# Stability Assessment of High and Steep Cutting Rock Slopes with the SSPC Method

Authors: Hongliang Tao; Guangli Xu; Jingwen Meng; Ronghe Ma; Jiaxing Dong
Journal: Advances in Civil Engineering
 (2021)

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## Abstract

The stability of high rock slopes has become a key engineering geological problem in the construction of important projects in mountainous areas. The original slope stability probability classification (SSPC) system, presented by Hack, has made obvious progress and been widely used in rock slope stability analysis. However, the selection and determination of some evaluation indexes in the original SSPC method are usually subjective, such as intact rock strength and weathering degree. In this study, the SSPC method based on geological data obtained in the prospecting tunnels was presented and applied. According to the field survey and exploration of the prospecting tunnels, the weathering degree of the slope rock mass was evaluated. The empirical equation for the maximum stable height of the slope was applied to the slope stability evaluation in the presented SSPC method. Then, the slope stability probability of numerous cutting slopes in the sandstone unit was evaluated using the presented system. Results of the Geostudio software based on the limited equilibrium analysis of the investigated slopes were compared with the results obtained by the SSPC method. The results indicate that the SSPC method is a useful tool for the stability prediction of high and steep rock slopes.


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## Body

## 1. Introduction

The geomorphology in southwest China changes rapidly over short distances; in this region, large-scale projects such as hydropower stations were constructed, with complex geological conditions [1–3]. In recent years, the heights of cutting rock slopes can be as high as 300–500 m. For instance, the maximum cutting slope height at the Dagangshan project located in the Dadu River is 530 m, and the maximum cutting slope height at the Xiaowan project located in the Lancang River is 700 m [4]. Cutting slopes are prone to fail due to the disturbance on original geometry and strength [5], and assessing the stability of these rock slopes is an important and difficult task, due to ensure slope safety in period of construction and running.Slope stability is affected by numerous factors, such as geological conditions, rock mass mechanical parameters, joint parameters, slope geometry, groundwater condition, and excavation methods. At present, rock mass quality assessment, kinematical, analytical, and numerical analyses are the common methods in rock slope stability assessments [6]. However, the estimation of the parameters needed for the abovementioned methods is always challenging due to the heterogeneity of jointed slope masses [7, 8]. Since 1970, many rock mass classification systems that consider many affecting factors, such as the slope geometry, presence of water or water pressures, weathering effects, and excavation methods, have been proposed or modified and applied in the quantitative stability prediction of rock engineering [9–13]. The existing rock mass classification systems are becoming increasingly popular and are used in research on slopes worldwide as an accurate and useful tool for the rock slope stability assessment. In fact, shortcomings exist in most of the mentioned classification systems; for instance, failure modes of the slopes are always not taken into account, and only single-point data are used, but the slopes always have large-scale and complex geological conditions. In addition, slope rock mass and exposure rock mass are always not distinctly differentiated in the existing approach [14]. To overcome the limitations previously, Hack (1998) [15] presented a new rock slope stability assessment approach (SSPC, slope stability probability classification), which has been used worldwide, especially in the research of road slopes in Spain [16], New Zealand, India [17], and Turkey [5, 6, 14] with good results. As a matter of fact, the method is generally suitable for slopes with a height of less than or equal to 45 m. Moreover, discontinuity property survey, weathering degree, and intact rock strength estimation involve high subjectivity and arbitrariness [14, 17, 18]. For these reasons, the SSPC method is rarely used in the high and steep cutting rock slopes [19].In this study, key points of the SSPC method are introduced. Then, discontinuity surveys were carried out and data were collected and analyzed at four different prospecting tunnels, and discontinuity properties were obtained and input for the SSPC assessment system; stability of six proposed cutting slopes of the supported project is evaluated using the SSPC method.


