Strain-softening Model Research Articles

An Influence Study of Face Length Effect on Floor Stability under Water-Rock Coupling Action

The Taiyuan Formation limestone aquifer and Ordovician limestone aquifer are widely distributed in the coal seam floor of coal measures in North China; the water hazard safety problem of the stope floor under the influence of mining is very prominent. The risk of the water inrush from the coal seam floor is closely related to the degree of full exploitation, so it is necessary to study the stability of the stope floor under aquifer conditions, especially the influence of the working face length effect on floor stability. Through numerical simulation of water-rock coupling action, the mine pressure behaviors of the water-resisting floor under different face lengths were analyzed based on the measured formation permeability coefficient. The Fish program was used to adjust rocks entering the plastic failure state into a strain softening model to investigate the influence of the face length effect, the damage degree of the water-resisting floor, and the morphology and deformation bearing capacity of the failure zone. The results show the following: (1) the face length effect is one of the main influence factors of the failure mode and failure degree of surrounding rocks in the stope; (2) as the face length increases, the obvious pressure relief zone of surrounding rocks presents a staged change, and the obvious pressure relief zone at the seam roof and floor is in an obvious “reverse saddle shape”; (3) the closer to the seam floor, the more remarkable the rock softening characteristic because of the compaction action of gangues caving from the roof; and (4) the rock mass close to the seam floor undergoes local tensile failure, and the water-resisting floor near the coal wall at two sides mainly bears compaction-shear action, leading to compression-shear failure of the rock mass at the floor and formation of water-conducting fractures. The study results can provide a reference for taking precautionary measures of safety mining above a confined aquifer.

Modelling the behaviour of sensitive clays experiencing large deformations using non-local regularisation techniques

This paper presents a methodology to simulate the strain-softening-hardening response of sensitive clays when subjected to extensive remoulding. A non-local strain-softening technique is implemented into the Abaqus Finite Element Analysis (FEA) software through its user defined material subroutine UMAT, in the form of a critical state based strain-softening constitutive model. For the comparison of conventional and non-local formulations, a series of analyses have been performed investigating mesh dependency issues and the validity of a simple softening-scaling rule for practical applications. The non-local model significantly reduces solution mesh-dependency for small-strain analyses of biaxial shear and updated Lagrangian analyses of buried pipe uplift. Finally, the non-local model is applied to simulate undrained cycles of penetration and the consolidated-undrained capacity of a T-bar in kaolin clay. This analysis highlights the limitations of the use of standard element tests (e.g. triaxial tests) to calibrate the model input parameters that control the strain-softening aspect of the constitutive law, and the need for a constitutive law that captures the partial recovery of sensitivity during consolidation.

A New Unified Solution for Deep Tunnels in Water-Rich Areas considering Pore Water Pressure

Pore water pressure has an important influence on the stresses and deformation of the surrounding rock of deep tunnels in water-rich areas. In this study, a mechanical model for deep tunnels subjected to a nonuniform stress field in water-rich areas is developed. Considering the pore water pressure, a new unified solution for the stresses, postpeak zone radii, and surface displacement is derived based on a strain-softening model and the Mogi-Coulomb criterion. Through a case study, the effects of pore water pressure, intermediate principal stress, and residual cohesion on the stress distribution, postpeak zone radii, and surface displacement are also discussed. Results show that the tangential stresses are always larger than the radial stress. The radial stress presents a gradually increasing trend, while the tangential stress presents a trend of first increasing and then decreasing, and the maximum tangential stress appears at the interface between the elastic and plastic zones. As the pore water pressure increases, the postpeak zone radii and surface displacement increase. Because of the neglect of the intermediate principal stress in the Mohr-Coulomb criterion, the postpeak zone radii, surface displacement, and maximum tangential stress solved by the Mohr-Coulomb criterion are all larger than those solved by the Mogi-Coulomb criterion. Tunnels surrounded by rock masses with a higher residual cohesion experience lower postpeak zone radii and surface displacement. Data presented in this study provide an important theoretical basis for supporting the tunnels in water-rich areas.

