Gravity Increase Method Research Articles

3D slope stability analysis considering strength anisotropy by a micro-structure tensor enhanced elasto-plastic finite element method

This article presents a micro-structure tensor enhanced elasto-plastic finite element (FE) method to address strength anisotropy in three-dimensional (3D) soil slope stability analysis. The gravity increase method (GIM) is employed to analyze the stability of 3D anisotropic soil slopes. The accuracy of the proposed method is first verified against the data in the literature. We then simulate the 3D soil slope with a straight slope surface and the convex and concave slope surfaces with a 90° turning corner to study the 3D effect on slope stability and the failure mechanism under anisotropy conditions. Based on our numerical results, the end effect significantly impacts the failure mechanism and safety factor. Anisotropy degree notably affects the safety factor, with higher degrees leading to deeper landslides. For concave slopes, they can be approximated by straight slopes with suitable boundary conditions to assess their stability. Furthermore, a case study of the Saint-Alban test embankment A in Quebec, Canada, is provided to demonstrate the applicability of the proposed FE model.

The three-dimensional stability analysis of piled slopes in unsaturated and inhomogeneous soils with nonlinear failure criterion

Under the nonlinear Mohr-Coulomb (MC) failure criterion, based on the upper-bound limit analysis theorem, the three-dimensional(3D) stability of piled unsaturated inhomogeneous slopes is analyzed. By incorporating the nonlinear strength parameters c t and φ t, the energy balance equation is established, and the explicit expression of slope safety factor (F S) is derived by the gravity increase method (GIM). In addition, a genetic algorithm (GA) is used to calculate the minimum F S. The results obtained were compared with those of existing literature to verify the effectiveness of the method used in this paper. The influence of nonlinear parameters on slope stability was studied through parameter analysis. The results show that the nonlinear parameters of soil have a significant influence on the stability of piled slopes. The F S increases with the increase of nonlinear coefficient and uniaxial tensile strength and decreases with the increase of initial cohesion of soil. In addition, the critical slip surface of the slope becomes shallower with the weakening of soil nonlinearity. Furthermore, ignoring the suction effect will overestimate the slope stability, and the slope stability intensified with decreased soil inhomogeneity.

Three-Dimensional Stability of Unsaturated Soil Slopes Reinforced by Frame Beam Anchor Plates

The frame beam anchor plate (FBAP) is a new supporting structure to reinforce backfill. The current studies of slope stability concentrate on homogeneous isotropic dry or saturated slopes according to two-dimensional assumptions. In engineering practice, however, the soils are heterogeneous and anisotropic and exhibit evident unsaturated characteristics, and the failure surface shows obvious three-dimensional (3D) characteristics universally. A new method for evaluating the 3D stability of unsaturated soil slopes reinforced with FBAPs is established in this paper. The upper-bound analytical solution of slope safety factor (Fs) is derived based on the energy balance equation incorporated with the 3D spiral failure mechanism and the gravity increase method (GIM). Comparisons verified the effectiveness of the methodology and the optimization program. The influence of unsaturated characteristics, support structure design parameters, and seismic force on the 3D slope stability is evaluated through parameter analysis. The results show that the shear strength prediction model is crucial in slope stability assessments. The stability of slopes can be significantly improved by about 29%–52% by using FBAPs. Seismic action has a significant negative impact on the slope stability. When kh increases from 0 to 0.3, Fs generally decreases by about 40%–55%.

Analytical approach for stability of 3D two-stage slope in non-uniform and unsaturated soils

In geological engineering, the unsaturation and non-uniformity of soil have significant influence on slope stability. However, they were common neglected in published literature. Based on the three-dimensional (3D) rotational failure mechanism, this paper introduces a method that combines the gravity increase method and the upper bound theorem, to evaluate the factor of safety (FS) of 3D stepped slope in non-uniform and unsaturated soils. The soil cohesion increases linearly with depth, and three nonlinear unsaturated shear strength models are adopted in this study. After the calculations of internal energy dissipation rate and external work rate, the analytical formula of FS is derived, and the lowest FS value is obtained through optimization. To prove the validity of the proposed method, the present results are compared with previously published solutions. A parametric study is carried out, and the influences of a number of factors on FS are discussed. For non-uniform and unsaturated soils, the new formula for calculating the FS of 3D two-stage slopes is presented for practical use in geological engineering.

