Optimizing Counterweight Backfilling for Slope Stability in Weak Strata: An Integrated Approach Combining High-Resolution Monitoring and Numerical Modeling

Abstract

Slope instability in open-pit coal mines threatens safety and infrastructure. Displacement phenomena (cracks, deflection, heaving) signal potential failure. While counterweight backfilling stabilizes slopes, site-specific protocols for heterogeneous settings, such as Indonesia’s Barito Basin (Warukin Formation), lack standardization. This study addresses this gap at PT. Bhumi Rantau Energi’s Mahoni Pit by integrating high-resolution displacement monitoring (Leica Nova TM50), geotechnical analysis (RQD, RMR), and numerical modeling (SLIDE 7.0, RS2 v11). The objectives were to characterize the displacement mechanisms, quantify the counterweight effectiveness, and optimize the geometry. The results show “warning”-level velocities (>10 mm.h⁻¹) across points, with peak displacement (907 mm.day⁻¹ at IPD_MHN_26) driven by pore pressure in weak fill/mud layers (c′: 2–20 kPa; thickness: 71–100 m). Counterweights significantly increased the Factor of Safety (FoS) from critical levels (e.g., 0.960, PF = 74.4%) to stable values (e.g., 1.160, PF = 1.8%), representing 20–35% improvements. RS2 identified fill material as the primary displacement zone (max: 2.10 m). Optimized designs featured phased backfilling (200 k–10 M BCM) with a 50 m width and 11° inclination. Tailored counterweight deployment effectively mitigated the instability in slopes underlain by weak strata. The integrated approach provides a validated framework for optimizing designs in similar sedimentary basins, enhancing safety and reducing costs.

1. Introduction

Cracks on slopes are fractures or fissures that develop on their surfaces, which occur in rock and soil formations [1,2,3]. These cracks exhibit variations in size, depth, and pattern [4]. Slope deflection, in contrast, refers to the progressive downward movement or subsidence of specific slope sections resulting from structural instability in soil or rock [5,6]. This phenomenon typically signifies an initial indicator of potential slope failure, such as landslides or mass-wasting events [7,8]. Such phenomena may arise from natural processes or anthropogenic activities. Another commonly observed phenomenon on slopes is heaving. Heaving involves the upward displacement of soil or rock material above the slope surface due to subsurface pressure [9]. This occurs primarily when subsurface materials expand or migrate, exerting an upward force on overlying layers. Heaving indicates slope instability and may precipitate hazardous events, including landslides [10].

Cracks, slope deflections, and heaving constitute displacement phenomena in slopes. Displacement refers to the movement or shifting of soil or rock masses along a slope [11,12]. Such movement may occur gradually (e.g., creep) or rapidly (e.g., landslides). Heavy rainfall, earthquakes, erosion, and rock weathering represent natural triggers for displacement [13]. Conversely, anthropogenic activities, including slope cutting, infrastructure construction, and groundwater extraction, induce displacement. Analytical methods, such as numerical modeling, deformation monitoring, and geotechnical analysis, are commonly employed to assess slope movements [14].

Counterweight implementation represents a key method for mitigating slope displacement [15]. This technique stabilizes slopes prone to failure or instability. Implementation utilizes readily available materials without requiring sophisticated technology. Common counterweight materials include earth fills, rocks, concrete, or other dense substances [16]. The method counteracts destabilizing forces, such as the gravitational load, soil pressure, or shear stress potentially triggering slope failure, by applying additional mass to specific slope sections [17,18]. Primary objectives comprise enhanced slope stability and prevention of undesirable soil or rock movement [19,20]. By increasing the safety factor, counterweights reduce the shear stress in potential failure zones through augmentation of the normal force acting upon these areas [21,22].

This study aims to (1) characterize displacement phenomena and classify their mechanisms within the coal mining pit at PT. Bhumi Rantau Energi, (2) quantify variations in the FoS pre- and post-mechanism, (3) optimize the backfill layer thickness for slope reinforcement, and (4) develop engineered designs to enhance the long-term slope stability at PT. Bhumi Rantau Energi.

2. Research Location

PT. Bhumi Rantau Energi operates as a coal-mining enterprise within a 2096-hectare Production Operation Mining Business License (IUP) area. The facility maintains an annual coal production capacity of 12 million tons. Geographically situated in Lokpaikat District, Tapin Regency, South Kalimantan Province, Indonesia, the study area is illustrated in Figure 1a.

The Warukin Formation represents one of the principal coal-bearing strata within the Barito Basin [24,25]. This geological unit constitutes a significant formation in PT. Bhumi Rantau Energi’s (BRE) mining concession. Designated by the symbol Tmw1 and conventionally depicted in light brown on geological maps, the Warukin Formation comprises 30–40 m thick coal seams interbedded with calcareous claystone, fine-grained sandstone, claystone, conglomerate, shale, and marl [26,27,28]. Dating to the Miocene epoch, this formation’s regional distribution within the study area is demarcated by the red rectangle in Figure 1b.

Sedimentation within the Barito Basin initiated during a megacycle of transgression from the Eocene through the Oligocene to the Miocene, followed by regression from the Miocene to Pliocene, resulting in the accumulation of Tertiary sedimentary rocks [29]. The Tanjung Formation, the region’s oldest Tertiary sedimentary unit, developed during the Late Eocene and comprises three distinct members. The upper member exhibits intercalations of shale and sandstone with thin coal seams, while the lower member consists of shale, sandstone, and conglomerate [29]. This formation is designated by the geological symbol Ksp.