## 2. Project Background

### 2.1. Study Area

The supported hydropower project is located upstream of the Dadu River, Sichuan Province, China, which flows through a valley with V shape. The reservoir has a normal pool level (NPL) of 2600 m, and the river’s natural water level was approximately 2597 m. The basic seismic intensity of this area is VII degrees, indicating a relatively stable area. Slopes in this area were mainly in the metamorphic sandstone unit with upper Triassic and Jurassic bonobo groups. Rock fall phenomena and rock failure (sliding, toppling, and wedge failure seen in Figure1) commonly occurred at natural slope in this region. In this paper, stability of six proposed cutting rock slopes seen in Figure 2 are studied, including tunnel-face slope (no. 1), intake slope (no. 2), the abutment slope (no. 3), slope of the toe board (no. 4), back-slope of the powerhouse (no. 5), and slope of the powerhouse in the left bank (no. 6) of the Dadu River. In Figure 2, four prospecting tunnels (PD09, PD01, PD07, and PD20) were arranged to find out the geological conditions of the abovementioned slopes. Specifically, discontinuity and rock mass properties, weathering degree, and other related parameters can be obtained by surveys and tests in the prospecting tunnels.Figure 1
Failure of the natural slopes investigated: (a) sliding, (b) toppling, and (c) wedge failure.
(a)(b)(c)Figure 2
Distribution of the prospecting tunnels in the dam site.


### 2.2. Discontinuity Properties

The discontinuity properties of the sandstone unit along the study area were determined by means of sample windows, scan lines performed at 5 locations, and other data that were collected by discontinuity statistics exposed in the 4 prospecting tunnels (PD09, PD01, PD07, and PD20, seen in Figure2) distributed in the dam site. Accordingly, parameters of discontinuity such as the spacing, persistence, roughness, infill condition, and weathering degree were obtained with the suggestions of the International Society for Rock Mechanics (ISRM 2007) [20]. A total of 1276 discontinuities were collected and described, and the main joint sets are shown in Table 1, and a contour plot with Dips software [21] is presented in Figure 3.Table 1
Characteristics of the surveyed discontinuity sets in the study area.
DiscontinuityDip direction (°)Dip (°)Trace length (m)Spacing (m)131866<20.1–0.3220162—0.3–13104343–50.2–0.6428493–50.1–0.3Figure 3
Contour plot of the field-surveyed discontinuity in the study area.Discontinuities develop in the studied slopes, collected in the corresponding prospecting tunnels, and natural exposures were divided into statistical and geological dominant joints based on the field survey and statistical analysis, as shown in Table2.Table 2
Characteristics of the main discontinuity sets in the surveyed slopes.
SlopeJointStatistical dominant discontinuityGeological dominant discontinuityNoteDip direction (°)Dip (°)Spacing (m)Dip direction (°)Dip (°)Spacing (m)Prospecting tunnel1B1217700.2–0.5190700.2–0.5PD09J1113320.1–0.375450.1–0.3J2138830.1–0.3305550.1–0.32B1217700.2–0.5215750.3–0.6J1113320.1–0.3130150.2–0.4J2138830.1–0.3130800.2–0.43B1194660.1–0.5190600.1–0.5PD01J1122540.2–0.6120550.2–0.6J2318690.2–0.6335600.2–0.64B1194660.1–0.5185650.2–0.6J1122540.2–0.6125600.3–0.7J2318690.2–0.6330650.3–0.75B1205680.1–0.4205700.1–0.4PD07J178380.1–0.470250.1–0.3J2327640.2–0.4315600.3–0.46B1195750.2–0.5200500.1–0.4PD20J1325450.1–0.3140850.2–0.4J2300850.2–0.635450.3–0.7Roughness and waviness parameters are of great importance for the stability of discontinuity-controlled failures. An increasing roughness profile of a discontinuity results in a substantial rise in the discontinuity shear strength. The sandstone unit in the study area commonly presents straight and rough discontinuity surfaces. In addition, the roughness of the same discontinuities can be classified as slightly curved (i = 2–4°) in large-scale roughness profiles and undulating (amplitude roughness >2–3 mm) in small-scale roughness profiles with respect to the SSPC system. Commonly, no infill material in the discontinuities can be observed in sandstone, whereas surface staining can be observed. In addition, no karst phenomenon can be observed.


