Introduction

To enhance personnel safety, the room-and-pillar method has long been used to extract gently dipping and horizontal thin veins. In this method, wide continuous columns and intermittent pillars in circular or square shapes are commonly retained. These pillars bear the load of the overlying strata in the mining area, restrict roof deformation and damage, and thus maintain stope stability. These pillars support the overlying strata load in the mining area, limit roof deformation and damage, and thus maintain stope stability1,2. Residual pillars can enhance stope stability, but their loss, which ranges from1 0% to 30%, in turn reduces the enterprise’s economic benefits3,4. Natural pillars under uniaxial loading tend to brittle failure and even rock burst5,6, so they can’t provide long-term support to the stope roof. If one pillar in a group fails, the roof load it bears shifts to adjacent pillars, increasing their load until they also fail. This triggers a domino effect, leading to widespread roof collapse and threatening the safety of personnel and equipment7,8. Based on pre-stressed expandable prop support technology, Li et al.9 developed a continuous mining method for gently inclined thin veins and named it room and expandable prop mining. It eliminates the requirement for traditional column and point pillars, instead employing pre-stressed expandable props to support the stope roof, thereby boosting the ore recovery rate. Meanwhile, it has the strain-hardening load-bearing characteristic, enabling yielding support for the stope roof10. Although this method has been widely applied, its support parameters are often determined empirically and are overly conservative11,12. Once the stope is excavated, if the stope roof is not supported in time or the support parameters are not properly designed, it may lead to stope instability and collapse. The key issue is that the magnitude of the load on the stope roof requiring support hasn’t been accurately determined. In other words, the required support strength of the stope roof and the load-bearing requirements of pillars are unclear.

The stress on the pillar can be determined by the tributary area theory, and the relationship between the roof characteristic curve and the support characteristic curve. The tributary area theory was first put forward by Salamon and Munro13 and then improved by Essex14. The theory is applicable to pillar group design and assumes the stope is large enough and the pillars bear the entire overlying weight of the stope roof. However, in stronger and stiffer rocks, individual pillars don’t bear the entire overburden weight. Most of the load is transferred to unmined barriers or stope abutments, thus reducing pillar stress15. This is referred to as the pressure arch theory16,17. Compared with the arch pressure theory, pillar dimensions designed using the more conservative tributary area theory are larger to bear a greater load, which reduces potential ore extraction18,19. The pressure arch theory is seldom used for calculating pillar loads as it’s hard to estimate the arch’s magnitude. Dinsdale20 first regarded the arch as part of a circle and suggested anchoring the stope’s two abutments. The NCB (National Coal Board of Britain)21 identified the arch as parabolic. Then it was revised to an elliptical shape22. Both Steart23 and Seldenrath24 proposed the arch takes a parabolic shape. Kenny25 thought the parabolic shape more realistic as he observed roof collapse shapes. Abel18 also proposed the use of a parabolic shape for the pressure arch. Previous researches have mainly focused on the shape of the pressure arch. However, the precise magnitude of the arch is crucial to determining pillar stress. Abel18 introduced the Load Transfer Distance (LTD) concept, which defines the maximum lateral stress transfer distance, to describe the magnitude of the pressure arch. Based on the LTD, Poulsen19 calculated the average stress on pillar groups. While the LTD provides a formula to describe the magnitude of the pressure arch based on 55 coal mine measurements, its results may not be applicable to other mines or hard rock stopes. Moreover, to calculate the magnitude of the pressure arch, it’s essential to determine the stope roof’s response. The main methods for researching the response of stope roof are on-site monitoring26,27,28 and numerical simulation29,30. On-site monitoring typically involves installing monitoring equipment between the support structure and the stope roof27,28. However, this method can only measure the roof response corresponding to specific artificial support. While numerical simulation is flexible, its parameters and conditions are hard to set accurately, and the reliability of its results requires further validation. Overall, current studies on roof response have two main limitations: most focus primarily on coal mines, while others concentrate on the formation and qualitative change process of the pressure arch31,32.