In the northern and western sectors of the Barito Basin, the Berai Formation interfingers with adjacent units. Dating to the Oligocene–Miocene interval, this formation is conformably overlain by the Warukin Formation, which has a thickness of approximately 1350 m [30]. The Berai Formation features (1) a 225 m thick upper section of marl, clay, silt, and interbedded limestone layers containing coal bands; (2) a 600 m thick middle section of crystalline limestone interbedded with thin marl layers; and (3) a 250 m thick basal sequence of marl, limestone, shale, silt, and interbedded coal seams.

The Warukin Formation is characterized by quartz sandstone (yellowish-white, medium-to-coarse-grained, locally conglomeratic, poorly sorted, subangular to subrounded grains, well-bedded with cross-stratification, and fine carbonaceous laminations) and claystone (brownish-gray, locally carbonaceous) [31]. Within the Rantau Block of this formation, coal resources are estimated at 295 million tonnes, averaging 8 m in thickness with a 35° dip. The coal is classified as sub-bituminous with a calorific value of 4700–5500 kcal/kg [27]. Figure 1c presents the stratigraphic column detailing the geological chronology of the study area.

3. Method

Displacement measurements were acquired using a Leica Nova TM50 Monitoring Station and Leica GPR112 monitoring prisms(Leica Geosystems AG, Heerbrugg, Switzerland), as illustrated in Figure 2a,b. Permanent instrumentation was installed at monitoring points IPD_MHN_23 through IPD_MHN_28. Prisms were positioned orthogonally to observed displacement vectors in the field. The data collection at points IPD_MHN_23, IPD_MHN_24, and IPD_MHN_25 spanned from 17 April to 4 June 2024, which yielded 50 measurement epochs per point. At IPD_MHN_26, monitoring occurred between 17 April and 13 May 2024, which generated 27 discrete data epochs.

Table 1. Threshold displacement [32].

Warning Status	Mine Slope Thresholds	Embankment Slope Thresholds
Stable	<10 mm.day−1 or <5 mm.h−1	<20 mm.day−1 or <5 mm.h−1
Caution	10–20 mm.day−1 or 5–7.5 mm.h−1	20–50 mm.day−1 or 5–7.5 mm.h−1
Alert	20–50 mm.day−1 or 7.5–10 mm.h−1	50–100 mm.day−1 or 7.5–10 mm.h−1
Critical	>50 mm.day−1 or >10 mm.h−1	>100 mm.day−1 or >10 mm.h−1

presents the displacement thresholds for the mine and embankment slopes based on field-measured displacement intensities. These thresholds enable slope stability evaluation and warning status assignment according to displacement rates measured in millimeters per day (mm.day⁻¹) or millimeters per hour (mm.h⁻¹). Mine slopes refer to those formed through mining operations, while embankment slopes comprise engineered structures constructed from compacted fill materials, such as soil or rock aggregates. The warning classification system comprises four distinct levels (Table 1).

The FoS data from prior to and following mechanism were processed using SLIDE version 7.0 [33], while the displacement values for each constituent slope layer were determined using RS2 version 11 [34,35]. The fundamental equation for slope failure criterion determination employs the Mohr–Coulomb equation [36]:

$${\tau }_f = c^{\prime }+ {\sigma }_n^{\prime }\mathit{tan}{\phi }^{\prime }$$

(1)

where c′ represents the effective cohesion, φ′ denotes the effective angle of internal friction, σₙ′ is the effective normal stress, and τ_f corresponds to the maximum shear stress. The FoS is derived from

$$FoS={\displaystyle \frac{\tau }{{\tau }_f}}$$

(2)

where τ represents the mobilized shear strength of the slope material and τ_f is the maximum shear stress. A FoS of 1.3 is generally regarded as the minimum allowable value for slope design when supported by reliable site investigation data [37]. Consequently, the selection of an appropriate FoS involves a balance between economic constraints and safety requirements. A higher value (e.g., 1.5) is typically adopted in cases involving significant uncertainty in geotechnical parameters or where the potential consequences of failure are deemed severe [38]. Slopes with FoS > 1.0 are considered stable, whereas those with FoS < 1.0 are unstable [39].The minimum FoS value of 1.0, as stipulated by the Ministry of Energy and Mineral Resources of the Republic of Indonesia (Regulation No. 1827 K/30/MEM/2018), is adopted as the design criterion for slope stability in this study [40].

In the limit equilibrium method, the analysis of complex failure surfaces is conducted by dividing the sliding mass into a series of vertical slices [41]. Among these techniques, the Simplified Bishop method is widely employed; it assumes that no shear forces act between slices, thereby simplifying the analysis while maintaining a high degree of accuracy. The governing equation for this method is presented below.

$$F={\displaystyle \frac{1}{\sum Wsin\alpha }}\sum {\displaystyle \frac{c^{\prime }b+\left(W-ub\right) tan{\phi }^{\prime }}{cos\alpha +\frac{sin\alpha tan{\phi }^{\prime }}{F}}}$$

(3)

where

• c′: Denotes the effective cohesion of the soil (kN/m²).
• b: Slice width (m).
• W: Total weight of the slice (kN).
• u: Pore water pressure at the slice base (kN/m²).
• φ′: Effective angle of internal friction (°).
• α: Inclination of the slice base relative to the horizontal (°).
• F: Factor of safety.