## 2.1. Study Area

The supported hydropower project is located upstream of the Dadu River, Sichuan Province, China, which flows through a valley with V shape. The reservoir has a normal pool level (NPL) of 2600 m, and the river’s natural water level was approximately 2597 m. The basic seismic intensity of this area is VII degrees, indicating a relatively stable area. Slopes in this area were mainly in the metamorphic sandstone unit with upper Triassic and Jurassic bonobo groups. Rock fall phenomena and rock failure (sliding, toppling, and wedge failure seen in Figure1) commonly occurred at natural slope in this region. In this paper, stability of six proposed cutting rock slopes seen in Figure 2 are studied, including tunnel-face slope (no. 1), intake slope (no. 2), the abutment slope (no. 3), slope of the toe board (no. 4), back-slope of the powerhouse (no. 5), and slope of the powerhouse in the left bank (no. 6) of the Dadu River. In Figure 2, four prospecting tunnels (PD09, PD01, PD07, and PD20) were arranged to find out the geological conditions of the abovementioned slopes. Specifically, discontinuity and rock mass properties, weathering degree, and other related parameters can be obtained by surveys and tests in the prospecting tunnels.Figure 1
Failure of the natural slopes investigated: (a) sliding, (b) toppling, and (c) wedge failure.
(a)(b)(c)Figure 2
Distribution of the prospecting tunnels in the dam site.


## 2.2. Discontinuity Properties

The discontinuity properties of the sandstone unit along the study area were determined by means of sample windows, scan lines performed at 5 locations, and other data that were collected by discontinuity statistics exposed in the 4 prospecting tunnels (PD09, PD01, PD07, and PD20, seen in Figure2) distributed in the dam site. Accordingly, parameters of discontinuity such as the spacing, persistence, roughness, infill condition, and weathering degree were obtained with the suggestions of the International Society for Rock Mechanics (ISRM 2007) [20]. A total of 1276 discontinuities were collected and described, and the main joint sets are shown in Table 1, and a contour plot with Dips software [21] is presented in Figure 3.Table 1
Characteristics of the surveyed discontinuity sets in the study area.
DiscontinuityDip direction (°)Dip (°)Trace length (m)Spacing (m)131866<20.1–0.3220162—0.3–13104343–50.2–0.6428493–50.1–0.3Figure 3
Contour plot of the field-surveyed discontinuity in the study area.Discontinuities develop in the studied slopes, collected in the corresponding prospecting tunnels, and natural exposures were divided into statistical and geological dominant joints based on the field survey and statistical analysis, as shown in Table2.Table 2
Characteristics of the main discontinuity sets in the surveyed slopes.
SlopeJointStatistical dominant discontinuityGeological dominant discontinuityNoteDip direction (°)Dip (°)Spacing (m)Dip direction (°)Dip (°)Spacing (m)Prospecting tunnel1B1217700.2–0.5190700.2–0.5PD09J1113320.1–0.375450.1–0.3J2138830.1–0.3305550.1–0.32B1217700.2–0.5215750.3–0.6J1113320.1–0.3130150.2–0.4J2138830.1–0.3130800.2–0.43B1194660.1–0.5190600.1–0.5PD01J1122540.2–0.6120550.2–0.6J2318690.2–0.6335600.2–0.64B1194660.1–0.5185650.2–0.6J1122540.2–0.6125600.3–0.7J2318690.2–0.6330650.3–0.75B1205680.1–0.4205700.1–0.4PD07J178380.1–0.470250.1–0.3J2327640.2–0.4315600.3–0.46B1195750.2–0.5200500.1–0.4PD20J1325450.1–0.3140850.2–0.4J2300850.2–0.635450.3–0.7Roughness and waviness parameters are of great importance for the stability of discontinuity-controlled failures. An increasing roughness profile of a discontinuity results in a substantial rise in the discontinuity shear strength. The sandstone unit in the study area commonly presents straight and rough discontinuity surfaces. In addition, the roughness of the same discontinuities can be classified as slightly curved (i = 2–4°) in large-scale roughness profiles and undulating (amplitude roughness >2–3 mm) in small-scale roughness profiles with respect to the SSPC system. Commonly, no infill material in the discontinuities can be observed in sandstone, whereas surface staining can be observed. In addition, no karst phenomenon can be observed.


## 3. The SSPC System and Its Application

The original SSPC system was presented by Hack (1998) [15] for probabilistic stability assessments of rock slopes, and a related detailed description can be found in some literature [14, 16]. In this paper, only key points and the steps of stability assessment are introduced.