Stability evaluation and potential failure process of rock slopes characterized by non-persistent fractures

Abstract. Slope failure, which causes destructive damage and fatalities, is extremely common in mountainous areas. Therefore, the stability and potential failure of slopes must be analysed accurately. For most fractured rock slopes, the complexity and random distribution of structural fractures make the aforementioned analyses considerably challenging for engineers and geologists worldwide. This study aims to solve this problem by proposing a comprehensive approach that combines the discrete fracture network (DFN) modelling technique, the synthetic rock mass (SRM) approach, and statistical analysis. Specifically, a real fractured rock slope in Laohuding Quarry in Jixian County, China, is studied to show this comprehensive approach. DFN simulation is performed to generate non-persistent fractures in the cross section of the slope. Subsequently, the SRM approach is applied to simulate the slope model using 2D particle flow code software (PFC2D). A stability analysis is carried out based on the improved gravity increase method, emphasizing the effect of stress concentration throughout the formation of the critical slip surface. The collapse, rotation, and fragmentation of blocks and the accumulation distances are evaluated in the potential failure process of the rock slope. A total of 100 slope models generated with different DFN models are used to repeat the aforementioned analyses as a result of a high degree of variability in DFN simulation. The critical slip surface, factor of safety, and accumulation distance are selected by statistical analysis for safety assurance in slope analysis and support.

Stability analysis of cohesive soil embankment slope based on discrete element method

In order to study the safety factor and instability process of cohesive soil slope, the discrete element method(DEM) was applied. DEM software PFC2D was used to simulate the triaxial test to study the influence of the particle micro parameters on the macroscopic characteristics of cohesive soil and calibrate the micro parameters of DEM model on this basis. Embankment slope stability analysis was carried out by strength reduction and gravity increase method, it is shown that the safety factor obtained by strength reduction method is more conservative, and the arc-shaped feature of the sliding surface under the gravity increase method is more obvious. Throughout the progressive failure process, the failure trends, maximum displacements, and velocity changes obtained by the two methods were consistent. When slope was destroyed, the upper part was cracked, the middle part was sheared, and the lower part was destroyed by extrusion. The conclusions of this paper can be applied to the safety factor calculation of cohesive soil slopes and the analysis of the instability process.

Stability analysis of flawed rock slope by using virtual-bond-based general particles dynamics

General particle dynamics code (GPD) with a virtual bond model is adopted to investigate the stability of rock slopes subjected to gravity. The natural discontinuities are represented by straight flaws in the numerical model. The failure process of rock samples containing three pre-existing and four pre-existing flaws subjected to uniaxial compression is simulated. The numerical failure processes of rock samples are in good agreement with the experimental observations as well as the complete stress–strain curves. Moreover, six en-echelon flaw arrays including collinear flaw array, en-echelon flaw array with bridge angle of 90°, en-echelon flaw array with bridge angle more than 90°, en-echelon flaw array with bridge angle less than 90°, multiple rows of en-echelon flaws with doubly periodic rectangular array, multiple rows of en-echelon flaws with diamond-shaped array in rock slope are studied. The crack initiation, propagation and coalescence process in rock slopes with six en-echelon flaw arrays subjected to gravity are analyzed. Two crack initiation modes including primary crack and secondary crack are found as well as nine crack coalescence modes. The stress distributions as well as displacement fields are investigated during the crack evolution. The gravity increase method is implemented into the VB-GPD to obtain the safety factor of rock slopes. The proposed method was then verified by the case study of the Xingluokeng mine in China. The results indicate a good accordance between simulation and field monitoring. This study reveals that the proposed method can tackle flawed rock slope failure problems.