The Mohr–Coulomb criterion was implemented as the elastoplastic constitutive model for the soil and rock materials in this study. This failure criterion is fundamental to the slope stability analysis performed by the RS2 software, which utilizes the Finite Element Method (FEM). The governing equation of the Mohr–Coulomb criterion is presented below:

$$\left({\sigma }_1-{\sigma }_3\right) = \left({\sigma }_1+{\sigma }_3\right) sin{\phi }^{\prime }+2c^{\prime }. cos{\phi }^{\prime }$$

(4)

where

• σ₁: major principal stress (kPa).
• σ₃: minor principal stress (kPa).
• c′: Effective cohesion (kPa).
• φ′: Effective angle of internal friction (°).

The FoS is defined as the factor by which the shear strength parameters must be reduced to bring a slope to the point of failure. In the Finite Element Method (FEM) analysis of slopes, the strength reduction technique is employed, whereby the following parameters are progressively reduced [42]:

$$c_{red} = {\displaystyle \frac{c^{\prime }}{FoS}}, tan{\phi }_{red} {\displaystyle \frac{tan {\phi }^{\prime }}{FoS}}$$

(5)

The factor of safety is determined computationally by iteratively reducing the material’s shear strength parameters until slope failure is indicated by numerical non-convergence. The original effective cohesion (c′) and effective angle of internal friction (φ′) are progressively reduced to values c_red and φ_red by increasing the FoS in each iteration. The lowest FoS value that causes the finite element solution to become unstable is defined as the factor of safety for the slope.

The principal method for determining the effective angle of shearing resistance (φ′) and effective cohesion (c′) involves laboratory testing conducted on representative, undisturbed samples. In this study, the direct shear test was employed in accordance with ASTM D3080 [43] for soil and ASTM D7012 [44] for rock. The samples were sheared under a range of normal stresses to ensure drained conditions. For each test, the shear stress at failure was plotted against the corresponding normal stress. The value of φ′ was determined from the slope of the line of best fit through these data points, while the intercept of this line was used to obtain the value of c′.

Rock quality assessment was conducted through weighting of Rock Quality Designation (RQD) [45], values derived from borehole cores obtained from depths of 0–61.7 m, which comprised 45 observational samples. Rock mass classification was performed using the Rock Mass Rating (RMR) system proposed by Bieniawski (1989) [45], incorporating five primary parameters and one controlling parameter [46].

Slope stability modeling and FoS calculations were performed using the finite element method (FEM) within the RocScience RS2 software (version 11). The analysis assumed that the slope material was homogeneous and isotropic, with material strength governed by the Mohr–Coulomb failure criterion. The applied boundary conditions were as follows: the base of the model was assigned as a fixed support (constrained in all directions), while the vertical side boundaries were designated as roller supports (permitted to move only in the vertical direction). The model was discretized using a mesh of six-noded triangular elements. The mesh was refined around the slope surface and potential failure zones to enhance the accuracy of the results. The FoS was determined using the Shear Strength Reduction (SSR) technique.

The integrated methodology adopted in this work is illustrated in the conceptual framework of Figure 3. The process commences with a field investigation of displacement phenomena, initiating simultaneous high-resolution geotechnical monitoring and comprehensive subsurface characterization. Data acquired from these campaigns are utilized to develop and calibrate numerical models (SLIDE 7.0, RS2 v11) to accurately diagnose the failure mechanism and precisely quantify the pre-intervention stability state. Subsequently, these calibrated models are applied iteratively to design and optimize the counterweight intervention. The final step entails validation of the model predictions through comparison with observed post-implementation field performance, thereby ensuring the proposed recommendations are both scientifically robust and practically effective. This iterative, integrated process ensures each phase directly informs the subsequent one, forming a robust and reliable framework for slope stabilization design.

4. Results

A dashed red line with black arrows designates field locations where displacement phenomena occur. Eight displacement monitoring stations, as indicated by red points in Figure 4, are equipped with displacement monitoring devices bearing the following location codes: IPD_MHN_23, IPD_MHN_24, IPD_MHN_25, IPD_MHN_26, IPD_MHN_27, IPD_MHN_28, IPD_MHN_29, and IPD_MHN_30.

At Point 1 (349° N, elevation 65.1 m) in the Mahoni Pit, a tension crack was identified. Without intervention, this slope crack may propagate, potentially leading to slope failure mechanisms, such as landslides. The crack aligns with the embankment slope direction, exhibiting an aperture width of 35 cm (Figure 5a). Slope deflection was observed at 320° NW between monitoring stations IPD_MHN_24 and IPD_MHN_25 (Figure 5b). This deformation may have originated from pore water pressure within soil/rock matrices, potentially triggering further instability. Point 3 (100° S, elevation 61.3 m) exhibited a crack with a maximum aperture width of 20 cm and 7 cm of slope deflection (Figure 5c). At Point 4 (124° SE, elevation 74.8 m), a crack with a maximum aperture width of 33 cm and 60 cm of settlement was recorded (Figure 5d). Point 5 displayed pavement heaving, inducing eastward road tilting, with measured heave displacement of 30 cm. This feature occurred at coordinates 2°56′20.9″ S, 115°13′40″ E (elevation 102 m) (Figure 5e).