Simulation of the Failure Process of Submarine Landslides on a Seabed by Coupled MPM

Mei, X.; Ma, G.; Hu, X.; Shi, B., and Huang, D., 2020. Simulation of the failure process of submarine landslides on a seabed by coupled MPM. In: Liu, X. and Zhao, L. (eds.), Today's Modern Coastal Society: Technical and Sociological Aspects of Coastal Research. Journal of Coastal Research, Special Issue No. 111, pp. 231–237. Coconut Creek (Florida), ISSN 0749-0208.Submarine landslides are large-scale natural marine disasters that commonly occur in coastal areas, which significantly threats important subsea infrastructures and offshore facilities. This paper presents a two-dimensional numerical model using the material point method and hydromechanical coupling to simulate a typical submarine landslide, named the Storegga Slide. The numerical simulation for modeling the submarine landslide, consisting of submarine clay with a strain-softening constitutive model, has provided information about the landslide failure process, as well as the failure mechanisms of retrogression deformation under the effect of water. The simulation reproduces the evolution process with a final deposit morphology, which is consistent with the previous investigation result. Based on the modeling, the landslide failure process, mechanisms, and plastic strain state are comprehensively discussed. It is found that because of the water effect, some distinct characteristics in the sliding process can be observed in submarine landslides: movement hinderance, a bulbous configuration, and high fluidization, which is valuable for disaster mitigation.

Numerical solutions for tunnels excavated in strain-softening rock masses considering a combined support system

In this article, an alternative numerical procedure to calculate displacements and stresses of supported circular tunnels is proposed, considering the whole process of tunnel advancement, and sequential installation of the primary and secondary support systems. In the derivation, the plastic area of the rock mass is divided into a large number of annuli around the tunnel, and then the Finite Difference Method is employed. First, the strain-softening behaviour model is taken to simulate the post-failure behaviour of the rock mass. Furthermore, the Mohr-Coulomb or the Hoek-Brown failure criteria can be chosen, a non-associated plastic flow rule is assumed and the dilatancy of the rock mass is considered. After that, the fictitious support forces concept is used to simulate the process of tunnel advancement, and thus, the three-dimensional effect of the tunnel face is considered. Finally, the solutions of displacements and stresses for the rock mass and the supports can be obtained, by using the compatibility conditions of stresses and displacements at both rock-support and support-support interfaces. The results obtained from these solutions agree well with those of the self-similar solutions for circular openings, and the compatibility conditions of supported tunnels were verified. The proposed method has been compared with the convergence-confinement method. Parametric analyses are then carried out to investigate the sensitivity of support forces and displacements to the rock mass behaviour model selection. Then, the application of the proposed solutions in the design of tunnels is presented. The proposed method provides a convenient alternative method for the preliminary design of tunnels.

A Macro-Distinct Element Model (M-DEM) for simulating the in-plane cyclic behavior of URM structures

In this work, a new Macro-Distinct Element Model (M-DEM) for the analysis of the in-plane behavior of unreinforced masonry (URM) structures, aimed at combining the efficiency of simplified approaches with the accuracy of discontinuum-based micro-modeling methods, is presented and validated through comparison against a number of both experimental and numerical tests on URM components. In the M-DEM framework, Finite Element (FE) homogenized macro-blocks are connected by discrete spring interfaces, whose layout is determined a priori as a function of the masonry texture. In-plane diagonal and sliding shear failure mechanisms, as well as flexural damage, are accounted for by the discrete spring interfaces. Meanwhile, a new methodology to simulate crushing, which makes use of a strain-softening model originally conceived for modeling concrete failure, is proposed and calibrated against small-scale tests on masonry samples. The strategy is to simulate shear/tension failure in the block interfaces and compression failure within the FE macro-blocks, while discretizing to allow the possibility of simulating out-of-plane failure modes. Using the M-DEM, the observed experimental damage and the hysteretic behavior of various reduced-scale URM specimens, subjected to shear-compression cyclic loading, were satisfactorily reproduced numerically. The capabilities of the M-DEM to predict the influence of the bond pattern on the monotonic behavior laterally-loaded URM piers were also scrutinized through comparison with standard micro-modeling outcomes, focusing on potential differences concerning both accuracy and computational expense. Finally, given the encouraging results obtained, the proposed approach was extended to the simulation of the in-plane cyclic response of a full-scale URM façade. Although the model marginally underestimated the energy dissipation in the first test phases, a good agreement was obtained in terms of peak and residual base shear capacity, initial in-plane stiffness and its progressive deterioration, governing failure mechanisms and final crack pattern, whilst simultaneously keeping computational costs within acceptable limits.