The intersection of their respective characteristic curves can be used to quantify the interaction between supporting elements and the stope roof, thus determining the support strength of the stope roof. The roof characteristic curve depicts the relationship between the stope roof’s vertical displacements and support forces. It’s theoretically possible to calculate the deformations of homogeneous and isotropic rock surrounding a circular excavation under hydrostatic loading, considering different support forces and far-field stresses33,34,35. However, deriving the deformations around a non-circular excavation of heterogeneous and anisotropic rock mass poses challenges. To obtain the roof characteristic curve, the complex variable function method is adopted to calculate deformations of the rock mass at key feature points around excavations. Gao et al.36 derived an analytical solution for deformation in rock surrounding a rectangular excavation, assuming equal vertical and horizontal far-field stresses. Exadaktylos and Stavropoulou37 studied the deformations of rock mass around a semicircular excavation, while Tan et al.38 did so for a horseshoe-shaped excavation. Kang39 derived an analytical solution for the deformations of a rectangular plate with a circular hole, considering linearly varying far-field stresses. Lei et al.40 and Ng and Lei41 presented an analytical solution for the deformation of rock surrounding a rectangular excavation under inclined far-field stress. Kong et al.42 presented an analytical solution for the elastic deformation of the rock mass surrounding a double-tunnel excavation. Currently, theoretical analytical solutions for rock deformation mainly focus on non-circular excavations, variations or inclinations in far-field stresses and multiple excavations. Compared with theoretical analysis, numerical simulation more flexibly and conveniently provides the deformations of the rock mass around excavations under various support forces for the roof characteristic curve. Yavuz et al.43 used the Finite Difference Method (FDM)44 to estimate the roof characteristic curves for circular, arched, and rectangular excavations under hydrostatic pressure. Prusek et al.45 employed the Phase2 method to estimate the roof characteristic curve for longwall mining. Creating multiple identical or similar excavations or stopes with different support forces in labs and fields is almost impossible, so actual roof characteristic curves can’t be obtained through laboratory or field tests. Based on Fenner’s formula33,34,46, which applies to circular excavations in homogeneous and isotropic rock under hydrostatic pressure, the interaction between the surrounding rock mass and common support elements like bolts has been revealed46. If the deformation threshold is determined, a summary table can be consulted to determine the type and support parameters of the support element34. Nevertheless, the support mechanism of the stope roof via support elements in a rectangular stope (part of a cuboid stope) remains unclear. One challenge is the difficulty of determining the actual roof characteristic curve, as previously mentioned. Additionally, installing pressure gauges in natural pillars or artificial props in the field is not easy, so obtaining the support characteristic curve is also challenging.

Unlike Prusek et al. (2016), who applied ground reaction curves to longwall shield support, and Li et al. (2023), who focused solely on determination of the expandable prop capacity, this study integrates damage-based regional division with roof characteristic curve analysis to determine optimal support strength specifically for room and expandable prop mining. A method is proposed to determine the strength of stope roof support for the room and expandable prop mining method. For a gold mine in Dandong, China, the Universal Distinct Element Code (UDEC) numerical simulation method is used, and its parameters are precisely determined to obtain the stope roof characteristic curve. The surrounding rock mass failure index is reintroduced. Based on the failure degree of the stope roof, its characteristic curve is divided. Meanwhile, the support strength of the stope roof is also determined. Based on the determined stope roof support strength, an on-site industrial test is carried out. The expandable props are designed, and their load-bearing performances as well as stope stability are monitored. This process aims to verify the applicability of the method for obtaining the stope roof’s support strength.