The primary cause of surface cracking at mining sites is attributed to mining-induced ground and rock deformation. Vibrations from mining activities, such as excavation processes and heavy equipment traffic, generate distinct tensile and compressive zones on the surface. Tensile zones initiate tension cracks, slope movement induces slope deflection, and compressive zones result in pavement heaving. These phenomena are classic indicators of ground instability induced by mining operations, necessitating rigorous geotechnical monitoring to ensure workplace safety. Furthermore, the study area is characterized by local geological conditions, including soft soil layers or friable rock strata, which exacerbate these instabilities.

Figure 6a presents temporal trends of the horizontal displacement, vertical displacement, and displacement velocity for monitoring station IPD_MHN_23. The blue bars quantify the horizontal displacement in mm.day⁻¹, red bars represent the vertical displacement trends (mm.day⁻¹), and the orange line graph indicates displacement velocity (mm.h⁻¹). Measurements were recorded from 17 April to 4 June 2024. IPD_MHN_23 exhibited a mean horizontal displacement of 293.14 mm.day⁻¹ (

Table 2. Statistical results of displacement measurements at IPD_MHN_23, IPD_MHN_24, and IPD_MHN_25.

Parameter	Horizontal Displacement (mm.day−1)	Velocity (mm.h−1)	Vertical Displacement (mm.day−1)
IPD_MHN_23
Mean	293.14	14.89	35.84
Min	67	3	3
Max	808	46	95
SD	202	10.33	25.71
CoV	68.91	69.38	71.73
N	50	50	50
IPD_MHN_24
Mean	258.27	13.63	41.82
Min	65	2.71	3
Max	684	38	107
SD	169.1	8.28	28.7
CoV	65.48	60.75	68.63
N	50	50	50
IPD_MHN_25
Mean	164.53	10.38	25.14
Min	38	1.58	−6
Max	442	24	69
SD	103.51	5.63	18.64
CoV	62.91	54.22	74.14
N	50	50	50

), with a mean vertical displacement of 35.84 mm.day⁻¹ and mean velocity of 14.89 mm.h⁻¹. According to regulatory thresholds, the mean velocity classifies this station at the warning level (v > 10 mm.h⁻¹).

Figure 6b displays the displacement monitoring results for IPD_MHN_24. This station recorded a mean vertical displacement of 258.27 mm.day⁻¹, mean horizontal displacement of 41.82 mm.day⁻¹, and mean displacement velocity of 13.63 mm.h⁻¹. Similarly classified at the warning level (v > 10 mm.h⁻¹), the peak mean vertical displacement reached 107.00 mm.day⁻¹, while the minimum mean was 3 mm.day⁻¹. These measurements correspond to the observed slope deflection phenomena at this location.

Figure 6c displays the displacement monitoring results for station IPD_MHN_25. The measurements revealed mean horizontal displacement of 164.53 mm.day⁻¹, mean vertical displacement of 25.14 mm.day⁻¹, and mean velocity of 10.38 mm.h⁻¹. This station maintained the warning classification status (v > 10 mm.h⁻¹). The peak horizontal displacement reached 442.00 mm.day⁻¹ on 19 May 2024, while the maximum vertical displacement was 69.00 mm.day⁻¹ on 23 May 2024. Collectively, these three stations yielded N = 50 displacement monitoring data points (Table 2).

Table 3. Statistical results of displacement measurements at IPD_MHN_26, IPD_MHN_27, and IPD_MHN_28.

Parameter	Horizontal Displacement (mm.day−1)	Velocity (mm.h−1)	Vertical Displacement (mm.day−1)
IPD_MHN_26
Mean	326.33	16.42	56.7
Min	14	0.58	−4
Max	907	48	170
SD	294.93	15.69	58.42
CoV	90.38	95.55	103.03
N	27	27	27
IPD_MHN_27
Mean	261.19	12.77	48.37
Min	19	0.08	−3
Max	629	34	116
SD	237.78	11.43	42.38
CoV	91.04	89.46	87.62
N	26	26	26
IPD_MHN_28
Mean	282.5	14.06	29.12
Min	29	1.21	−2
Max	768	34.5	79
SD	259.19	11.97	28.61
CoV	91.75	85.16	98.26
N	26	26	26

presents statistical results of displacement measurements at three locations: IPD_MHN_26, IPD_MHN_27, and IPD_MHN_28. At IPD_MHN_26, the maximum horizontal displacement was 907.00 mm.day⁻¹, recorded on 19 April 2024; this represents the highest value among all the monitored sites (Figure 6d). The maximum vertical displacement reached 170.00 mm.day⁻¹, with a mean value of 56.70 mm.day⁻¹. The peak velocity was 48.00 mm.h⁻¹ (mean: 16.42 mm.h⁻¹), indicating a “caution” status (v > 10 mm.h⁻¹). Figure 6e displays the displacement monitoring results for IPD_MHN_27, where the mean horizontal displacement was 261.19 mm.day⁻¹, the mean vertical displacement was 48.37 mm.day⁻¹, and the velocity averaged 12.77 mm.h⁻¹, also categorizing this location at the “caution” level (v > 10 mm.h⁻¹). Figure 6f depicts the displacement trends for IPD_MHN_28, with mean values of 282.50 mm.day⁻¹ (horizontal), 29.12 mm.day⁻¹ (vertical), and 14.06 mm.h⁻¹ (velocity), likewise falling under the “caution” classification. All six monitored sites exhibited a “caution” status, defined as v > 10 mm.h⁻¹ for embankment slopes. Displacement at IPD_MHN_23 decreased and stabilized after 2 June 2024, as evidenced by a flat trend until monitoring ceased. Similarly, IPD_MHN_24 stabilized on 2 June 2024. IPD_MHN_25 showed displacement on 31 May 2024, but increased again from 2 June 2024, onward. IPD_MHN_26 declined after 2 May 2024, stabilizing from 13 May 2024. IPD_MHN_27 decreased between 30 April and 12 May 2024, while IPD_MHN_28 declined from 2 May to 12 May 2024. The data counts were 27 points for IPD_MHN_26 and 26 points each for IPD_MHN_27 and IPD_MHN_28.