### 3.1. Key Points of the SSPC

The SSPC method encompasses a three-step evaluation of the slope stability probability, accordingly identifying three different rock masses (ERM, exposure rock mass; RRM, reference rock mass; SRM, slope rock mass) during evaluation [16].(a)
ERM: exposed rock mass, which is directly observed on the exposure site of a natural or an old engineering slope(b)
RRM: reference rock mass, which is the theoretical and imaginary fresh rock mass, undistributed due to the excavation(c)
SRM: slope rock mass, which is the existing or proposed new slope to be cut (see Figure4)(d)
Two types of slope failure modes (orientation independent and orientation dependent) and the corresponding stability probability estimation methods are considered, with clear and simple needed-data collecting procedureFigure 4
Sketch of exposures in rock masses of various degrees of weathering and different types of excavation indicating the concept of the reference rock mass.Figure5 is the schematic diagram of the SSPC method; in the SSPC system, the slope stability probability can be evaluated on the basis of parameters obtained from the investigated exposure rock mass, such as the intact rock strength (IRS), discontinuity spacing (SPA), and condition of the discontinuities (CD). Obviously, the parameters obtained on the outcrop are significantly affected by weathering or excavation disturbances. The parameters of the ERM with different weathering and excavation disturbance degrees in the same geotechnical unit can be converted to the RRM parameters [16]. The SRM stability is determined from the RRM with the adjustment of the parameters of SRM.Figure 5
Flowchart of the SSPC method (modified after Canal A and Akin M, 2016).The shear strength parameters of the rock mass including internal friction angleϕmass and cohesion Cohmass are used to assess the slope stability together with the height of the investigated slope (Hslope) [22]. In case the dip of slope dipslope is bigger than the internal friction angle ϕmass, the maximum height of a stable slope (Hmax) can be determined by some empirical equations. The orientation-independent stability probability can be assessed using the parameters of Hmax, Hslope, ϕmass, and dipslope. In addition, the probability of orientation-dependent stability can also be assessed according to the judgment graphs of the SSPC methods.


### 3.2. Calculation of the Shear Strength Parameters of the RRM

Rock mass shear strength calculation is an important step in SSPC system; when calculation is carried out, parameters such as the intact rock strength (IRS), discontinuity spacing (SPA), roughness, infill, and karst are considered together. The IRS obtained in the laboratory or by the in situ test is divided by the weathering degree factor (WE) for calculating the reference rock intact rock strength (RIRS, see equation (1)). IRS is originally estimated using hammer blows and figure pressure; in this study, laboratory tests were performed, and the results show that intact rock strength of the fresh sandstone ranges from 136 MPa to 274 MPa, with an average value of 206 MPa. In addition, the slightly weathered sandstone has an average value of 148 MPa [23].(1)RIRS=IRSWE.The RSPA (discontinuity spacing of RRM) is determined considering three discontinuity sets that reveal minimum spacing values under the condition of more than three discontinuity sets revealed in the investigated rock mass. Consequently, factors 1, 2, and 3 are obtained using the graph presented in Figure6. Then, SPA is calculated by equation (2), and the RSPA is calculated by equation (3), considering the factors of the weathering degree (WE) and method of excavation (ME). Referring to [15, 16], values of the WE and ME can be determined. In this paper, the weathering degree is divided according to the total joint number in a 5 m section of the prospecting tunnel, which is shown in Table 3.(2)SPA=Factor1×Factor2×Factor3,(3)RSPA=SPAWE×ME.Figure 6
Factor determination graph in accordance with the discontinuity spacing [16].Table 3
Weathering degree and its classification.
DegreeJoint number in a 5 m sectionValue of WEComplete50–600.35High40–500.62Moderate-high30–400.77Moderate-slight20–300.92Slight10–200.95Fresh0–101.00TC, as the condition factor of a discontinuity, is calculated by equation (3). Here, Rl is a the large-scale roughness, Rs is the small-scale roughness, and Im and Ka are the factors of infill and karst, respectively. Considering weathering degree correction, TC of the reference rock mass named RTC is defined by equation (5).(4)TC=Rl×Rs×Im×Ka,(5)RTC=TC1.452−1.22×e−WE0.5.In the SSPC system, the weighted discontinuity condition CD is calculated by equation (5). Here, DS represents the discontinuity spacing. Similarly, the reference discontinuity condition (RCD) is calculated considering the weathering degree factor in Equation (7).(6)CD=TC1/DS1+TC2/DS2+TC3/DS31/DS1+1/DS2+1/DS3,(7)RCD=CDWE.The friction angle (ϕRM) and cohesion (CRM) of a rock mass are calculated by equations (8) and (9). Here, RIRS is the intact rock strength, RSPA is the spacing, and RCD is the condition of discontinuities of the reference rock mass.(8)ϕRM=RIRS×0.2417×RSPA×52.12×RCD×5.779,(9)CRM=RIRS×94.27×RSPA×28629×RCD×3593.