Determining method for support strength of stope roof

Engineering background

A gold mine in Dandong, China, with a 20 degree inclination and 4 m thickness, uses the room-and-pillar mining method for orebody extraction. The orebody mainly consists of gold-bearing silicified altered rocks and altered brilliant porphyry. The surrounding rock mass is black mica schist with a distinct laminated structure, making it prone to spalling and collapse. To ensure both local and regional stability, natural pillars are often left to support the stope roof, providing a safe working environment for personnel. Though reserved natural pillars can stabilize the stope, the resulting ore loss will shorten the mine life and cut mining economic benefits. Once the load on natural pillars exceeds their ultimate strength, the pillars will shear and fail, losing their ability to support the stope roof. The load of the stope roof originally borne by the damaged natural pillar is mainly transferred to adjacent natural pillars, which can lead to their further failure. The pillar group may experience a ‘domino effect’ damage, which may eventually cause the stope roof to collapse. Based on the pre-stressed expandable prop support technology9,10,11,12, an improved room-and-pillar mining method (without natural pillars) has been developed and applied in a Dandong gold mine. This method is called room and expandable prop mining. The stope roof is supported by expandable props. As seen in Fig. 1a, the expandable props are in good working condition, enhancing the stability of the stope roof, as shown in Fig. 1b. From the perspective of economic benefits, the ore recovery rate increases by 12% due to the reduction in natural pillars. Overall, expandable props are suitable for mining gently dipping and horizontal thin veins. However, in actual field tests, to guarantee the stope roof’s safety, the support spacing of expandable props is empirically set to 5 m, which is relatively dense and conservative. Because of the rock’s mechanical property anisotropy and structural complexity, it’s difficult to determine suitable support parameters for expandable prop group.

Fig. 1
figure 1

The room and expandable prop mining method, (a) design of the room and expandable prop mining, (b) field application.

Full size image

Determination for the support strength of stope roof

The key to determining the supporting parameters of the expandable prop group is calculating the stope support strength, namely the supporting force needed for the stope roof. This procedure includes three essential steps. Firstly, on the basis of the mechanical parameters, stress states, and dimensions of the rock mass, the stope roof characteristic curve is obtained through numerical simulation and semi-empirical analytical calculation47. Secondly, the surrounding rock damage factor is introduced, and based on the damage distribution of the surrounding rock mass around the stope under different support forces, the roof characteristic curve is divided into different zones. Thirdly, based on the requirement that the support and roof characteristic curves intersect within the potential rupture zone, the necessary support strength for the stope roof is determined. Concurrently, the expandable prop group is designed, and the determination method for the practicality of the stope roof support strength is verified through field-scale industrial trials.

The stope roof characteristic curve

Numerical model

Universal Distinct Element Code (UDEC) is used to obtain the stope roof characteristic curve. The on-site mining area is shown in Fig. 2a. The orebody is long along the strike direction. Only the cross-section of the stope perpendicular to the strike is analyzed. It’s a plane strain problem, as shown in Fig. 2b. The stope length along the dip direction is 24 m, the stope height (orebody thickness) is 4 m, and the stope dip (orebody dip) is 20°. To enhance computational efficiency, the model’s outer part is a continuum and its inner part is discrete, as shown in Fig. 2b. The surrounding rock near the stope is treated as an equivalent discrete rock mass composed of triangular blocks and their contacts. The overall model has dimensions of 120 m in length and 100 m in height. The equivalent discrete rock mass inside has dimensions of 52 m in length and 46 m in height. Based on the size of the equivalent discrete rock mass, the triangular blocks are designed to be 0.5 m in size. As shown in Fig. 2b, the horizontal in-situ stress KH is applied to the lateral boundaries, and the vertical boundaries are subject to the vertical in-situ stress SV. The vertical and horizontal in-situ stresses are calculated using the formulas: SV = 0.027H and KH = λ × SV, where λ is the lateral pressure coefficient, defined as λ = µ/(1 - µ), and µ is the Poisson’s ratio48.

The orebody is buried at a depth (H) of 400 m. The rock mass has a Poisson’s ratio (µ) of 0.23. The vertical stress (SV) and horizontal stress (KH) are 8.7 MPa and 7.4 MPa, respectively.

Fig. 2
figure 2

Numerical model, (a) on-site mining area, (b) design of the numerical model.