Claystone and sandstone exhibit enhanced stability (c′ > 100 kPa, φ′ > 39°); however, the limited sandstone thickness (10 m) constrained its effectiveness. The coal at Pit Mahoni is classified as compact coal, demonstrating high compressive strength with a UCS value of 5.72 MPa. Nevertheless, its low shear resistance (reduced cohesion and φ′) poses landslide risks under loading conditions. Fill material and mud constitute the most problematic strata, exhibiting null UCS, diminished shear parameters, and significant thickness. The counterweight employs soft clay fill material, whose accumulated thickness results from long-term layering since the initial embankment. Comprehensive material properties for the Pit Mahoni slope are detailed in

Table 4. Material properties of the Pit Mahoni slope.

Type of Material	UCS (MPa)	Unit Weight (kN/m3)	Cohesion (kPa)	φ (°)	Thickness (m)
Claystone	2.62	19.79	110	39	70
Sandstone	1.73	17.15	107	42	10
Coal	5.72	13.72	36	27	40
Fill Material	0	21	20	16	100
Mud	0	23	2	2	71

.

Table 5. Water table elevation at observation points for sites A and B.

Observation Point	X Coordinate (m)	Y Coordinate (m)	Water Table Elevation (m a.s.l.)
Location A
P-A1	433.464	37.939	0
P-A2	596.195	31.383	8.617
P-A3	798.457	17.618	12.684
P-A4	956.279	1.371	12.588
P-A5	978.978	−5.000	8.958
P-A6	1129.890	−60.000	0
Location B
P-B1	339.400	69.000	78.772
P-B2	136.700	69.000	88.071
P-B3	299.800	35.000	107.104
P-B4	818.500	35.000	30.802

presents groundwater elevation data measured at specific monitoring points, including wells and piezometers, at two distinct locations: A and B. Groundwater elevation, defined as the upper surface of the zone of saturation, marks the boundary below which soil and rock are fully saturated with water. For each monitoring point, the dataset comprises the precise spatial coordinates (X, Y) and the corresponding groundwater elevation. These elevation data are represented by a blue piezometric surface on the slope model.

Based on Rock Quality Designation (RQD) observations from borehole core samples across a 0–67.1 m depth interval, 18% of measurements fell within the “Very Poor” category. These intervals occurred at elevations of 5.5–7, 10.75–12.25, 28.63–30.23, 45.05–46.55, 46.55–48.05, 52.58–54.05, 64.65–66.25, and 66.25–67.1 m. The “Poor” classification comprised 11% of the RQD values, corresponding to elevations of 4–5.5, 13.75–15.25, 19.75–21.25, 49.55–51.07, and 54.05–55.58 m. A “Fair” rating was recorded for 13% of the samples at 0–3.25, 8.5–9.25, 9.25–10.75, 16.75–18.25, 35.98–37.57, and 57.08–58.58 m. The “Good” category represented 13% of measurements at elevations of 3.25–4, 7–8.5, 30.23–31.15, 48.05–49.55, 51.07–52.58, and 61.75–63.2 m. Conversely, “Excellent” ratings constituted 45% of the results, occurring at 12.25–13.75, 15.25–16.75, 18.25–19.75, 21.25–28.63, 31.15–35.98, 37.57–45.05, 55.58–57.08, 58.58–61.75, and 63.23–64.65 m. Analysis of the 45 RQD core datasets from Pit Mahoni revealed the highest rock quality classification as “Excellent” (45%), while the lowest was “Poor” (11%). The RQD value percentages for Mahoni Pit are presented in Figure 7.

The borehole depth-run data (in meters) reveal distinct rock classifications: 0–5.5 m as Fair rock and 5.5–7 m as Poor rock. The 7–13.75 m interval was classified as Fair rock, while 13.75–15.25 m was Poor rock. Subsequently, 15.25–28.63 m exhibited a Fair rock classification. The 28.63–30.23 m interval registered Very Poor rock. Fair rock predominated from 30.23–45.05 m, interrupted by Poor rock at 45.05–46.55 m and Very Poor rock at 46.55–48.05 m. The 48.05–49.55 m stratum reverted to Fair rock, whereas 49.55–51.07 m was Poor rock. Fair rock resumed at 51.07–54.05 m, followed by Poor rock at 54.05–55.58 m. Fair rock continued through to 55.58–64.65 m, with Very Poor rock concluding the sequence at 64.65–67.1 m. Analysis of all the Rock Mass Rating (RMR) data yielded the following distribution: Fair rock (80%), Poor rock (11%), and Very Poor rock (9%), with no Very Good or Good rock classifications (0%) (Figure 8).

