Stability Analysis and Reinforcement of a High-Steep Rock Slope with Faults : Numerical Analysis and Field Monitoring

Sanjiangyuan Ecological and Plateau Husbandry National Key Laboratory, Department of Water Conservancy and Electric Power, Qinghai University, Xining, Qinghai 810016, China Key Laboratory for Special Area Highway Engineering of Ministry of Education, School of Highway, Chang’an University, Xi’an, Shannxi 710064, China Research and Development Center of Transport Industry of Technologies, Materials and Equipment of Highway Construction and Maintenance, Gansu Road & Bridge Construction Group, Lanzhou, Gansu 730030, China


Introduction
Faults or weak intercalations can adversely affect the stability of rock slopes during the construction process and also make the stability analysis become more complicated [1][2][3].e slope stability analysis was originally developed based on the analysis of lateral soil pressure and foundation bearing capacity in soil mechanics.Coulomb's method [4] for estimating the lateral soil pressure on retaining walls and Rankine's method [5] for calculating active and passive soil pressures are considered as the origin of the limit equilibrium method of the slope stability analysis.
is traditional method has also been continuously improved, including Swedish method [6], Bishop method [7], simplified Janbu method [8], Spencer method [9], Morgenstern-Price method [10], and Sarma method [11].Since the 1970s, with the rapid development of the computer technology, various numerical analysis methods including finite element, finite difference, and discrete element methods have been proposed and applied to slope stability analyses [12][13][14], which significantly improved the speed and accuracy of a slope stability analysis.In recent years, the strength reduction method proposed by Zienkiewicz et al. [15] has gradually become to the focus of theoretical research and widely used in engineering projects for slope stability analyses [16][17][18][19][20][21][22][23].
is case study focuses on evaluating how the excavation process can influence the stability of a high-steep rock slope with faults and the effectiveness of the proposed reinforcement method.A 3D finite difference model was established based on the strength reduction method using FLAC3D software.
e movement of the rock slope was monitored during the excavation process and compared to the numerical analysis results.e rock slope is a cutting slope located behind the powerhouse of the Yangqu hydropower station at the Hainan Tibetan Autonomous Prefecture in Qinghai province, China (Figure 1).e height of the slope is 118.6 m, and the elevation at the toe of the slope is 2560.4 m.

Site Descriptions and Soil Properties
e cross-sectional profile of the slope before and after the excavation is shown in Figure 2. e original slope was consisted of four layers: (1) the slope surface was covered with loosened quaternary soil (Q4pl + dl); (2) the second layer was a highly weathered silty slate with 25 to 30 m thickness; (3) the third layer was a layer of moderately weathered sandy slate with phyllite with 15 to 45 m thickness; and (4) the bottom rock below the ground water table (2605 m) was slightly weathered sandy slate.
Based on the site investigation, there were two faults (f14 and f20) existing in the rock slope, and both of the two faults were approximate 50 cm wide filled with crushed rocks and clay.e angles of the f14 and f20 faults were 72 °and 75 °, respectively (Figure 2).Before the excavation, no landslide or large deformation was observed.

Mechanical Properties of Rock Mass and Structural Plane.
e mechanical properties of representative samples collected from each of the layers and the two faults are summarized in Tables 1 and 2, respectively.e elastic modulus and Poisson's ratio of the samples were measured by uniaxial compression tests, and the cohesion and friction parameters were measured by direct shear tests.
e required bulk modulus (K) and shear modulus (G) were calculated based on the measured elastic modulus and Poisson's ratio.e intact rock properties determined using the laboratory tests may be different with those of the rock mass, and some empirical correlations were found in previous studies (e.g., [24]).

3.1.
e Strength Reduction Method.According to the strength reduction method, the FOS of a slope is defined as the ratio between the actual shear strength and the shear strength when the critical failure occurred.When applying the strength reduction method in finite difference models, the gravitational acceleration of the rock and soil is usually considered as a constant.By reducing the cohesion (c) and internal friction angle (φ) of the soils gradually, a new set of shear strength parameters can be generated after dividing both parameters by a reduction factor (F s ), as shown in equations ( 1) and (2).Based on the Mohr-Coulomb failure criterion, the FOS of the slope is smallest F s before failure: Compared to the traditional slope stability analysis method, the strength reduction method combining with the finite difference method has the following advantages: (1) Both the constitutive relationships of rock and soil and the effect of deformation on stress are considered in the method (2) It does not need to assume the shape of the slip surface or to divide the slope into many strips for calculations (3) Failure processes and actual shape of slip surfaces can be simulated (4) Support structures and reinforcement can be simulated