### 3.3. Orientation-Dependent Stability Assessment of the SRM

As mentioned above, in the SSPC system, both orientation-dependent and orientation-independent conditions are considered in the slope rock mass stability evaluation. As the term suggests, failures controlled by discontinuities such as planar sliding and toppling usually occur in the orientation-dependent stability analysis, while failures occur irrespective of a certain sliding surface in orientation-independent stability analysis. However, the probability of wedge failures cannot be evaluated in the SSPC system.For the former type of stability assessment, factors such as the discontinuity condition (STC) and the apparent angle of the discontinuity dip in the direction of the slope dip (AP) are considered for evaluating the stability probability. The AP is obtained based on equation (10), where αs represents the direction, αj represents the dip direction of the discontinuity, and βj represents the discontinuity dip. Meanwhile, the discontinuity condition of the slope (STC) is determined by equation (11).(10)AP=arctancosαs−αjtanβj,(11)STC=RTC×1.452−1.220×e−SWE0.5.For sliding failure, a relationship graph (see Figure7(a)) between the STC and AP is employed to assess the occurrence probability of the slope. Furthermore, a relationship graph of the STC, AP, and dipslope (see Figure 7(b)) is employed to evaluate the occurrence probability of the slope for toppling failure. In this paper, the probability results and the necessary parameters for probability calculations in the study area are summarized in Table 4.Figure 7
Flowchart of the SSPC methods determined by sliding and toppling (slope 1). (a) Sliding. (b) Toppling.
(a)(b)Table 4
Orientation-dependent stability probabilities of discontinuities at the typical investigated slopes.
SlopeDiscontinuitySTCAPSliding probabilityToppling probabilitySlope stability probability1B10.45−65.78100%95%70%J20.2725.5870%100%J30.2773.80100%100%2B10.4558.23100%100%95%J10.2721.8895%100%J20.2782.28100%100%3B10.61−42.41100%＞95%95%J10.6545.65＞95%100%J20.42−54.08100%95%4B10.61−42.41100%＞95%95%J10.6545.65＞95%100%J20.42−54.08100%95%5B10.76−60.26100%＞95%＞95%J10.6537.73＞95%100%J20.65−24.76100%＞95%6B10.7667.37＞70%100%＞70%J10.659.85＞95%100%J20.6581.33100%100%