Figure 9a presents the stability analysis results for the Mahoni Ipd design at RL + 40 prior to the mechanism, with water conditions in the Sump maintained at elevation +37 m at Location A. Under critical conditions, the deterministic FoS was 1.036, with a probability of failure (PF) of 9.3%. The mean FoS was 1.035, and the normal reliability index (RI) was 1.320. Figure 9b displays the corresponding analysis following the counterweight application at Location A for the identical RL + 40 design. Under standardized critical conditions (Sump water elevation: +37 m), the deterministic FoS was 1.298 with 8.1% PF. The mean FoS remained consistent at 1.298, while the normal RI increased substantially to 1.398.

Figure 10a delineates the compositional stratification of the Mahoni IPD slope at Location A, which was classified into three distinct geotechnical units: original material, fill material, and mud. Figure 10b presents the total displacement distribution derived from the RS2 finite element analysis for the same slope section. The RS2 analysis quantified the total displacement ranges as follows: original material (0–0.26 m), mud (0.26–0.59 m), and fill material (0.59–0.85 m). The fill material exhibited the maximum displacement magnitude (0.85 m), while the original material showed minimal displacement (0 m), as represented by blue contours in Figure 10b.

Figure 11a presents the stability analysis results for the Mahoni IPD slope at Location B prior to the mechanism. Under critical boundary conditions, the deterministic FoS was 0.960, with a probability of failure (PF) of 74.400%. The mean FoS was 0.958, and the normal reliability index (RI) was −0.645. Figure 11b illustrates the corresponding analysis following the counterweight deployment at Location B. The post-intervention analysis yielded a deterministic FoS of 1.160, with the PF reduced to 1.800%. The mean FoS increased to 1.158, while the normal RI improved significantly to 2.054.

Figure 12a delineates the geotechnical composition of the Mahoni IPD slope at Location B, while Figure 12b presents the total displacement distribution derived from the RS2 finite element analysis. The quantitative analysis revealed displacement magnitudes of original material (0–0.63 m), mud (0.63–1.47 m), and fill material (1.47–2.10 m). The fill material exhibited peak displacement (2.10 m), as indicated by red contours, whereas blue contours denote the minimal displacement (0 m) in the original material.

The red line delineates the May 2024 slope design at +42 m above sea level (RL + 42). The bold black line represents the pre-fill topography as of April 2024 (elevation: −100 m). Meanwhile, the green line indicates the Week 18 topography, while the blue line demarcates the South Cendana High Wall of the Mahoni Pit. The fill material was engineered with an 11° inclination angle. For the green line fill operation, 10,000,000 bank cubic meters (BCM) of material was required to span elevations from −100 to +42 m. The mechanism comprised four discrete construction blocks. The magenta line operation required 100,000 BCM with a 2-week construction duration. The mud elevation ranged from −30 to +41 m (Figure 13). A primary function of this pit’s counterweight was gradual mud encapsulation through a controlled elevation increase. The finalized Mahoni IPD counterweight design for Location A is presented in Figure 13.

The green contour represents the 2024 annual design at RL + 90 elevation. The blue contour indicates the Week 19 topography, while the pink contour delineates the original Mahoni IPD base at Location B. Excavation between pink and blue contours yielded 100,000,000 bank cubic meters (BCM) of material. The zone between the blue (current elevation: +80 m) and green contours remained unfilled, with a designed slope height of 10 m at 37° inclination. The Location B counterweight required approximately 200,000 BCM volume at a 50 m width. The finalized Mahoni IPD counterweight design for Location B is detailed in Figure 14.

Figure 15 identifies two locations of critical concern for counterweight design implementation. Location A is demarcated by a red boundary, while Location B is delineated by a blue boundary.

The following long-term design recommendations are proposed for Locations A and B:

At Location A, the elevation should be increased solely to cover mud/voids, with implementation phased gradually post-counterweight completion. The dumping sequence must be regulated to prevent excessive load thrust toward the northeast orientation. Widening of the dumping area is recommended to confine the South Mahoni IPD to RL + 80. Engineering modifications for the active coal-hauling road are required, as the red boundary area will experience ongoing subsidence and minor cracking, necessitating immediate remediation to maintain operational integrity. This subsidence will persist due to ongoing infill operations on the southern and western sectors.

At Location B, immediate construction of a counterweight—minimum width 50 m, length spanning three blocks (Blocks 17–19), and height 10 m—is required. Additionally, load-balance distribution and dumping-area widening in Blocks 8–12 should be implemented. Long-term elevation of the blue line to RL + 90 may induce minor westward slope failure, which is attributable to extant soft mud/material within the black boundary at elevations +30 to +55; consequently, relocation and elevation of the active road to RL + 55 (green boundary) are advised.

A displacement of 2.10 m was recorded at Location B, occurring entirely prior to the counterweight intervention. This measurement was taken at the peak of slope movement, immediately before emergency stabilization measures were implemented. The pre-intervention FoS value of 0.96 confirms that the slope was in a state of active catastrophic failure; therefore, the magnitude of the recorded displacement is technically consistent with this condition. Following the installation of the counterweight, no further significant or catastrophic displacements were observed.

The post-intervention stability was validated using in situ monitoring data from a Total Station at Location B. These data demonstrate that the slope deformation rate decreased markedly to a negligible level of less than 1 mm.month⁻¹ following counterweight installation. This stabilization is evidenced by a displacement rate of 0 mm.day⁻¹, recorded at Location B from 13 June to 31 July 2024, as shown in Figure 16. This confirms that catastrophic movement has ceased and the slope has reached a new state of equilibrium.