e FLAC3D Model.
To explore the influence of the faults on the stability of the slope during excavation, a 3D model was established based on the actual geological conditions to simulate the excavation process, as shown in Figure 3. e simulated slope was 175 meter in length (ydirection), 85 meter in width (x-direction), and 150 meter in height (z-direction), and the tetrahedron mesh was used.In this study, the rock mass and faults were simulated using 3D solid elements, and the interface between the faults and rock mass was treated as a continuous medium according to [25], and the Mohr-Coulomb plastic model was selected as the constitutive model.In reality, it is possible that the rock mass contains yield regions with the initial stress state.erefore, the initial stress state of the rock mass was calculated using the elastic-plastic method in each model, which is more reasonable than using the elastic method.
e simulation process was divided into three stages: (1) the cohesive force and tensile strength of the components were set to very large values, and the elastic method was used for the simulation until the system reaches to the force equilibrium state under gravity; (2) the cohesive force and tensile strength were then reset to initial values to solve the plastic stage until the system reaches to the force equilibrium state; and (3) the velocity and displacement elds of each model were then cleared, and only the stress eld was retained.After calculating the initial stress eld of each model, the null model in FLAC3D was used to simulate the excavation process, and the elastic-plastic solution of the Mohr-Coulomb constitutive model was used again until the rock mass and faults system reaches to the force equilibrium state.
Four di erent fault condition combinations were evaluated using the 3D nite di erence model, as shown in Table 3.
In the 3D model, the boundary of the X-direction (short edge) and Y-direction (long edge) was restraint in normal direction.While the bottom boundary of the Z-direction was fully constraint, and the top was free.e excavation process was simulated using six stages in the model, as shown in Figure 3.
ree commonly used criteria for determining whether a slope reached to the critical failure state in the numerical analysis are listed below:

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(1) A sudden large displacement observed: When increasing the reduction factor (F s ), a sudden large displacement of the slope occurred indicating the slope reached to the critical failure state.(2) Plastic zone connected: Due to the elastoplastic behavior of soil and rock masses, the plastic deformation occurs when the stress reaches to a certain level.It is believed that the failure of rock mass is closely related to the expansion of plastic strain zones.If the slope failure occurred, the plastic strain zones have to be connected which will cause the overall instability of the slope.(3) e numerical model cannot converge: When a slope reaches to the critical failure state, a sudden large deformation on the slip surface will occur, so changes of the displacement and strain level will not remain at a constant level, and the numerical model cannot nd a solution which can satisfy both the static equilibrium and the stress-strain relationship.Consequently, the static equilibrium equations have no solution, and the numerical model cannot converge.
According to Zhao et al. [26], when a slope reaches to the failure state, neither of the force or displacement can converge.
erefore, they believe that the static equilibrium equations have no solution; so, it can be an indicator of the slope failure.Also, Gri ths and Lane [27] and Dawson et al. [28] concluded that the nonconvergence is a rational sign for a slope failure in numerical analyses.Hence, in this study, the nonconvergence is used as the slope failure criterion.

Influences of the Faults on the Slope Stability during Excavation
e numerical analysis results of the four di erent cases (Table 1) are compared in Figure 4.For all the four cases, the FOS of the slope decreases during the excavation process.For the Cases 1 and 2, changes of the FOS yield similar trends, and the FOS of the slope without a fault is slightly higher than that of the slope with fault f14 during excavation.
is phenomenon indicates that the fault f14 further away from the slope surface has little in uence on the stability of the slope during the excavation process.Compared to the Cases 1 and 2, the FOS of the Cases 3 and 4 shows greater reduction during the excavation process and signi cantly decrease after the excavation Stage 5 begun.e comparison results suggest that fault f14 further away from the slope surface has little in uence on the stability of the slope, but the fault f20 close to the slope surface can signi cantly in uence the FOS of the slope.
e excavation Stage 1 of the slope was mainly in the Layer 1, so the calculated FOS of the four cases are approximately the same.For the Case 4, the newly formed slope after excavation between the Stages 1 and 2 of the excavation was small; so, the reduction in the FOS was relatively small.From Stage 3 to 5, the high-steep slope was formed, but the numerical analysis results showed relatively small reduction in the FOS, which indicates that the rock mass close to the toe of the slope can prevent the slope from moving downward.However, after the excavation Stage 5 completed, the rock close to the toe of the slope was almost removed, so the FOS signi cantly reduced from 1.93 to 1.46.
For the Case 4, according to the maximum shear strain increment contour plot after the excavation (Figure 5), the potential failure region of the slope distributed along the Advances in Civil Engineering fault f20, but there was no potential slip zone around the fault f14.By analyzing the maximum shear strain increment calculation, fault f20 can yield more signi cant in uence on the slope stability during the excavation, which is consistent with the nding derived from the FOS aspect.

