Thin Weak Layer Research Articles

Impact of the thin weak layer on the interaction of closely spaced shallow foundations resting on sand bed

Impact of the thin weak layer on the interaction of closely spaced shallow foundations resting on sand bed

Analysis of the Internal Structure of Brenna Sandstone Samples with Respect to the Differences in Measured Quasi-elastic Moduli

The Young’s modulus and Poisson’s ratio determined for the rocks under uniaxial or triaxial loading conditions represent necessary input parameters for solving many geotechnical tasks. However, these effective stiffness moduli, particularly the Poisson’s ratios, measured on different samples sometimes substantially differ, even for visually compact and macroscopically homogeneous rock. This has been observed for Brenna sandstone, especially under conditions of conventional triaxial extensions. The aim of this study was, thus, to reveal differences in rock structure that could cause such behavior. Several complementary methods were used to investigate the structure of this sandstone: X-ray computed tomography (CT), visual analysis using optical scanning and stereo-microscopy, and a new method combining water jet erosion with these visualization techniques. Analyses of this structure revealed mechanically more resistant compact thick and adjacent thin weak layers. In rock samples, these layers have different patterns and orientations. To demonstrate the influence of layer orientation on effective stiffness moduli measured under different loading conditions, FEM calculations were performed for idealized structural models. The outcomes of this numerical analysis are in qualitative agreement with the results of the loading experiments and the layered structure revealed in the samples. The ability of the proposed method using water erosion to analyze the rock structure in detail was verified. The method offers an interesting alternative to standard visual and X-ray CT techniques. The numerical calculations indicate the importance of latent layered defects in sedimentary rocks for fine measurements of stiffness moduli (especially the Poisson’s ratios) used as inputs for geotechnical applications.

A fast pseudo-3D model for inversion of full SH waves in layered half-spaces

SH and Love waves have certain advantages over P-SV and Rayleigh waves when inverting shear-wave velocity (VS) profiles. They can also supplement Rayleigh waves to provide better model constraints on characterizing anisotropic media. Since the true 3D forward solution of full SH waves requires intensive computation, we propose, in this paper, a simple 2D wavefield solution and further modify it as an efficient pseudo-3D solution. This is achieved by applying an empirical amplitude correction function for geometric attenuation. In the transformed domain, this newly proposed pseudo-3D solution yields a dispersion image (frequency-velocity spectrum, FVS) practically equivalent to that of the true 3D solution which is also developed by the authors. Furthermore, this pseudo-3D solution is significantly more accurate than the modal summation method. Thanks to its fast computation speed and accuracy, the pseudo-3D algorithm is demonstrated to be an excellent surrogate for full wavefield inversion based on FVS. The FVS of SH waves is shown to be much more sensitive to embedded thin weak layers than that of P-SV waves. The superiority of FVS inversion over fundamental mode inversion is further demonstrated by examining their corresponding error functions, showing that FVS provides a much stronger constraint on the possible VS models. Examples demonstrate that the FVS inversion based on the pseudo-3D model outperforms the modal summation approach in both accuracy and generalization. The proposed pseudo-3D solution is quite general. It takes into account the source-to-receiver geometry and deals with special layer profiles where Love-type wave does not exist.

FEM Modelling of Thin Weak Layers in Slope Stability Analysis

Modelling the presence and the effect of a thin weak layer of soil or rock in a slope stability analysis performed through the finite element method (FEM) presents several problems of purely numerical nature. This paper deals with a parametric analysis of three different 2D numerical case studies (both ideal and real) of unstable or potentially unstable slopes containing a thin soft band (or weak layer). The FEM software used is RS2 (Rocscience®). The aim is investigating the influence of some geometrical and numerical characteristics of the soft bands in the stability analyses. The Mohr–Coulomb elastic-perfectly plastic constitutive model for all the involved materials was assumed, and the mechanical parameters were kept constant. Instead, other fundamental parameters of the weak layer, such as the type of mesh elements, the mesh density, and the geometry, in terms of both thickness and outcrop shape, were changed, and results in terms of the critical Strength Reduction Factor (SRF) were compared. The main outcomes of this study represent practical suggestions on some numerical and technical aspects to users of FEM slope stability analyses, in order to obtain a precautionary assessment of slope stability.