Elastoplastic Cosserat continuum model considering strength anisotropy and its application to the analysis of slope stability

Aiming at solving the problems of strength anisotropy and strain localization of cohesive soil, Pietruszczak’s method, in which the microstructure tensor is combined with stress invariance, is developed to analyze the cohesion anisotropy and is introduced into the Drucker-Prager constitutive model under Cosserat continuum theory. A consistent algorithm of the corresponding constitutive model is derived. The characteristics of strength anisotropy and the reliability of the developed numerical method are verified by the experiments in laboratory. The importance and necessity of developing the numerical model with strength anisotropy under the framework of Cosserat theory are evaluated via simulation of a plane strain compression model. It indicates that the degree of the cohesion anisotropy has an important influence on the bearing capacity, and that the numerical model can overcome the ill-posedness of the mesh sensitivity and maintain the well-posedness of the strain localization problem. Furthermore, the effects of strength anisotropy and strain softening on the safety factor of the slope are analyzed via the gravity increase method. It is demonstrated that the Cosserat continuum model can effectively overcome the problems of mesh-dependence encountered by the classical continuum model and yield a reasonable safety factor with mesh refinement.

Stability analysis of strain-softening slopes based on the gravity increase method

With traditional slope stability analysis methods, it is difficult to accurately describe the progressive failure process and dynamic variation law of slope stability. The strain-softening constitutive model was therefore used to simulate the progressive failure process of a strain-softening slope based on the gravity increase method (GIM), with the displacement interface employed to determine the sliding surface. A sensitive analysis of the characteristic parameters within the softening stage was then conducted. The results are as follows: There are similar space-time evolution laws of residual strength factor and shear strain increment, with failure starting from the slope toe and extending gradually. The sliding surface of strain-softening slopes is located between that of the slope with peak strength and the sliding surface of the slope with residual strength. The stability coefficient shows an exponential growth trend with the increase of residual cohesion and residual plastic shear strain threshold, with a positive linear correlation between the residual friction angle and stability factor. The residual friction angle is the most sensitive factor in slope stability, followed by the residualcohesion, with the residual plastic shear strain threshold being the least sensitive.

Consistency analysis of Hoek–Brown and equivalent Mohr–coulomb parameters in calculating slope safety factor

In slope stability analysis, the Mohr–Coulomb (MC) criterion is usually adopted, however, it has some limitations with regard to the rock mass description. Then the Hoek–Brown (HB) criterion was created and then widely used, and the equivalent Mohr–Coulomb (MC) parameters were proposed. However, the consistency of the HB and equivalent MC parameters in calculating slope safety factor remains to be further explored and confirmed. In this study, the gravity increase method and HB parameters were combined to analyze slope stability, and the calculation results of safety factor were compared with those of equivalent MC parameters in the same conditions. This approach was conducted to explore the parameter equivalence by analyzing the consistency of the two safety factors. Then, the HB parameters and slope height (H), which can cause the safety factor distinction (∆Fs), were studied, and the expression of ∆Fs to influencing factors was tested to examine their relationship. The results indicate the following: (1) The HB and equivalent MC parameters are not completely consistent in calculating the slope safety factor, unless the safety factor is relatively small. (2) The sensitivity of the HB parameters to ∆Fs is GSI > D > mi >σci. Moreover, when H is 20 m or 30 m, each HB parameter is linearly related with ∆Fs, in which GSI, mi, and σci are positively correlated with ∆Fs, while D is negatively correlated. (3) The H is found to be in an inversely proportional relationship with ∆Fs. The ∆Fs decreased in a slow downward trend as the H increased. Simultaneously, the linear relationship between HB parameters and ∆Fs is gradually destroyed by the increase of H.

Modification of the gravity increase method in slope stability analysis

The gravity increase method (GIM) has an inherent defect that may result in an incorrectly calculated safety factor or result in a failure to obtain the expected outcome. In this study, the error source of the GIM was quantitatively analyzed through theoretical derivation to address this problem. Hence, the modified gravity increase method (MGIM), which can eliminate the error in the GIM, was developed by adding a correction factor to the friction angle during the gravity increase procedure. The MGIM was comparatively studied by applying the GIM, shear strength reduction method (SSR), and MGIM to homogeneous slope models under different dimensions, and an ACADS (Australian Computer Aided Design Society) test was introduced to validate the applicability of the MGIM to heterogeneous slopes. The analysis results proved that the MGIM does not have the inherent defect present in the GIM, and can provide accurate results in the stability analysis of both homogeneous slope and heterogeneous slopes with various slope angle and slope height. Finally, the MGIM and GIM were applied to the numerical analysis of a geotechnical centrifugal model test of a soil slope. The results indicate that the MGIM is capable of capturing the deformation and failure characteristic of geotechnical centrifugal model test of soil slopes.