Full size image

Simulation parameters

From laboratory tests and field surveys, the mechanical parameters of intact rock and rock mass are calculated using the Hoek-Brown evaluation procedure49,50, as shown in Table 1. The simulated rock mass has an external continuum and an internal discontinuity. The external continuum uses the rock mass’s mechanical parameters directly. In UDEC numerical simulations, the internal discontinuity is modeled using the Trigon method. This method simulates the rock mass as an assembly of blocks and contacts51,52. In the internal equivalent rock mass, each triangular block is considered elastic, with mechanical parameters matching those of the rock. The mechanical interactions between the triangular blocks are governed by Coulomb’s friction law.

Table 1 Mechanical parameters of intact rock and rock mass10.
Full size table

The contact surfaces between blocks can fail either in shear or tension, depending on their strength53. As shown in Fig. 3, the normal contact stress and displacement are linear and controlled by the normal stiffness kn:

$$\Delta \sigma _{n} = - k_{n} \times \Delta \mu _{n}$$
(1)

Where Δσn and Δµn represent the effective normal stress increment and normal displacement increment, respectively. If the normal stress exceeds the tensile strength, then σn is set to 0.

In the tangential direction, the mechanical response of the triangular block is governed by the constant shear stiffness (ks). The shear stress (τ) is determined by the contact characteristics, cohesion (c), and friction angle (φ).

$$|\tau _{s} | \le c + \sigma _{n} \times \tan \varphi = \tau _{{\max }}$$
(2)

Then

$$\Delta \tau _{s} = - k_{s} \times \Delta \mu _{n}^{e}$$
(3)

or else, if | τs | ≥ τmax, then

$$\tau _{s} = {\text{ }}sign(\Delta \mu _{n}^{e} ) \times \tau _{{\max }}$$
(4)

Where Δ\(\mu _{n}^{e}\) is the elastic portion of the incremental shear displacement, Δµs is the total incremental shear displacement, and τmax represents the shear strength.

Fig. 3
figure 3

Failure mechanism of block contact.

Full size image

To determine the contact mechanical parameters between rock blocks in the discrete medium, an inversion calculation method is adopted. Equivalent rock mass specimens are established, and a series of uniaxial compression and tensile tests are carried out to determine the uniaxial compressive strength, elastic modulus, tensile strength and other mechanical parameters of the equivalent rock mass specimens, and the contact mechanical parameters of the equivalent rock mass are calculated by matching on-site rock mass parameters. However, the equivalent rock mass specimen exhibits significant size effect, i.e., its mechanical parameters change with the model size54,55. Hence, prior to contact parameter calibration, it’s essential to perform a sensitivity analysis of the equivalent rock mass size to identify the characteristic unit size. This determines the characteristic unit size and eliminates the model size’s impact on contact mechanical parameter calibration results. As shown in Fig. 4, the triangular block size is set to 0.5 m. The equivalent rock mass specimens have a width-to-height ratio of 1:2. Models sized 1 m × 2 m, 2 m × 4 m, 3 m × 6 m, 4 m × 8 m, 5 m × 10 m, 6 m × 12 m, and 7 m × 14 m are established. The mechanical parameters of the blocks are derived from those of the rock. However, the contact mechanical parameters between blocks are adjusted within a specific range. Uniaxial compression tests are carried out, with the model’s bottom boundary fixed and its top boundary under a velocity-controlled loading condition at 0.001 m/s56. As shown in Fig. 4, the stress-strain curves of equivalent rock masses with different sizes are obtained. When the equivalent rock mass specimen reaches a size of 6 m × 12 m, its mechanical properties are less affected by further size increases. Thus, a size of 6 m × 12 m is chosen as the characteristic unit size.

Once the characteristic unit size is determined, the contact mechanical parameters between the blocks are calibrated. Considering the normal stiffness kn, the shear-to-normal stiffness ratio ks/kn, cohesion cj, internal friction angle φj and tensile strength, 49 orthogonal experiments with 6 factors and 7 levels are designed, as shown in Table 2. Mechanical parameters of the block are based on those of the rock. For each project, separate uniaxial compression and tension experiments are conducted to obtain key mechanical parameters of the rock mass, including uniaxial compressive strength (σc), elastic modulus (E), Poisson’s ratio (u), and tensile strength (σt). Additionally, a sensitivity analysis is performed to examine how variations in contact mechanical parameters affect the rock mass’s mechanical properties.