### 3.4. Orientation-Independent Stability Assessment of the SRM

Parameters needed in the calculation of stability of slope rock mass such as SIRS, SSPA, and SCD are determined as equation (12), in which the RRM values are corrected by the the weathering degree (SWE) and method of excavation (SME) for existing natural/excavated slopes.Accordingly, the friction angle and cohesion of the slope mass are defined by equation (13). Obviously, an orientation-independent stability problem cannot occur under the condition of the dipslope ≤ ϕSRM of the investigated slopes. However, the stability condition is evaluated on the basis of the maximum slope height (Hmax) [14, 16]. The orientation-independent slope stability probability can be easily determined by the chart seen in Figure 8. However, the assessment method of the maximum slope height (Hmax) was modified by Li et al. [19] if the height of slope is larger than 45 m. In this study, we assessed the Hmax using the modified formulation Hmax-Huang. The necessary parameters and probability calculations in the study area are summarized in Table 5. A final assessment of the slopes (see Table 5) was performed by choosing the largest failure probability determined via the two analyses.(12)SIRS=RIRS×SWE,SSPA=RSPA×SWE×SME,SCD=RCD×SWE,(13)ϕSRM=SIRS×0.2417×SSPA×52.12×SCD×5.779,CSRM=SIRS×94.27×SSPA×28629×SCD×3593,(14)Hmax−SSPC=1.6×104×CSRM×sindipslope×cosϕSRM1−cosdipslope−ϕSRM,Hmax−Huang=0.00651+0.00037mi1.5×σciγeGSI−0.0003mi+0.0483.Figure 8
Flowchart of the SSPC methods determined by orientation-independent failure (slope 1).Table 5
Summary of the orientation-independent stability probability at the investigated slopes.
SlopeHslope (m)dipslope (°)CSRM (MPa)ϕSRM(°)Hmax (m)Hmax/HslopeϕSRM/dipslopeSlope stability probability1105630.58437.841322.5612.600.60＞95%2105631.52553.715044.8548.050.85＞95%3180731.03039.272010.8811.170.54＞95%4180731.38545.023045.1616.920.62＞95%590730.64830.891322.5614.700.42＞95%665730.88241.431849.9828.460.57＞95%


## 3.1. Key Points of the SSPC

The SSPC method encompasses a three-step evaluation of the slope stability probability, accordingly identifying three different rock masses (ERM, exposure rock mass; RRM, reference rock mass; SRM, slope rock mass) during evaluation [16].(a)
ERM: exposed rock mass, which is directly observed on the exposure site of a natural or an old engineering slope(b)
RRM: reference rock mass, which is the theoretical and imaginary fresh rock mass, undistributed due to the excavation(c)
SRM: slope rock mass, which is the existing or proposed new slope to be cut (see Figure4)(d)
Two types of slope failure modes (orientation independent and orientation dependent) and the corresponding stability probability estimation methods are considered, with clear and simple needed-data collecting procedureFigure 4
Sketch of exposures in rock masses of various degrees of weathering and different types of excavation indicating the concept of the reference rock mass.Figure5 is the schematic diagram of the SSPC method; in the SSPC system, the slope stability probability can be evaluated on the basis of parameters obtained from the investigated exposure rock mass, such as the intact rock strength (IRS), discontinuity spacing (SPA), and condition of the discontinuities (CD). Obviously, the parameters obtained on the outcrop are significantly affected by weathering or excavation disturbances. The parameters of the ERM with different weathering and excavation disturbance degrees in the same geotechnical unit can be converted to the RRM parameters [16]. The SRM stability is determined from the RRM with the adjustment of the parameters of SRM.Figure 5
Flowchart of the SSPC method (modified after Canal A and Akin M, 2016).The shear strength parameters of the rock mass including internal friction angleϕmass and cohesion Cohmass are used to assess the slope stability together with the height of the investigated slope (Hslope) [22]. In case the dip of slope dipslope is bigger than the internal friction angle ϕmass, the maximum height of a stable slope (Hmax) can be determined by some empirical equations. The orientation-independent stability probability can be assessed using the parameters of Hmax, Hslope, ϕmass, and dipslope. In addition, the probability of orientation-dependent stability can also be assessed according to the judgment graphs of the SSPC methods.