Influence of a Thin Horizontal Weak Layer on the Mechanical Behaviour of Shallow Foundations Resting on Sand

The presence of minor details of the ground, including soil or rock masses, occurs more frequently than what is normally believed. Thin weak layers, shear bands, and slickensided surfaces can substantially affect the behaviour of foundations, as well as that of other geostructures. In fact, they can affect the failure mechanisms, the ultimate bearing capacity of footings, and the safety factor of the geotechnical system. In this research, numerically conducted through Finite Element Code Plaxis 2D, the influence of a horizontal thin weak layer on the mechanical behaviour of shallow footings was evaluated. The obtained results prove that the weak layer strongly influences both the failure mechanism and the ultimate bearing capacity if its depth is lower than two to four times the footing width. In fact, under these circumstances, the failure mechanisms are always mixtilinear in shape because the shear strains largely develop on the weak layer. However, the reduction in the ultimate bearing capacity is a function of the difference between the shear strength of the foundation soil and the layer. The presence of a thin weak layer decreases the ultimate bearing capacity up to 90%. In conclusion, this research suggests that particular attention must be paid during detailed ground investigations to find thin weak layers. Based on the obtained results, it is convenient to increase the soil volume investigation to a depth equal to four times the width of the foundation.

Constraints on Mantle Viscosity From Intermediate‐Wavelength Geoid Anomalies in Mantle Convection Models With Plate Motion History

AbstractThe Earth's long‐ and intermediate‐wavelength geoid anomalies are surface expressions of mantle convection and are sensitive to mantle viscosity. While previous studies of the geoid provide important constraints on the mantle radial viscosity variations, the mantle buoyancy in these studies, as derived from either seismic tomography or slab density models, may suffer significant uncertainties. In this study, we formulate 3‐D spherical mantle convection models with plate motion history since the Cretaceous that generate dynamically self‐consistent mantle thermal and buoyancy structures, and for the first time, use the dynamically generated slab structures and the observed geoid to place important constraints on the mantle viscosity. We found that non‐uniform weak plate margins and strong plate interiors are critical in reproducing the observed geoid and surface plate motion, especially the net lithosphere rotation (i.e., degree‐1 toroidal plate motion). In the best‐fit model, which leads to correlation of 0.61 between the modeled and observed geoid at degrees 4–12, the lower mantle viscosity is ∼1.3–2.5 × 1022 Pa⋅s and is ∼30 and ∼600–1,000 times higher than that in the transition zone and asthenosphere, respectively. Slab structures and the geoid are also strongly affected by slab strength, and the observations prefer moderately strong slabs that are ∼10–100 times stronger than the ambient mantle. Finally, a thin weak layer below the 670‐km phase change on a regional scale only in subduction zones produces stagnant slabs in the mantle transition zone as effectively as a weak layer on a global scale.

Stability of Embankments Resting on Foundation Soils with a Weak Layer

The presence of weak layers in geotechnical systems, including soil or rock masses, both natural and man-made, is more frequent than is normally believed. Weak layers can affect both failure mechanisms, in drained and in undrained conditions, as well as in static and seismic conditions, and the safety factor. In the present study, conducted numerically using the finite-element method (FEM) Plaxis 2D code, the influence of a horizontal thin weak layer on stress and strain distribution, on failure mechanisms and on the overall stability of an embankment was evaluated. The results obtained prove that when the weak layer is located at a significant depth from the foundation plane, the failure mechanisms are normally mixtilinear in shape because the shear strains largely develop on the weak layer. As a result, the safety factor highly decreases compared to the same case without a weak layer. Then, in the presence of weak layers, even embankments that, if founded on homogeneous soils, would have very high global safety factors (higher than 2) can become unstable, i.e., the safety factor can become unitary. So particular attention must be paid during detail ground investigations to finding thin weak layers.

Application of dynamic fracture mechanics to dry snow slab avalanche release

Field observations and measurements show that dry snow slab avalanches initiate by propagating shear fractures within a relatively thin weak layer sandwiched between a planar, stronger, thicker slab above and stronger material below. After initiation, the weak layer fracture can propagate up and down slope for distances which range from about 10 to 100′s of meters to cause tensile fracture through the body of the slab which results in avalanche release. In this paper, dynamic fracture mechanics is applied to slab tensile fracture after which avalanche release is imminent. Two mechanisms for production of tensile stress are explored employing field measurements of slab properties and lab measurements. The first considers inertial effects related to quasi-brittle fracture near the tip of a propagating weak layer shear fracture. The second is concerned with the tensile stress generation from the stress drop behind the crack front as the fracture propagates in the weak layer. Analysis suggest that both mechanisms can contribute to produce the tensile fracture line which precedes avalanche release. Even though both mechanisms may operate together, they are analyzed separately in this paper.