Fig. 4
figure 4

Sensitivity analysis of the equivalent rock mass size, (a) stress-strain curves of equivalent rock masses with different sizes, (b) variation law of mechanical properties of multi-scale sample models.

Full size image
Table 2 Orthogonal tests of contact parameter calibration in numerical model.
Full size table

Uniaxial compression and tensile tests on rock mass specimens are conducted. A correlation coefficient matrix between the contact parameters and rock mass parameters is plotted, as shown in Fig. 5. Additionally, the correlation between contact parameters and rock mass parameters is analyzed through uniaxial compression/tension tests on rock mass specimens. The uniaxial compressive strength (σc) of the rock mass is closely related to the block contact’s cohesion (cj) and internal friction angle (φj). The elastic modulus E of the rock mass largely depends on the contact normal stiffness kn and the shear-to-normal stiffness ratio ks/kn of the block contact. The rock mass’s Poisson’s ratio (µ) is mainly determined by the block contact’s shear-to-normal stiffness ratio (ks/kn). The rock mass’s Poisson’s ratio (µ) is primarily determined by the block contact’s shear-to-normal stiffness ratio (ks/kn). The rock mass’s tensile strength (σt) is linked to the block contact’s tensile strength (σtj).

Fig. 5
figure 5

Correlation coefficient matrix of joint parameters and rock mass parameters.

Full size image

Based on a multi-nonlinear regression model57,58,59, the rock mass’s mechanical parameters and the block’s contact mechanical parameters are fitted, as shown in Fig. 6. The mechanical parameters of the rock mass and the contact mechanical parameters of the block exhibit nonlinear relationships. The uniaxial compressive strength (σc), internal friction angle (φj), and cohesion (cj) are interrelated, while the elastic modulus (E) correlates with the normal stiffness (kn) and the shear-to-normal stiffness ratio (ks/kn). Additionally, Poisson’s ratio (µ) correlates with the normal stiffness (kn) and the shear-to-normal stiffness ratio (ks/kn). The tensile strength (σt) of the rock mass and the contact tensile strength (σtj) of the block contact exhibit an approximately linear relationship. Moreover, the rock mass parameters predicted by the machine learning model57,58,59 are in close agreement with UDEC calibration values. The machine learning model accurately describes the relationship between microscopic contact parameters and macroscopic rock mass parameters. By matching the mechanical parameters of prototype rock masses, the mechanical parameters of block contacts in the UDEC model can be determined, as shown in Table 3. The errors between the calibrated rock mass properties and the target parameters are within 2%, which validates the accuracy of the microscopic contact mechanical parameters, as shown in Table 4.

Fig. 6
figure 6

Fitting results of rock mass mechanical parameters and block contact parameters, (a) uniaxial compressive strength (σc), internal friction angle (φj) and cohesion (cj), (b) elastic modulus (E), normal stiffness (kn) and shear-to-normal stiffness ratio (ks/kn), (c) Poisson’s ratio (µ), normal stiffness (kn) and stiffness ratio (ks/kn), (d) tensile strength (σt) and contact tensile strength (σtj).

Full size image
Table 3 Mechanical parameters of block and contact in numerical model.
Full size table
Table 4 Calibrated rock mass properties in the trigon model.
Full size table

Monitoring design

The stope roof characteristic curve is obtained through the surrounding rock mass stress-relief method. After the stope is excavated, a support force (P₀) equivalent to the vertical stress of the surrounding rock mass is applied to the stope roof and floor. Then, the support force (Pi) is gradually reduced by applying a stress release coefficient (β), where Pi = βP₀ and β ≤ 1. The displacement response of the stope roof is monitored under varying support forces. The roof displacement is monitored at the roof’s center, as shown in Fig. 3.

The stope roof characteristic curve

The roof characteristic curve of a stope with an aspect ratio of 6:1 is obtained by numerical simulation by connecting the deformation points of the stope roof under different support forces. Meanwhile, the roof characteristic curve is also derived by the semi-empirical method47, as shown in Fig. 7. The semi-empirical analytical solution of the roof characteristic curve closely matches the UDEC numerical simulation results. During the plastic deformation phase of the surrounding rock mass, the stope roof deformation exceeds the predictions of elastic analytical solutions. The transition point from elastic to plastic deformation on the roof characteristic curve is associated with a support force of 5.2 MPa.