Unified Overload Method of Slope Stability Analysis Based on Potential Sliding Direction

The overload method is difficult to be promoted in slope stability analysis for its disunity of loading forms and directions. Based on the traditional overload method and the Strength Reduction Method (SRM) in which the limit equilibrium state of the slope was reached by reducing sliding resisting force without changing the sliding force, a new way to reach the limit equilibrium state of the slope was developed by increasing sliding force without changing resisting force. Referring the loading forms in Gravity Increase Method (GIM) and sliding direction determination in Vector Sum Method (VSM), the theoretical relationship was built between overload coefficient and safety factor of Vector Sum Method (VSM) and the unified overload method based on overall potential sliding direction was proposed. The loading forms and directions were unified by this method, respectively. Sliding surface could be determined while solving the safety factor and the developing direction of overload method in slope stability analysis application was indicated. Three representative slopes with fixed sliding surfaces and two slopes with unknown sliding surfaces were taken as examples to compare results from Limit Equilibrium Method (LEM), Strength Reduction Method (SRM), Vector Sum Method (VSM), Gravity Increase Method (GIM) and overloading method along the horizontal direction with each other. The safety factor resulted from the method proposed in this paper was close to the one from Vector Sum Method (VSM) and the location of sliding surface was close to the one from Strength Reduction Method (SRM). Thus the reliability of the method was testified.

Modelling Coastal Cliff Recession Based on the GIM–DDD Method

The unpredictable and instantaneous collapse behaviour of coastal rocky cliffs may cause damage that extends significantly beyond the area of failure. Gravitational movements that occur during coastal cliff recession involve two major stages: the small deformation stage and the large displacement stage. In this paper, a method of simulating the entire progressive failure process of coastal rocky cliffs is developed based on the gravity increase method (GIM), the rock failure process analysis method and the discontinuous deformation analysis method, and it is referred to as the GIM–DDD method. The small deformation stage, which includes crack initiation, propagation and coalescence processes, and the large displacement stage, which includes block translation and rotation processes during the rocky cliff collapse, are modelled using the GIM–DDD method. In addition, acoustic emissions, stress field variations, crack propagation and failure mode characteristics are further analysed to provide insights that can be used to predict, prevent and minimize potential economic losses and casualties. The calculation and analytical results are consistent with previous studies, which indicate that the developed method provides an effective and reliable approach for performing rocky cliff stability evaluations and coastal cliff recession analyses and has considerable potential for improving the safety and protection of seaside cliff areas.

A Numerical Study on Toppling Failure of a Jointed Rock Slope by Using the Distinct Lattice Spring Model

In this work, toppling failure of a jointed rock slope is studied by using the distinct lattice spring model (DLSM). The gravity increase method (GIM) with a sub-step loading scheme is implemented in the DLSM to mimic the loading conditions of a centrifuge test. A classical centrifuge test for a jointed rock slope, previously simulated by the finite element method and the discrete element model, is simulated by using the GIM-DLSM. Reasonable boundary conditions are obtained through detailed comparisons among existing numerical solutions with experimental records. With calibrated boundary conditions, the influences of the tensional strength of the rock block, cohesion and friction angles of the joints, as well as the spacing and inclination angles of the joints, on the flexural toppling failure of the jointed rock slope are investigated by using the GIM-DLSM, leading to some insight into evaluating the state of flexural toppling failure for a jointed slope and effectively preventing the flexural toppling failure of jointed rock slopes.