The numerical model was calibrated against the actual geometry of the slope following deformation (i.e., after the 2.10 m displacement had occurred). Subsequently, the counterweight was designed to stabilize this altered slope configuration, rather than the initial pre-failure geometry. Consequently, the post-intervention FoS value of 1.16 represents the safety factor of the modified slope profile under the influence of the counterweight, explaining how stability was achieved despite the occurrence of a major deformation.

The slope stability analysis reveals two distinct chronological phases: pre-intervention and post-intervention. The first phase was a period of active failure, marked by a pre-intervention FoS of 0.96, indicating that the slope was in a state of active movement. During this phase, the slope underwent catastrophic displacement, accumulating to 2.10 m. The second phase was a stabilization period, during which the counterweight installation successfully increased the FoS to 1.16. This intervention successfully halted catastrophic movement, resulting in a stable slope at its new geometry. As a result, subsequent deformations were minimal and are categorized as creep.

5. Discussion

This study reveals significant soil displacement dynamics and the effectiveness of geotechnical engineering interventions at Mahoni Pit. All monitoring points (IPD_MHN_23 to IPD_MHN_28) exhibited a “warning” status (velocity > 10 mm.h⁻¹), indicating active deformation. The highest horizontal displacement was recorded at IPD_MHN_26 (907 mm.day⁻¹), which was attributed to pore water pressure within soft materials (fill and mud) dominating the stratigraphy. Tensile cracking (widths up to 35 cm) and slope deflection were consistent with a rotational slide failure mechanism due to reduced shear strength [47]. Although stability was restored at some points (e.g., IPD_MHN_23) after 2 June 2024, owing to environmental changes (e.g., reduced rainfall), resurgent displacement trends at other points (e.g., IPD_MHN_25) indicate residual risks necessitating continuous monitoring [48,49].

To ensure the accuracy and precision of the numerical simulation results, a systematic mesh convergence analysis was performed. A series of simulations was conducted with progressively finer mesh element sizes until a density was achieved wherein the changes in key outcomes (e.g., maximum stress or deformation) were less than 2%, indicating that the results had become mesh-independent [50]. Appropriate boundary conditions were applied to accurately represent the in situ field conditions: the model’s bottom boundary was assigned a fixed support condition, while the side boundaries were constrained with roller supports, permitting movement only in the normal direction. This configuration prevents unrealistic model displacements arising from artificial boundary effects. An elasto-plastic material model employing the Mohr-Coulomb failure criterion was adopted to represent the soil/rock mass behavior. This model was selected for its capability to simulate linear elastic behavior under low loading conditions and its transition to plastic behavior (permanent deformation) upon reaching the yield point—a fundamental characteristic of geotechnical materials. The material parameters, including the elastic modulus, Poisson’s ratio, cohesion, and angle of internal friction, were derived from laboratory test data and relevant empirical correlations.

Implementation of counterweights significantly enhanced the FoS. At Location A, the FoS increased from 1.036 (critical) to 1.298 (stable), with the RI surging from 1.320 to 1.398. At Location B, the FoS rose from 0.960 (unstable, PF = 74.4%) to 1.160 (stable, PF = 1.8%), accompanied by an RI increase from −0.645 to 2.054. This improvement occurred because counterweights functioned as restraining loads, increasing the normal stress on potential slip surfaces, thereby enhancing the shear resistance [21]. RS2 analysis confirmed that the fill material zone (maximum displacements: 0.85 m at A, 2.10 m at B) constituted the primary deformation source, demonstrating the targeted efficacy of the counterweight intervention.

The material properties played a critical role. Fill and mud materials (low cohesion: 20 and 2 kPa; φ′: 16° and 2°) constituted the primary mechanism for instability. Their substantial thicknesses (100 and 71 m) and susceptibility to pore pressure established critical weak zones. In contrast, claystone and sandstone exhibited high shear strength (>100 kPa, >39°), though the limited sandstone thickness (10 m) restricted its contribution. Despite its relatively high UCS (5.72 MPa), the coal exhibited landslide susceptibility under load due to low cohesion (c′) and φ′ (36 kPa, 27°) [51].

The rock quality data (RQD and RMR) reveal heterogeneity in rock mass conditions. The RQD distribution (45% “Excellent”, 45% “Fair/Poor/Very Poor”) and RMR distribution (80% “Fair”, 20% “Poor/Very Poor”) reflected the variable conditions. Zones classified as “Very Poor” RQD (e.g., 28.63–30.23 m, 45.05–48.05 m) and “Poor/Very Poor” RMR correlated strongly with a high deformation potential. These zones featured a weak load-bearing capacity and high permeability, exacerbating the pore pressure, and thus, requiring focused mitigation design.

Engineering design validation yielded favorable outcomes in simulations optimizing the backfill thickness and counterweight geometry. Long-term recommendations include (i) a gradual elevation increase at Location A to cover mud/voids, (ii) restricted backfilling zones, and (iii) mine road relocation at Location B to RL + 55. This is critical because soft materials in Location B’s black boundary (+30 to +55 m) retain the potential to induce minor slope failures under mismanaged loading. Regulation of dumping sequences to avoid excessive thrust toward the northeast (Location A) is equally vital to prevent new instabilities.

This study is subject to limitations primarily related to its temporal scope. The monitoring period was relatively brief, spanning 49 days from April to June 2024, which corresponded exclusively to the dry season. Consequently, seasonal variations—such as significant differences in key parameters (e.g., rock strength, unit weight, cohesion, and internal friction angle) during the rainy season—were not captured in this dataset. Therefore, our findings are primarily representative of conditions prevalent during the dry season, and extrapolating these results to annual conditions requires caution. Hence, further investigations encompassing a full annual hydrological cycle or longer are highly recommended to achieve a comprehensive understanding of the system dynamics.