MPM evaluation of the dynamic runout process of the giant Daguangbao landslide

Giant landslides can cause significant damage to their dynamic runout processes. Understanding the mechanics of the runout process is essential for landslide risk assessment and mitigation design. This paper investigates the runout process of the 1.16 × 109 m3 giant Daguangbao landslide triggered by the 2008 Ms 8.0 Wenchuan earthquake. The Daguangbao landslide is a typical bedding-plane slide and the properties of basal sliding surface play a key role in the runout behaviors of the landslide. The material point method (MPM) is adopted as a numerical tool of the simulations. A thermal-based velocity-weakening friction law is used to simulate the contact between the sliding body and the basal sliding surface. A strain-softening constitutive model is used to evaluate the damages inside the landslide body and their effects on the runout behaviors of the landslide. Numerical results reveal that landslide mass slides along the bedding-plane as a whole body initially and then disintegrates during the runout process. The calculated duration of sliding is 64 s and the maximum velocity reaches 60 m/s. The friction coefficient of the slip surface decreases sharply as the landslide body starts to move, and a steady-state friction coefficient μ ≈ 0.06 is reached when the velocity exceeds approximately 20 m/s. Friction degradation of the slip surface shows a sensible influence on the final runout distance and the depth of the deposit zone. The dynamic fragmentation of the landslide body, the final runout distance, and deposition topography are also significantly affected by material softening.

Optimized strain softening model for marine clay from cyclic full-flow penetration and extraction tests

Strain softening is a major feature of marine clay that plays an important role in offshore geotechnical problems. One of the widely used strain softening models is introducing an exponential relation of the undrained strength to the accumulated shear strain into a simple constitutive model. The strain softening model of seabed sediments can be obtained by the resistance degradation with cyclic full-flow penetration tests. However, for structured soils, the normally used exponential relation failed to reflect the brittleness of the soil under small strain. This paper proposed an optimized exponential strain softening model by adding a parameter β. The fitting results of 20 cyclic penetration tests on different soils show that the proposed model can reflect both the initial brittleness of soil and its fully remolded state well. Based on the LDFE analysis on the process of pipe penetration, a maximum difference of 22.8% on the pipe resistance may be caused by the value of β. For the estimation of ductility parameter (N95) in the strain softening model, a new method is proposed by the percentage of strength degradation (Psu,n), which can improve the accuracy of N95 up to 58.8% for the clay from the South China Sea.

Macrohomogeneity condition for strain gradient homogenization of periodic heterogeneous media with interfacial strong discontinuities

The Hill macrohomogeneity condition is revisited in the context of strain gradient homogenization for heterogeneous materials prone to interfacial displacement jumps. The consideration of strain gradient effects is motivated by their use as a regularization method for strain-softening constitutive damage models leading to strain localization and displacement discontinuity. Starting from the weak form of the boundary value problem formulated at the microscopic level, a polynomial expression of the virtual velocity is adopted as the minimum microscopic kinematics consistent with the selected macroscopic kinematics of the strain gradient effective continuum. The effective volumetric and interfacial mesoscopic strains and stress measures for the effective substitution are obtained versus the microscopic strains and stresses. The Hill macrohomogeneity condition is successively formulated for continuous interfaces and discontinuous interfaces witnessing strong discontinuities. It highlights the expressions of the effective stress measures associated to the volumetric and interfacial behavior for both classical and higher-order effects.

A Study on the Distribution and Evolution of Mining Induced Stress under the Condition of Multiple Mining

Mining of multiple coal seams and sections is the main method adopted by the vast majority of coal mines in China at present. However, because of multiple mining, the damage and deformation of surrounding rock increases a lot when comparing with single coal seam mining. Moreover, the normal production and safety of coal mine may also get affected. In multiple coal seam mining, the distribution and alteration of mining induced stress are the main reasons of the above problems. In this study, based on the geological conditions and mining design of Weijiagou Coal Mine, the mining induced stress under multiple mining conditions were studied. According to the failure state, the surrounding rock was divided into the damaged zone, plastic zone and elastic zone. The distribution and range of mining stress in different areas were calculated by utilizing Strain Softening Model. Based on FLAC3D numerical simulation, the distribution and change of mining induced stress along the strike and dip direction of coal seam were obtained. By using the Logarithmic function and the Fourier function, the empirical formula of the relationship between the maximum mining stress in front of the working face and the advancing distance of the working face is obtained. This study provides a reference for the design of roadway support and mining face under multiple mining conditions.