## 3.2. Calculation of the Shear Strength Parameters of the RRM

Rock mass shear strength calculation is an important step in SSPC system; when calculation is carried out, parameters such as the intact rock strength (IRS), discontinuity spacing (SPA), roughness, infill, and karst are considered together. The IRS obtained in the laboratory or by the in situ test is divided by the weathering degree factor (WE) for calculating the reference rock intact rock strength (RIRS, see equation (1)). IRS is originally estimated using hammer blows and figure pressure; in this study, laboratory tests were performed, and the results show that intact rock strength of the fresh sandstone ranges from 136 MPa to 274 MPa, with an average value of 206 MPa. In addition, the slightly weathered sandstone has an average value of 148 MPa [23].(1)RIRS=IRSWE.The RSPA (discontinuity spacing of RRM) is determined considering three discontinuity sets that reveal minimum spacing values under the condition of more than three discontinuity sets revealed in the investigated rock mass. Consequently, factors 1, 2, and 3 are obtained using the graph presented in Figure6. Then, SPA is calculated by equation (2), and the RSPA is calculated by equation (3), considering the factors of the weathering degree (WE) and method of excavation (ME). Referring to [15, 16], values of the WE and ME can be determined. In this paper, the weathering degree is divided according to the total joint number in a 5 m section of the prospecting tunnel, which is shown in Table 3.(2)SPA=Factor1×Factor2×Factor3,(3)RSPA=SPAWE×ME.Figure 6
Factor determination graph in accordance with the discontinuity spacing [16].Table 3
Weathering degree and its classification.
DegreeJoint number in a 5 m sectionValue of WEComplete50–600.35High40–500.62Moderate-high30–400.77Moderate-slight20–300.92Slight10–200.95Fresh0–101.00TC, as the condition factor of a discontinuity, is calculated by equation (3). Here, Rl is a the large-scale roughness, Rs is the small-scale roughness, and Im and Ka are the factors of infill and karst, respectively. Considering weathering degree correction, TC of the reference rock mass named RTC is defined by equation (5).(4)TC=Rl×Rs×Im×Ka,(5)RTC=TC1.452−1.22×e−WE0.5.In the SSPC system, the weighted discontinuity condition CD is calculated by equation (5). Here, DS represents the discontinuity spacing. Similarly, the reference discontinuity condition (RCD) is calculated considering the weathering degree factor in Equation (7).(6)CD=TC1/DS1+TC2/DS2+TC3/DS31/DS1+1/DS2+1/DS3,(7)RCD=CDWE.The friction angle (ϕRM) and cohesion (CRM) of a rock mass are calculated by equations (8) and (9). Here, RIRS is the intact rock strength, RSPA is the spacing, and RCD is the condition of discontinuities of the reference rock mass.(8)ϕRM=RIRS×0.2417×RSPA×52.12×RCD×5.779,(9)CRM=RIRS×94.27×RSPA×28629×RCD×3593.


## 3.3. Orientation-Dependent Stability Assessment of the SRM

As mentioned above, in the SSPC system, both orientation-dependent and orientation-independent conditions are considered in the slope rock mass stability evaluation. As the term suggests, failures controlled by discontinuities such as planar sliding and toppling usually occur in the orientation-dependent stability analysis, while failures occur irrespective of a certain sliding surface in orientation-independent stability analysis. However, the probability of wedge failures cannot be evaluated in the SSPC system.For the former type of stability assessment, factors such as the discontinuity condition (STC) and the apparent angle of the discontinuity dip in the direction of the slope dip (AP) are considered for evaluating the stability probability. The AP is obtained based on equation (10), where αs represents the direction, αj represents the dip direction of the discontinuity, and βj represents the discontinuity dip. Meanwhile, the discontinuity condition of the slope (STC) is determined by equation (11).(10)AP=arctancosαs−αjtanβj,(11)STC=RTC×1.452−1.220×e−SWE0.5.For sliding failure, a relationship graph (see Figure7(a)) between the STC and AP is employed to assess the occurrence probability of the slope. Furthermore, a relationship graph of the STC, AP, and dipslope (see Figure 7(b)) is employed to evaluate the occurrence probability of the slope for toppling failure. In this paper, the probability results and the necessary parameters for probability calculations in the study area are summarized in Table 4.Figure 7
Flowchart of the SSPC methods determined by sliding and toppling (slope 1). (a) Sliding. (b) Toppling.
(a)(b)Table 4
Orientation-dependent stability probabilities of discontinuities at the typical investigated slopes.
SlopeDiscontinuitySTCAPSliding probabilityToppling probabilitySlope stability probability1B10.45−65.78100%95%70%J20.2725.5870%100%J30.2773.80100%100%2B10.4558.23100%100%95%J10.2721.8895%100%J20.2782.28100%100%3B10.61−42.41100%＞95%95%J10.6545.65＞95%100%J20.42−54.08100%95%4B10.61−42.41100%＞95%95%J10.6545.65＞95%100%J20.42−54.08100%95%5B10.76−60.26100%＞95%＞95%J10.6537.73＞95%100%J20.65−24.76100%＞95%6B10.7667.37＞70%100%＞70%J10.659.85＞95%100%J20.6581.33100%100%