Fig. 7
figure 7

The roof characteristics curve for the stope with an aspect ratio of 6:1.

Full size image

Support strength for the stope roof

Regional division of the stope roof characteristic curve

The stope roof characteristic curve illustrates the roof deformation under varying support forces but doesn’t specify the optimal support force required for the stope roof. In this study, the damage degree of surrounding rock mass in the stope roof under different support forces Pi is analyzed. Then, the roof characteristic curve is divided into different damage zones. Finally, the support strength of the stope roof is determined based on the load-bearing performance of the expandable prop. To quantitatively assess the damage to the surrounding rock mass after stope mining, the Fish language in UDEC is used to calculate the lengths of shear and tensile cracks in the rock mass. A damage index (D) is proposed to analyze the damage degree of the surrounding rock mass caused by shear and tensile stresses due to mining activities. D can be calculated as:

$$D~ = ~\frac{{L_{s} ~ + ~L_{t} }}{{L_{c} }}~ \times ~100\%$$
(5)

Where Ls is the total length of the shear cracks, Lt is the total length of the tensile cracks, and Lc is the total contact length between the blocks in the model.

Under different β values, the damage index (D) of the surrounding rock mass around the stope is calculated, and the damage distribution cloud map is presented in Fig. 8. During the numerical simulation, the stope’s side walls lack support. Thus, when β is 1.0, failure occurs in the surrounding rock mass. When β > 0.5, the surrounding rock mass in stope roof shows no damage. However, stress concentration on the stope sides creates damage zones. At this stage, the stope roof and floor rock masses remain in the elastic deformation stage, in line with prior studies52,60. When the damage index D exceeds 45%, the surrounding rock mass experiences through-cracking failure, as shown in Fig. 8. When the stress release coefficient β is between 0.05 and 0.5, as the support force of the stope roof and floor decreases, the damage in the upper right corner of the stope roof gradually increases and spreads to the entire roof. In this stage, the roof and floor rock mass enters the plastic deformation stage, and the overall stope roof damage degree remains relatively low. As the stress release coefficient β continues to decrease, the damage and propagation depth of the surrounding rock mass gradually increase. During this stage, the damage does not fully penetrate the roof but remains localized, allowing the rock mass to maintain stability. This stage is defined as the fracture zone. When β ≤ 0.02, areas with significant damage in the stope roof may experience breakthroughs, leading to instability failures in the surrounding rock mass due to the breakthrough of damaged zones.

Fig. 8
figure 8

Damage distribution of surrounding rock mass around the stope under different stress release coefficients.

Full size image

Based on how surrounding rock mass damage distributes under different stress release coefficients, the stope roof characteristic curve is divided into four sections: elastic, plastic, fracture and potential damage zones, as shown in Fig. 9. By varying β, the corresponding points on the roof characteristic curve can be identified based on the support force from the stress-strain curve. The region with a stress release coefficient of 0.5 < β < 1.0 is identified as the elastic zone. The region with 0.05 < β < 0.5 is the plastic zone. The region with 0.02 < β < 0.05 is defined as the fracture zone. The region with 0 < β ≤ 0.02 corresponds to the potential damage zone.

Fig. 9
figure 9

Determination for the support strength of stope roof.

Full size image

Support strength for the stope roof

Based on the load-bearing performance and supporting strength of the pre-stressed expandable prop10,11, the optimal stope roof support strength should make the expandable prop’s support characteristic curve intersect the stope roof characteristic curve within its fracture zone. Yielding support of the expandable prop for the stope roof is achieved61,62. The deformation and failure of the stope roof can be effectively controlled with proper release of roof stress, and the expandable prop bears the smaller load of the stope roof. The support characteristic curves for expandable props with varying pre-stresses and support forces are plotted and presented in Fig. 9. The stope roof support strength for the gold mine in Dandong, China, is determined to be 0.35 MPa.