Coal Mine Abutment Pressure Distribution Based on a Strain-Softening Model

The coal in front of mining face presents strain softening deformation characteristics. An analytical model is proposed to simulate the abutment pressure distribution over the coal in front of mining face under elastic and inelastic conditions. A new theoretical formula is derived to calculate the abutment pressure distribution and its width in elastic and inelastic regions of the coal under limit equilibrium condition. The influences of UCS, residual strength, mining height, softening modulus and deformation angle on abutment pressure distribution are discussed. The study results show that, (1) stress gradient in plastic area is larger than crushed zone; (2) the width of plastic region is independent of the peak abutment pressure, but it is dependent of UCS, residual strength, mining height, softening modulus and deformation angle; (3) the width of crushed zone in inelastic area is closely related to peak abutment pressure, coal-floor interface cohesion and friction coefficient; (4) the width of elastic zone is dependent of mining height, coefficient of horizontal pressure, coal-floor interface friction coefficient and peak abutment pressure where the coefficient of horizontal pressure has the highest impact that the width of elastic zone has logarithmic decrease with the increase of the coefficient of horizontal pressure. A case study is carried out at longwall panel 07 of No. 5 coal seam in Dongjiahe Coal Mine to verify the analytical model. The abutment pressure distribution and the widths of elastic and inelastic zones under limit equilibrium condition are calculated based on the relevant parameters. The theoretical results are compared with the field monitoring data which shows very good fit. It is proved that the proposed analytical model has high accuracy and the feasibility of the model is verified. The study results can provide guidance for similar engineering applications.

Effect of using different approximation models to the exact Mohr\u2013Coulomb material model in the FE simulation of Anchor Foundations in sand

Singularities in the Mohr–Coulomb (MC) yield criterion create numerical difficulties when implemented in the finite element model (FEM). In this research, a two-dimensional (2D) and a three-dimensional (3D) elasto-plastic FEM coupled with isotropic strain hardening–softening or simple strain-softening law incorporating non-associated flow rule including shear band, is used to investigate the effect of singularities, embedment, shape, soil frictional as well as dilation angle on vertically uploaded shallow anchor foundations buried in Toyoura sand. Mohr–Coulomb–Drucker Prager (MC–DP) model provides a more appropriate solution than Drucker Prager–Drucker Prager (DP–DP) model. Besides, the peak resistance factor and the settlement at the ultimate capacity have been found as the functions of embedment, shape, and sand density. Also, the numerical model gives satisfactory agreement with the previous studies. In particular, a simple strain-softening model cannot capture the settlement behavior of anchor foundations in sand efficiently.

The Research on Strain-Softening Characteristics and Local Fracture Law of Deep Granite Roadway

The complex mechanical properties of deep surrounding rocks during excavation and unloading have always been a concern in engineering communities. Based on deep roadway engineering, the mechanical properties of granite strain-softening were investigated by laboratory tests. An exponential relationship between granite peak softening modulus and confining pressure was obtained using a nonlinear fitting method. A strain-softening model was developed based on plasticity theory for granite which took into account the nonlinear dilatancy angle and confining pressure. A mathematical model was developed using FLAC3D as platform. By developing a numerical model for a deep roadway, the local fracture characteristics of deep surrounding rocks under strain-softening conditions were evaluated. It has been found that the postpeak failure of granite had a tendency for brittle-ductile transformation. Under high confining pressure conditions, granite exhibited brittle failure characteristics during the postpeak period, and the postpeak softening modulus was decreased with the increase of confining pressure. From FLAC3D numerical calculations, it was found that the numerical models of different mesh densities had basically the same characteristic curves of surrounding rocks, which showed that the local cracking phenomenon had little effect on calculation results when the convergence constraint method was applied for the calculation of the stability of supporting structures and surrounding rocks. It was seen from the numerical simulation analyses of surrounding rock local fracture properties in deep roadways that plastic shear strain appeared in the local areas of roadway vault and arch foot, which basically coincided with the damage location and depth of surrounding roadway rocks.