Effectiveness of the Proposed Reinforcement Method
Although the slope was under the e ect of two faults, its FOS still reached to 1.46, which is stronger than the required FOS of the rst-grade slope (1.25 to 1.3) under normal operation condition [29].e exposed area of the fault f20 and the nearby fractured rock mass may have considerable in uence on the slope stability under external loads, including construction equipment and disturbances caused by the construction.erefore, in this study, we proposed using prestressed anchor cables to reinforce the slope, as shown in Figure 6.
To reinforce the fault f20, the 1000 and 2000 kN prestressed anchor cables were installed with 10-degree angle and 4 m by 4 m spacing, as shown in Figure 6. e properties of the prestressed anchorage cable and the grouting materials are listed in Tables 4 and 5, respectively.e established 3D model was also used to evaluate the e ectiveness of the proposed reinforcement method for Case 4 with two faults.e prestress anchor cables were simulated using the cable element in the FLAC3D, and the parameters of the anchorage are set to the maximum value to simulate the tray.e prestress was loaded on the free segment of the cable.Due to the excavation angles of the Stages 1 and 2 were relatively small, no prestressed anchor cable support was installed.For the rest excavation stages, the excavated area was anchored immediately after completing each stage.
To verify the numerical simulation results and also evaluate the e ectiveness of the proposed reinforcement method, the calculated displacement results were compared to the eld displacement monitoring data collected from the monitoring Point Y9 of slope.e position of the monitoring Point Y9 is shown in Figure 6.
Figure 7 shows the calculated and eld monitored downward displacement data of the monitoring Point Y9.It has been found that from June 20 to August 20, 2015, the displacement of the Point Y9 increased by 19.69 mm.According to eld construction reports, a local collapse happened on July 7, 2015, at the exposed area of fault f20 from the elevation of 2603 to 2572 m, which resulted in an obvious slope displacement.In the later period, the displacement of the monitoring point kept increasing during the excavation process, because the construction platform was disturbed by external force of the construction tra c and equipment, and the rock mass close to the toe of the slope was removed.
e slope displacement reached to 34.59 mm when the excavation of the slope was completed.Several treatments were then applied on the collapse area such as back lling of microexpansive self-compacting concrete and installing the prestressed anchor cables after the excavation Stages 4 and 5. e monitoring data show that the displacement rate of the monitoring Point Y9 started reducing after the reinforcement.e maximum displacement (35.81 mm) was begun to be monitored on November 4, 2016, and the displacement remained at a relatively constant level.Based on the eld monitoring data, the displacement reduced to 22.51 mm (∼37%) on February 19, 2018, and there was a trend to further decrease, which indicates the reinforcement measure can e ectively improve the stability of the rock slope.
According to the eld displacement monitoring data, the maximum displacement value of the slope was 30.48 mm without any reinforcement treatments, while the displacement reduced to 17.63 mm after the reinforcement.e calculated values are slightly smaller than the eld monitoring data. is discrepancy may be due to three reasons: (1) the external force disturbance (i.e., construction tra c and equipment) on the platform was not simulated in the numerical analysis, (2) the collapse rock mass around the monitoring Point Y9 was not included in the model, and (3)  the complicated fractured structures of the faults were simpli ed in the numerical simulation model.e calculated FOS values of the rock slope with and without the reinforcement are compared in Table 6.Because the anchor cable was installed after the Stage 3 completed, the FOS of the Stages 1 and 2 was the same.e FOS of the Stages 3, 4, and 5 was improved after the reinforcement installed.e FOS of the slope after the excavation Stage 6 increased by 19.2% (from 1.46 to 1.74) with the reinforcement treatment, which indicates that installing the anchorage measure is an e cient way to improve the stability of the rock slope during the excavation process.

Summary and Conclusions
In this study, the stability of a high-steep rock slope with two faults during the excavation process and the e ectiveness of the proposed reinforcement method were numerically evaluated using the strength reduction method.A 3D nite di erence model was established in FLAC3D software to evaluate the in uence of various fault combination conditions on the stability of the rock slope during excavation.e FOS of the slope with and without installing the prestressed anchor cables compared.To verify the numerical simulation results, the calculated displacement data were compared to eld displacement monitoring data.Several key ndings from this study are summarized below: (1) Based on the numerical analysis results of the four simulated fault conditions, it has been found that the fault f20 close to the slope surface had more signi cant in uence on the slope stability, while the fault f14 further away from the surface had little in uence.(2) e numerical analysis results showed that the potential slip surface of the slope is along the fault f20.During the excavation process, the fault f20 and its in uenced zone were prone to local instability under external force caused by the construction tra c and equipment loads. is nding was veri ed by an actual local landslide occurred at the slope surface.(3) Both the numerical simulation results and eld monitoring data showed that the strength reduction method performed well for simulating eld conditions, and the proposed reinforcement method of installing the prestressed anchor cables can e ectively reduce the downward movement and improve the stability of the rock slope with faults.
Data Availability e data used to support the ndings of this study are available from the corresponding author upon request.Advances in Civil Engineering

Figure 2 :
Figure 2: Representative geological cross-sectional pro le of the slope.

Figure 3 :
Figure 3: e 3D nite di erence model of the rock slope with two faults.

Figure 4 :Figure 5 :
Figure 4: Changes of the FOS of the rock slope with di erent fault conditions during excavation.

Figure 6 :
Figure 6: e cross-sectional layout of the prestressed anchorage cables installed in the slope.

Figure 7 :
Figure 7: Numerical calculated and eld monitored downward displacement data of the monitoring Point Y9 before and after the reinforcement.

Table 1 :
Mechanical properties of the intact rock specimens.

Table 2 :
Mechanical properties of the two faults.

Table 3 :
Mechanical properties of the rock masses.

Table 4 :
Parameters of the prestressed anchorage cable.

Table 5 :
Parameters of the grouting.

Table 6 :
Calculated FOS values of the rock slope with and without the reinforcement.