Field test

The expandable prop, though vertical, forms a 20° angle with the mining face roof due to the orebody’s 20° dip. The vertical support force of the expandable prop can be calculated as: P = 0.35 MPa / cos20° = 0.37 MPa. The stope has a dip length of 24 m. The support force (F) needed to maintain stope roof stability is calculated by:

$$F = P \times S = {\text{ }}0.37{\text{ }}MPa{\text{ }} \times {\text{ }}10^{6} \times {\text{ }}24{\text{ }}m{\text{ }} \times {\text{ }}1{\text{ }}m = {\text{ }}8880{\text{ }}kN$$
(6)
Fig. 10
figure 10

On-site industrial test.

Full size image

The 1 m diameter expandable prop, as tested in the laboratory10, has a load capacity of 2,800 kN. The quantity of expandable props needed in the stope is calculated as 8880 kN divided by 2,800 kN, which equals 3.17. Rounding up to three, this is the final quantity of expandable props required to support the stope. The on-site room and expandable prop mining method is implemented. In the three-dimensional scenario of the stope, nine expandable props are installed, as shown in Fig. 10a. The load-bearing performance of the three central cross-section expandable props is monitored. The monitoring process aligns with earlier studies9,11. As shown in Fig. 10b, once the expandable props are built, the initial pre-stress of 1,120 kN is rapidly generated. During mining, the load on expandable props continues to increase. Once the stope is fully mined, the expandable props maintain a stable bearing load. At this point, the central prop equipped with pressure gauge A bears the maximum load of 1,625 kN. The loads on the expandable props near the walls are relatively smaller. The left-and right-wall props bear 1,510 kN and 1,205 kN with pressure gauges B and C respectively. After the stope is mined, visually, except for minor cracks in the stope roof, the roof and expandable props appear to remain stable. Although the actual bearing loads on the expansion props are less than their maximum bearing strength, i.e., the design value. This indicates that the stope roof support strength calculation method used in this study is also on the conservative side, probably because the load of the stope roof may have been partially transferred to the two walls of the stope. Therefore, the calculation method for the stope roof support strength is more practical and safer.

Conclusions

Based on the room and expandable prop mining method, a determination method for stope roof support strength is proposed for a case of the gold mine in Dandong, China, leading to the following conclusions:

  1. (1)

    The three-step process for determining the strength of stope roof support is as follows: obtain the stope roof characteristic curve, divide it into regions based on damage levels, and determine the support strength of the stope roof.

  2. (2)

    The semi-empirical analytical solution of the roof characteristic curve closely matches the UDEC numerical simulation results. In the plastic deformation stage of the surrounding rock mass, the deformation of the stope roof exceeds the predictions of elastic analytical solutions. The transition point from elastic to plastic deformation on the roof characteristic curve is associated with a support force of 5.2 MPa.

  3. (3)

    A damage index (D) is introduced, and the characteristic curve of stope roof is divided into regions based on the failure degree of stope roof. The region with a stress release coefficient of 0.5 < β < 1.0 is identified as the elastic zone. The region with 0.05 < β < 0.5 is the plastic zone. The region with 0.02 < β < 0.05 is defined as the fracture zone. The region with 0 < β ≤ 0.02 corresponds to the potential damage zone. Meanwhile, the stope roof support strength for the gold mine in Dandong, China, is determined to be 0.35 MPa.

  4. (4)

    The on-site room and expandable prop mining method is implemented. The final quantity of expandable props required to support the stope is nine. After the stope is mined, visually, minor cracks in the stope roof are the only noticeable issue, while the roof and expandable props remain largely stable. Furthermore, the calculation method for the stope roof support strength proves to be both practical and safe in application. Meanwhile, it is recommended that the support spacing of on-site expandable props be 6 m to facilitate subsequent wider application.

It should be noted that this study focused on static loading conditions and did not examine the effects of dynamic loading on expandable prop performance. Additionally, the variability of rock mass properties and its influence on determination of the support strength were not explicitly investigated.