Manifold Analysis of the Rock Slope Failure Process Based on the Gravity Increase Method

Manifold Analysis of the Rock Slope Failure Process Based on the Gravity Increase Method

Microseismic Monitoring and Numerical Simulation of Rock Slope Failure

A numerical code with an elastic-brittle failure model has been developed to simulate the seismic activities in rock failure problems. The feasibility in principle of monitoring and prediction of rock failure was numerically simulated. The heterogeneity was considered to be the main reason for the existence of slope failure precursors. Seismic events could be observed in heterogeneous rock, whereas the homogeneous rocks showed an abrupt fracture mode without any early seismic precursors. The failure process of a slope was numerically investigated by using a gravity increase method (centrifugal loading method), and the application of the microseismic monitoring system in the slope was introduced. The numerical results showed that the fracture of the main faults caused the slope slide, and the microcracking caused by the heterogeneity in the faults prior to the landslide could be considered as the precursors of the slope failure, which were captured by the microseismic monitoring system. The microseismic monitoring technique was proved to be successful in predicting the failure in the slope, and the numerical results will be helpful in interpreting the microseismic monitoring results.

Applications of rock failure process analysis (RFPA) method

Brittle failure of rocks is a classical rock mechanical problem. Rock failure not only involves initiation and propagation of single crack, but also is associated with initiation, propagation and coalescence of many cracks. The rock failure process analysis (RFPA) tool has been proposed since 1995. The heterogeneity of rocks at a mesoscopic level is considered by assuming that the material properties follow the Weibull distribution. Elastic damage mechanics is used for describing the constitutive law of the meso-level element. The finite element method (FEM) is employed as the basic stress analysis tool. The maximum tensile strain criterion and the Mohr-Coulomb criterion are utilized as the damage threshold. In order to solve the stability problem related to rock engineering structures, fundamental principles of strength reduction method (SRM) and gravity increase method (GIM) are integrated into the RFPA. And the acoustic emission (AE) event rate is employed as the criterion for rock engineering failure. The prominent feature of the RFPA-SRM and RFPA-GIM for stability analysis of rock engineering is that the factor of safety can be obtained without any presumption for the shape and location of the failure surface. In this paper, several geotechnical engineering applications that use the RFPA method to analyze their stability are presented to provide some references for relevant researches. The principles of the RFPA method in engineering are introduced firstly, and then the stability analysis of tunnel, slope and dam is focused on. The results indicate that the RFPA method is capable of capturing the mechanism of rock engineering stability and has the potential for application in a larger range of geo-engineering.

On the Application of Finite Element Method (FEM) to the Slope Stability Analyses

The finite element method (FEM) is widely adopted in the geotechnical engineering, but there exist some problems in practical applications, such as the lack of unified standard to determine parameters and the limitation of the calculation method. This article determines the reasonable value of Poisson ratio, by comparing different Poisson ratios selected in the strength reduction of FEM calculations, and improves the gravity increase method in order to enhance its accuracy in the gentle slope stability analyses.

Numerical analysis of slope stability based on the gravity increase method

A micromechanical model is proposed for studying the stability and failure process of slopes based on the gravity increase method (GIM). In this numerical model the heterogeneity of rock at a mesoscopic level is considered by assuming that the material properties conform to the Weibull distribution. Elastic damage mechanics is a method used for describing the constitutive law of the meso-level element, the finite element method (FEM) is employed as the basic stress analysis tool, and the maximum tensile strain criterion and the Mohr–Coulomb criterion are utilised as the damage threshold. The numerical model is implemented into the Realistic Failure Process Analysis (RFPA) code using finite element programming, and an extended version of RFPA, i.e., RFPA-GIM, is developed to analyse the failure process and stability of slopes. In the numerical modelling with RFPA-GIM, the critical failure surface of slopes is obtained by increasing the gravity gradually but keeping material properties constant. The acoustic emission (AE) event rate is employed as the criterion for slope failure. The salient feature of the RFPA-GIM in stability analysis of slopes is that the critical failure surface as well as the safety factor can be obtained without any presumption for the shape and location of the failure surface. Several numerical tests have been conducted to demonstrate the feasibility of RFPA-GIM. Numerical results agree well with experimental results and those predicted using the FEM strength reduction method and conventional limit equilibrium analysis. Furthermore it is shown that selection of the AE rate as the criterion for slope failure is reasonable and effective. Finally, the RFPA-GIM is applied to several more complex cases, including slopes in jointed rock masses and layered rock formations. The results indicate that the RFPA-GIM is capable of capturing the mechanism of slope failure and has the potential for application in a larger range of geo-engineering.