the system by changing the bearing path, stress transfer mode, and overall stiffness matching relationship of the system.

When the thickness of the isolation pillar is small, the mining disturbance is difficult to be effectively attenuated in the near field of the goaf, and the disturbance is easily transmitted to the overlying slope along the pillar. The overall stiffness of the system is insufficient, and the slope deformation is highly sensitive to the mining process; with the increase of the isolation pillar thickness, its isolation effect and bearing capacity gradually increase, the stress arch structure is formed and stably developed, and the system stability and deformation control ability are significantly improved.

However, when the pillar thickness continues to increase, the stability improvement range decreases significantly, showing a typical characteristic of diminishing marginal benefits, indicating that simply increasing the pillar thickness to improve the safety reserve is not the optimal strategy.

From the perspective of the entire process, the dynamic conversion of the bearing system during sequential mining and filling is a key link affecting system stability. The numerical results show that during the transition from the original rock pillar to the backfill-surrounding rock cooperative bearing, stress redistribution and local deformation may increase temporarily, but under the condition of reasonable isolation pillar thickness, this adjustment process has good recoverability, and the system can re-establish a stable mechanical balance state after the backfill fully participates in bearing.

This indicates that the backfill pillar formation stage is a sensitive node in the evolution of system stability. In engineering practice, emphasis should be placed on the control of filling quality and the monitoring of deformation response at this stage to avoid the cumulative amplification of adverse disturbances.

Compared with existing studies, most current researches on the stability and thickness design of isolation pillars mainly focus on underground stopes, and the analysis methods are mostly limited to empirical formulas, limit equilibrium theory or 2D numerical models^37–40, which rarely consider the 3D coupling effect of open-pit slope and underground mining disturbance. The research focus is usually on the stability of the pillar itself or local surrounding rock, lacking systematic consideration of the overall slope-goaf-backfill system.

For the recovery of hanging-wall orebodies under open-pit to underground conditions, although existing studies have explored the impact of underground mining on open-pit slope stability from a 2D or local 3D perspective, most of the work still separates slope stability analysis from pillar thickness design, lacking systematic research on the overall “slope-goaf-backfill” system within a unified 3D spatial framework, especially insufficient attention to the bearing path reconstruction and system stiffness matching mechanism during sequential mining.

To address the above deficiencies, under the specific engineering scenario of open-pit to underground mining, this study constructs a 3D numerical model based on real geological conditions, incorporates the isolation pillar into the overall bearing system of the “open-pit slope-goaf-backfill”, and reveals the threshold characteristics and mechanical mechanism of the influence of isolation pillar thickness on system stability through multi-thickness working condition comparison and full-process dynamic simulation.

The research results show that under the premise of meeting the overall stability requirements, there is a reasonable range of isolation pillar thickness that balances safety, deformation control, and resource recovery rate, providing a quantifiable engineering basis for the optimization of isolation pillar thickness during the open-pit-underground coordinated mining stage of hanging-wall orebodies.

It should be noted that the research conclusions are still subject to certain simplifying assumptions. The numerical model ignores groundwater, tectonic stress, structural planes, joints, and weak interlayers, which may cause deviations between simulation results and actual engineering stability. Additionally, dynamic disturbance, rock mass time-dependent behavior are not considered, and parameters are mainly from static tests.

To reduce these deviations, future research can gradually relax the above assumptions: conduct seepage-stress multi-field coupling analysis, introduce discrete fracture networks to characterize joints and weak layers, and combine on-site monitoring with dynamic simulation to optimize pillar thickness and improve stability evaluation accuracy.

Conclusions

Based on the open-pit-underground coordinated mining conditions of Shizhuyuan open-pit mine, this study uses FLAC3D numerical simulation to build a 3D mechanical model including open-pit slopes, underlying goafs, and backfills. It analyzes the overall system stability during hanging-wall orebody recovery. The results show continuous slope stress distribution, principal stress within rock mass strength, and no through plastic failure zone, verifying the model’s engineering applicability.

Taking isolation pillar thickness as the core factor, comparative analysis of different working conditions reveals: thin pillars lead to obvious mining disturbance transmission and large slope deformation. With increased thickness, system stiffness and isolation effect improve, stabilizing the slope. The 30 m scheme performs reasonably in stability and deformation control, with limited gains from further thickening.

Analysis of the 30 m thickness condition shows controllable stress, displacement, and plastic zone evolution of goafs and backfills during sequential mining and filling. No strength failure or plastic zone penetration occurs, and the bearing system smoothly transitions to backfill-surrounding rock cooperative bearing. The 30 m thickness balances stability, safety, and resource recovery, providing a reference for similar projects.

Author contributions

Shuai Li: Conceptualization, methodology, numerical simulation, data analysis, and drafting of the original manuscript. Liuyu Wang: Model construction, mesh generation, and validation of simulation results. Zhenyu Dan: Supervision, project administration, funding acquisition, and critical revision of the manuscript for important intellectual content. Tubing Yin: Analysis of stress-displacement evolution characteristics and visualization of results. Lifeng Yu: Literature review, collation of geological data, and supplementary validation of mechanical parameters. Zeming Zhao: Participation in simulation scheme design and discussion of key findings.

Funding

Major National Science and Technology Project for Deep Earth of China (Grant No. 2024ZD1003808). Science and Technology Innovation Program of Hunan Province (Grant No. 2023RC3035).

Data availability

Data will be made available on request.

Declarations

Competing interests

The authors declare no competing interests.