Study limitations include a short monitoring period (April–June 2024), which omitted full seasonal variation, and an FoS model using averaged parameters that may misrepresent field variability. Practically, the persistent “warning” status necessitates real-time monitoring and emergency response protocols. Counterweight efficacy requires further validation via medium-to-long-term performance monitoring and periodic parameter evaluation, particularly in fill/mud zones. Future research should prioritize (i) detailed hydro-mechanical modeling, (ii) FoS sensitivity analysis to fill/mud parameter variations, (iii) alternative counterweight material assessment, and (iv) integration of long-term deformation data with predictive models.

Probabilistic Sensitivity Analysis (PSA) is a technique used to quantify the influence of input parameter variability on the output variability of the Probability of Failure (PoF) [52]. In this approach, soil or rock parameters are not treated as fixed values but rather as random variables that follow specific probability distributions. The scope of this study is limited to the calculation of the deterministic FoS, the mean FoS, the Probability of Failure (PF), and the Reliability Index (RI) for both Normal and Log-Normal distributions. However, the analysis of the mean value (μ) and standard deviation (σ) for each parameter, along with the determination of the PoF, fall beyond the scope of this investigation. Furthermore, sensitivity analysis tools available in RS2, such as Tornado Charts, Scatter Plots, and Pearson/Spearman Correlation Coefficients, are not employed or discussed herein.

The novelty of this study is established through an integrated monitoring-modeling framework, delivering a site-specific and validated protocol for counterweight design in heterogeneous sedimentary basins. This represents a significant departure from prior research approaches. Although previous studies, both in Indonesia and globally, have utilized monitoring or modeling in isolation for slope stability assessment [e.g., citations], a standardized approach for complex geological settings such as the Warukin Formation has been lacking. Our research addresses this gap by synthesizing three critical data streams: (1) high-temporal-resolution displacement monitoring to capture real-time, ‘warning’-level failure kinematics (>10 mm.h⁻¹); (2) detailed geotechnical and rock mass characterization (e.g., RQD, RMR) to define material heterogeneity and weak zones accurately (e.g., fill/mud, with cohesion values of 2–20 kPa); and (3) advanced numerical modeling (SLIDE 7.0, RS2 v11), calibrated against field data, to diagnose the pore-pressure-driven failure mechanism and quantitatively optimize the counterweight design. This integration facilitates a truly prescriptive design approach, precisely quantifying the required counterweight volume (200 k–10 M BCM), geometry (50 m width, 11° inclination), and implementation phasing to achieve a FoS improvement of 20–35%—a level of quantitative detail seldom documented in the literature. Consequently, this framework transcends general guidance by offering a replicable and validated methodology to enhance safety and reduce costs in geotechnically challenging open-pit environments worldwide.

6. Conclusions

Slope instability in open-pit coal mines situated within heterogeneous formations, such as the Warukin Formation (Barito Basin, Indonesia), poses substantial safety and operational hazards. Here, displacement phenomena serve as critical failure precursors; however, site-specific counterweight backfilling protocols remain inadequately standardized. This study bridges this gap through the integration of high-resolution displacement monitoring (Leica Nova TM50), geotechnical analysis (RQD, RMR), and numerical modeling (SLIDE 7.0, RS2 v11). Key findings indicate that displacement mechanisms across all eight instrumented points attained “warning”-level velocities (>10 mm.h⁻¹), which were predominantly driven by the pore pressure within weak fill/mud layers (c′: 2–20 kPa; thickness: 71–100 m). The peak horizontal displacement reached 907 mm.day⁻¹ at IPD_MHN_26. Crucially, tailored counterweight deployment significantly enhanced the stability, elevating the FoS from critical pre-intervention thresholds (Location A: 1.036; Location B: 0.960, PF = 74.4%) to stable values (Location A: 1.298; Location B: 1.160, PF = 1.8%). Concurrent RS2 simulations identified the fill material as the principal displacement zone (maximum: 2.10 m). The installation of the counterweight successfully achieved significant slope stabilization. No further substantial displacement has been observed, and the deformation rate has been drastically reduced to below 1 mm.month⁻¹, with periods of negligible (0 mm.day⁻¹) movement. This indicates that catastrophic movement has been arrested. Consequently, the slope has attained a new state of stable equilibrium following the implementation of emergency stabilization measures. Optimized phased backfilling (200,000 BCM at Location B; 10,000,000 BCM at Location A), designed with a 50 m bench width and an 11° inclination, achieved 20–35% FoS improvements. This validates the technique’s viability in high-risk zones, which is contingent upon designs that account for material heterogeneity and hydro-mechanical feedback. This integrated monitoring–modeling framework offers a replicable solution for slope stabilization in analogous sedimentary basins worldwide. Operational recommendations encompass (1) implementing phased elevation increases at Location A to cover mud voids via strictly regulated dumping sequences, (2) relocating the active haul road at Location B to RL + 55 to avoid failure-prone materials (elev. +30 to +55 m), and (3) establishing real-time displacement monitoring to enable adaptive counterweight adjustments for residual warning-level velocities. Future research should prioritize extended monitoring to validate the counterweight performance across full seasonal cycles, notably monsoon impacts, thereby capturing long-term hydro-mechanical feedback.