Numerical Modeling Study of the Influence of Softcover on Strata and Support Behavior in a Bord and Pillar Depillaring Working

This research focuses on the strata control issues in a Bord and Pillar depillaring working under the influence of dead load condition of voluminous and fragmented softcover of overburden dump material. It reports the modeling of a mine working through the FLAC 2D software under the Indian geo-mining conditions. The modeling results of an actual mine working under softcover were compared with that under the intact overburden condition to assess the influence of the soft overburden over the depillaring working. The modeling work involved progressive caving of the strata and the cyclic goaf filling following the model-simulated occurrence of main fall and periodic caving. Mohr-Coulomb Failure criteria along with a simplified strain-softening (MCSS) model was used to study the failure and caving mechanism. Salamon’s compaction model was used to simulate compaction and resultant stress recovery in the goaf material. Comparison of the model findings was done in terms of load on supports, abutment stress, and convergence, apart from the stress redistribution and failure mechanism. The load transfer mechanism of the soft overburden was also studied for an overall understanding of the strata behavior in such workings.

Fault reactivation induced by tunneling activity in clay material: Hints from numerical modeling

Seismic events with magnitude 3 and above have been associated with the removal of rock mass in mining environment since long-time. On the contrary, little is known about the possible seismic events induced by tunneling, although it presents similarities with mining. One great example is the case of the 57 km long Gotthard Base Tunnel excavation, which has been associated more than hundred seismic events, with the largest one having magnitude of ML 2.4, damaging the tunnel infrastructures (e.g. gallery floor or portal area).Different underground structures will be built probably up to 1000 m below ground for the construction of future deep geological for the storage of nuclear waste. While seismic risk will probably not constitute a liability for the storage site construction, it is important to understand the potential for reactivation of seismogenic features located nearby the future location of emplacement tunnels.Here we present numerical simulations aimed at understanding the potential for fault reactivation during tunnel construction in clay material, a potential host rock for nuclear waste repository. We evaluate the evolution of the stress changes during the simulation of the excavation with FLAC3D numerical solver. A strain-softening friction model is used to simulate the occurrence of a sudden slip on a fault zone when critical conditions for reactivation are satisfied. This constitutes a worst-case scenario, given the low seismogenic potential of clay rocks. We also present a sensitivity analysis on several critical parameters including fault frictional properties, stress conditions, as well as different tunnel sizes at varying distance from a nearby failure plane, with the final purpose of evaluating safety of a potential nuclear repository site on the short- and long-term.

Numerical modelling of slope damage in large, slowly moving rockslides: Insights from the Downie Slide, British Columbia, Canada

The deformation of rock slopes is associated with the formation and accumulation of internal and external features (such as tension cracks, rock mass bulging and dilation, rockfall, etc.) that can be comprehensively referred to as “slope damage”. In this paper, we use a 3D distinct element numerical modelling approach to investigate the role of shear zone morphology and groundwater pressure on the displacement and slope damage accumulation at the Downie Slide, a large, extremely slowly moving rockslide in British Columbia (Canada). First, we briefly review the external slope damage features that can be observed in an airborne laser scanner (ALS) dataset, allowing four slope damage domains (upper, central, northern, and southern domain) to be interpreted within the slide area, based on the orientation and type of features. Using the same ALS dataset we construct a 3D model of the present-day slope, explicitly including the two shear zones along which displacements occur, in order to investigate their role in the later stage of the landslide evolution. We assign a strain-softening constitutive model to the slide body, in order to account for the decrease in material properties due to damage accumulation. Virtual inclinometers are also implemented in the model, allowing for the comparison of simulated and observed displacement direction along the shear zones. The progressive deformation and failure of the slope is then simulated both assuming dry and wet conditions, in order to examine the role of pore water pressure, and the morphology of the upper and lower shear zones on the magnitude, orientation, and distribution of displacements. For each numerical model, the simulated slope damage features are recorded, by analyzing the zone volumetric strain and failure state, and compared with the type and orientation of features observed in each of the interpreted slope damage domains, thus allowing the numerical results to be better constrained and validated. It is clearly demonstrated that the orientation and distribution of slope damage and displacements observed in both the surface ALS and the subsurface borehole inclinometer data can be well reproduced in the 3D numerical models. Numerical modelling results show that the principal factor controlling the spatial distribution of slope damage at the Downie Slide is the morphology of the lower shear zone, whereas a negligible role is played by the upper shear zone morphology. We also observe that models incorporating a groundwater table display larger displacements, without significant effects on the orientation and distribution of simulated slope damage. This paper demonstrates that an analysis of slope damage is very important for understanding the mechanisms underlying the behavior of large landslides and should be a fundamental step in the comprehensive characterization of any major slope failure.