## 3.4. Orientation-Independent Stability Assessment of the SRM

Parameters needed in the calculation of stability of slope rock mass such as SIRS, SSPA, and SCD are determined as equation (12), in which the RRM values are corrected by the the weathering degree (SWE) and method of excavation (SME) for existing natural/excavated slopes.Accordingly, the friction angle and cohesion of the slope mass are defined by equation (13). Obviously, an orientation-independent stability problem cannot occur under the condition of the dipslope ≤ ϕSRM of the investigated slopes. However, the stability condition is evaluated on the basis of the maximum slope height (Hmax) [14, 16]. The orientation-independent slope stability probability can be easily determined by the chart seen in Figure 8. However, the assessment method of the maximum slope height (Hmax) was modified by Li et al. [19] if the height of slope is larger than 45 m. In this study, we assessed the Hmax using the modified formulation Hmax-Huang. The necessary parameters and probability calculations in the study area are summarized in Table 5. A final assessment of the slopes (see Table 5) was performed by choosing the largest failure probability determined via the two analyses.(12)SIRS=RIRS×SWE,SSPA=RSPA×SWE×SME,SCD=RCD×SWE,(13)ϕSRM=SIRS×0.2417×SSPA×52.12×SCD×5.779,CSRM=SIRS×94.27×SSPA×28629×SCD×3593,(14)Hmax−SSPC=1.6×104×CSRM×sindipslope×cosϕSRM1−cosdipslope−ϕSRM,Hmax−Huang=0.00651+0.00037mi1.5×σciγeGSI−0.0003mi+0.0483.Figure 8
Flowchart of the SSPC methods determined by orientation-independent failure (slope 1).Table 5
Summary of the orientation-independent stability probability at the investigated slopes.
SlopeHslope (m)dipslope (°)CSRM (MPa)ϕSRM(°)Hmax (m)Hmax/HslopeϕSRM/dipslopeSlope stability probability1105630.58437.841322.5612.600.60＞95%2105631.52553.715044.8548.050.85＞95%3180731.03039.272010.8811.170.54＞95%4180731.38545.023045.1616.920.62＞95%590730.64830.891322.5614.700.42＞95%665730.88241.431849.9828.460.57＞95%


## 4. Discussion

Results seen in Tables4 and 5 show that the calculated slopes were defined as stable. In addition, we also calculated the slope stability by the Geostudio software according to the step of the building model, parameters inputting, and calculating. Figure 9 is the typical simulation model of slope 2; compared with the outcome through the Geostudio software (Table 6), the results prove the validity and convenience of the SSPC methods introduced above. In addition, it is important selecting the suitable discontinuities for assessment of the stability probability in the SSPC method. In this study, statistical dominant discontinuities obtained in the prospecting tunnels and natural outcrops were selected, but not the geological dominant discontinuities only obtained and determined by the natural outcrops.Figure 9
Typical simulation model of slope 2 using the Geostudio software.Table 6
Summary of the stability assessment result using the Geostudio software and the SSPC method.
SlopeSafety factor values under different conditionsStability assessment result by GeostudioStability probability by the SSPC methodNormalRainstormEarthquake11.3251.1981.206Stable70%21.1881.3011.377Stable95%31.4761.2661.376Stable95%41.4081.2851.293Stable95%51.4801.2791.290Stable＞95%61.2821.4051.135Stable＞70%


## 5. Conclusions

In this study, the SSPC method based on geological data obtained in the prospecting tunnels was presented, and the slope stability probability of very high (50–300 m) and steep (60°–75°) cutting slopes in the sandstone unit was investigated using the proposed system. The following conclusions can be drawn.Firstly, three sets of joints were presented in each studied slope. To overcome bias, laboratory data of the uniaxial compressive strength and rock mass strength parameters can be used for SSPC directly.Secondly, statistically dominant discontinuities obtained in the prospecting tunnels and natural outcrops were suitable for the SSPC method, but not the geological dominant discontinuities only obtained and determined by the natural outcrops.Finally, the formula of the critical slope height is optimized and applied to the stability evaluation, and the SSPC method based on geological data obtained in the prospecting tunnels can be accurately applied to the stability evaluation of high and steep rock slopes.



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*Source: 8889526-2021-04-20.xml*