Hydromechanically Coupled Analysis of Transient Phenomena in a Rainfall-induced Landslide

Heavy rainfall can lead to shallow slips in slopes that are initially in a state of partial water saturation. Multiphysics numerical modelling approaches taking into account the involved physical key processes in variably saturated soils during rainfall events could help in understanding the main slip mechanisms. The concerned processes are related to water flow through the solid matrix, soil water retention behaviour and the effects of matric suction on the mechanical behaviour. In this paper, the elasto-plastic constitutive model ACMEG-s that captures some key features of the behaviour of variably saturated soils is used in a fully coupled hydromechanical finite element analysis for the assessment of destabilizing, transient processes in a steep slope during rain infiltration. It is shown that at the onset of failure, wetting pore collapse and plastic shear strains occur in the lower part of the slope and develop upwards towards the slope surface to delimit a probable failure mechanism. conditions subjected to rain infiltration (Springman et al. 2009). The simulation results show the usefulness of considering partial saturation in hydraulic and mechanical terms for the modelling of the predominant transient processes and key physical mechanisms, such as soil hardening effect of matric suction, wetting pore collapse and plastic shearing. 2 PHYSICAL PROCESSES IN UNSATURATED SOIL SLOPES Commonly, two flow regimes are encountered in natural slopes: a deep flow regime, most often parallel to the slope surface with possible complex bedrock interactions and a superficial flow regime with capillary pressures or positive, compressive pore water pressures controlled by rainfall. The slope response to a rainfall event depends mainly on rainfall intensity and duration, on soil hydraulic characteristics, on the thickness of the sliding mass and on antecedent weather conditions (Klubertanz et al. 2009). The occurrence and type of landslide triggering mechanism depends strongly on hydraulic predisposition factors, but also on slope angle and mechanical soil characteristics. Shallow slope failures are often reported to occur along an interface between soil deposits and underlying bedrock under fully saturated conditions due to a build-up of positive pore water pressures and subsequent loss in soil shear strength (Johnson and Sitar 1990). This is especially the case for slopes where the effective internal friction angle of the soil is close to the slope angle. Slopes with an angle much steeper than the soil’s internal friction angle rely on suction stresses and/or root reinforcement in order to be stable. In the case presented in this paper, the average slope angle is noticeably higher (α=38°) than the effective internal friction angle (φ’=33°) determined in the laboratory. A real-scale slope failure has been triggered artificially by sprinkling the test-site with water (Springman et al. 2009). During a rainfall event, water infiltrates predominantly vertically under the influence of gravity and capillary forces into the soil. Several hydromechanical processes act in a destabilizing sense on the slope during and after rain infiltration: The degree of saturation of the upper soil layer increases, thereby reducing the capillary tension between the soil particles, which weakens in most cases the slope. Deposited soils, as well as heavily weathered residual soils are susceptible to a collapse of the loose soil matrix upon wetting. The wetting pore collapse in parts of the slope can lead to differential settlements (Jia et al. 2009). At high degrees of saturation, the rapid volume reduction may be a cause for debris flow initiation. A slope-parallel flow regime installs itself after the rainfall event in the upper partially saturated soil layer when the volume of infiltrated water is large enough. Water is consequently carried to the toe region. Upon that, due to the mobilized fluid flow inside the soil matrix, the fluid exerts a destabilizing, downhill frictional drag. Unsaturated zone physical processes govern the time-dependent response of soil slope to a rainfall event. Considering that they take place in a timescale relevant to a single rainfall event, their identification and integration in the modelling process is necessary in order to perform an analysis of the onset of failure. This can be achieved with a hydromechanically coupled approach and an adequate constitutive model for variably unsaturated-saturated soils. 3 THEORETICAL FRAMEWORK FOR UNSATURATED SOILS In order to capture the main features of soil slope behaviour in unsaturated conditions for modelling purpose, an elasto-plastic constitutive model including the soil water retention behaviour is used in the framework of hydromechanically coupled porous media. The principal model concepts are reviewed in this section. The Advanced Constitutive Model for Environmental Geomechanics (ACMEG-s) (Nuth & Laloui 2007; Nuth & Laloui 2008a) is a Cam-Clay-type elasto-plastic model (Schofield & Wroth 1968) and is based on the so-called initial Hujeux’s model (Hujeux 1985). The increment of strain ij dε is decomposed into: e p ij ij ij d d d ε ε ε = + (1) Where e ij dε is the elastic strain increment and p ij dε the plastic strain increment. The elastic deformation can be expressed as: e ij ijkl kl d C d ε σ ′ = (2) The tensor ijkl C is the mechanical elastic tensor and is composed of non-linear elastic moduli. The elastic strain increment e ij dε can be decomposed in volumetric and deviatoric increments which are related to mean effective, respectively deviatoric stress by means of spherical stress-dependent elastic moduli. kl σ ′ in Eq. (2) is the effective stress for unsaturated soils (Laloui & Nuth, 2009): ( ) ( ) kl kl a kl r a w kl u S u u σ σ δ δ ′ = − + − (3) Where kl σ is the total stress, a u is the air pressure, w u is the water pressure, r S is the degree of saturation and kl δ is the Kronecker’s delta. The difference between the total stress kl σ and the air pressure a u is called the net stress kl net σ . The difference between a u and w u is defined as the matric suction s . The critical state line is defined in the plane of deviatoric stress q versus mean effective stress p′ , with a slope M . The slope of the critical state line in the plane volumetric plastic strain vs. mean effective stress ( ) ln p v p ε ′ − is β , 0 CR p′ being the initial critical state pressure: 0 ln p CR v CR p p βε ′ = ′ (4) In the ACMEG-s model, the plastic irreversible strain increment p ij dε is induced by two coupled dissipative processes: an isotropic and a deviatoric plastic mechanism. The yield limits of each mechanism, bounding the elastic domain in the effective stress space, can be written as: ( , , ) . . p iso v iso iso CR f p r p r d p ε ′ ′ ′ = − % (5) ( , , , , ) 1 ln p p dev dev v d dev CR p f p q r q Mp b r p ε ε ⎛ ⎞ ′ ′ ′ = − − ⎜ ⎟ ′ ⎝ ⎠ % (6) Where CR p′ is the critical state pressure. , , iso d b r and dev r are material parameters. p v ε and p d ε are respectively the volumetric plastic strain and the deviatoric plastic strain. The critical state pressure in Eq. (4) can be related to the preconsolidation pressure ' c p using the material parameter d, that represents the distance in the volumetric plane between the normally consolidated line and the critical state line: . c CR p d p ′ ′ = (7) Using the space of triaxial stress variables q and p’, the elastic domain is enclosed by an ellipsoidal surface which is cut by the isotropic yield limit (see Figure 1). Adding the suction s as a third axis of the space, Figure 1 shows that the elastic domain gets larger with suction. This accounts for the fact that a dryer material will have higher strength and stiffness. Eq. (8) gives the mathematical formulation of the contribution of the capillary effects to the mechanical behaviour. The principle is to introduce a dependency of the preconsolidation pressure c p′ on the level of suction s and using a material parameter s γ :