Strain-softening composite damage model of rock under thermal environment

To ensure the safe and effective application of deep geotechnical engineering, it is necessary to establish a suitable constitutive model of the rocks in thermal environment, including geothermal energy mining, and deep geological treatment of nuclear waste and tunnel fire. A strain-softening damage model of the rocks with defect growth is established based on damage evolution. According to the change in the tangent modulus from the compression phase to the elastic stage, we established a constitutive model reflecting the nonlinearity characteristics of the compression phase. According to the change in the energy conversion, the energy consumption coefficient is introduced to describe the deformation characteristics of the rocks when the residual stress is reached. The specific physical meaning and the calculation method of the energy consumption coefficient are given to correct the shortcomings of the evolution of the damage variable. We then analyzed the relationship between parameters in the constitutive model of the rocks at high temperature and normal temperature. Based on the constitutive model of the rocks at normal temperature, we established a constitutive model reflecting the influence of high temperature. Finally, the established model fit the stress-strain curves of several kinds of the rocks at different temperatures and generated desired results. The established model can be used to describe the stress-strain curve characteristics of the rocks at different temperatures.

Factor of safety of strain-softening slopes

Abstract Stability analysis of strain-softening slopes is carried out using the shear strength reduction method and Mohr-Coulomb model with degrading cohesion and friction angle. The effect of strain-softening behavior on the slope factor of safety is investigated by performing a series of analyses for various slope geometries and strength properties. Stability charts and equations are developed to estimate the factor of safety of strain-softening slopes from the results of traditional stability analysis based on perfectly-plastic behavior. Two example applications including an open pit mine in weak rock and clay shale slope with daylighting bedding planes are presented. The results of limit equilibrium analysis and shear strength reduction method with perfectly-plastic models were in close agreement. Using perfectly-plastic models with peak strength properties led to overly optimistic results while adopting residual strength properties gave excessively conservative outcomes. The shear strength reduction method with a strain-softening model gave realistic factors of safety while accounting for the process of strength degradation.

Dynamic modeling of large deformation slope failure using smoothed particle finite element method

In this paper, a novel node-based explicit smoothed particle finite element method (SPFEM), on the basis of the particle finite element method (PFEM) framework, is utilized to evaluate the stability of slopes and to simulate the post-failure behavior of soil. The main advantage of SPFEM in slope stability analysis lies in its capabilities to consider the whole dynamic failure process of slope and to simulate large deformation and post-failure of soils. For the stability analysis of a cohesive soil slope, the shear strength reduction technique with a kinetic energy-based criterion for distinguishing slope failure is adopted to obtain the factor of safety (FOS) of a slope, and the FOS is compared with that obtained by the classical FEM and LEM approaches for further validation. Then, the dynamic failure process of a non-cohesive granular material slope is simulated using Drucker-Prager constitutive model. The influence of friction resistance of granular material, as well as the repose angle of slope after failure, is discussed. Finally, the progressive failure behavior of a long clayey slope is modeled using SPFEM in conjunction with a strain-softening Tresca constitutive model. The retrogressive failure behavior of a long clayey slope is analyzed.

Experimental and numerical investigation of the Saint-Adelphe landslide after the 1988 Saguenay earthquake

On 25 November 1988, after the Saguenay earthquake, a landslide occurred in the municipality of Saint-Adelphe. The soil profile indicated that the deposit was composed of a stiff clay crustal layer overlying sensitive plastic clay with a soft-to-stiff consistency. A geotechnical investigation was carried out in situ and in the laboratory and included the use of a new seismic simulator to develop a geotechnical model of the Saint-Adelphe clay. The model was incorporated in a finite-difference slope stability analysis before and during the earthquake. The results showed the development of plastic zones and the generation of pore water pressure, but the global safety factor remained above unity. A post-seismic analysis that utilized a strain-softening behavior model showed the initiation and propagation of the plastic zone, as well as the development of a failure surface close to the observed failure surface. Therefore, it is proposed that the Saint-Adelphe landslide could be explained by a progressive failure mechanism.