Analysis of the Finite Element Strength Reduction Method to Slope Stability with a thin weak layer

The strength of the weak layer not only controls the instability mechanism of the slope, but also the factor of safety to the slope. Studying the stability of the weak layer slope has important theoretical significance and practical engineering value. The instability mechanism and the factor of safety to slope stability with a thin weak layer were studied by finite element strength reduction method and limit equilibrium method. The results show that factor of safety to slope stability decreases with the strength of the weak layer decreases. When the strength of the weak layer is less than 0.6 times the strength of the soil, the instability mechanism of the slope changes from circular arc sliding to polygonal sliding, and its stability is controlled by the strength of the weak layer. The slope stability analysis by limit equilibrium method must be based on the analysis of the instability mechanism to accurately evaluate the slope stability. However, the finite element strength reduction method can be applied to calculate the factor of safety to slope stability and analyze the instability mechanism, and to previous limit equilibrium method.

Automatic identification of the critical slip surface of slopes

Although numerical methods based on strength reduction are becoming popular in slope stability analysis, they fail to provide a distinct critical slip surface and only provide a shear band. The widely used visualization techniques for defining the critical slip surface are susceptible to subjective judgment and are inefficient for batch analysis and three-dimensional analysis. When a slope fails, the displacements on the two sides of the critical slip surface will be substantially different. Based on this observation, an automatic identification method for locating the critical slip surface is proposed. The k-means clustering algorithm is first applied to automatically separate the nodal displacements into two categories representing the sliding mass and the stable block. Then, the scatters near the separation surface are obtained by constructing the alpha shape of the sliding mass. Finally, the critical slip surface is obtained by fitting the extracted scatters. A homogeneous slope, a slope with a thin weak layer and a real landslide are used to test the effectiveness of the proposed method. The results show that the proposed method can automatically and accurately identify two-dimensional and three-dimensional critical slip surfaces.

Controls on Global Mantle Convective Structures and Their Comparison With Seismic Models

AbstractSeismic observations suggest (1) significant accumulation of subducted slabs above the 670‐km discontinuity in many subduction zones, (2) possible structure change at ~1,000‐km depth, and (3) the large low shear wave velocity provinces above the core‐mantle boundary in the African and Pacific lower mantle be associated with chemical heterogeneity. Global mantle convection models with realistic plate motion history reproduce most of these structures. However, it remains unclear how the convection models compare with seismic models at different spatial wavelengths and depths. By conducting quantitative analysis between mantle convection and seismic models, we found that mantle convective structures show significant correlations with seismic structures in the upper mantle and mantle transition zone for wavelengths up to spherical harmonic degree 20. However, the global correlation is weak at intermediate to short wavelengths (for degrees 4 and higher) in the lower mantle below ~1,000‐km depth. A weak layer beneath the spinel‐to‐postspinel phase change help consistently reproduce stagnant slabs in the western Pacific, while having insignificant effects elsewhere, that is, the large low shear wave velocity province structures. The cold slab structures and their correlations with the seismically fast anomalies are nearly identical for our convection models with and without the plumes, indicating that seismically fast anomalies in the mantle mainly result from the subducted slabs. Models with viscosity increase at 1,000‐km depth and the 670‐km depth phase change may reproduce seismic slab structures including the stagnant slabs in the mantle transition zone equally well as models with a thin weak layer below the 670‐km phase boundary.

Formation of Complex Craters in Layered Targets With Material Anisotropy

AbstractMeteorite impacts often occur in layered targets, where the strength of the target varies as a function of depth, but this complexity is often not represented in numerical impact simulations because of the high computational cost of resolving thin layers. To address this limitation, we developed a method to approximate the effect of multiple thin weak layers within a sedimentary sequence using a single material layer to represent the entire sequence. Our approach, implemented in the iSALE (impact‐Simplified Arbitrary Lagrangian Eulerian) shock physics code, combines an anisotropic yield criterion with a cell‐based method to track the orientation of layers. To demonstrate the efficacy of the method and constrain parameters of the anisotropic strength model required to replicate the effects of thin, weak layers, we compare results of simulations of an ~20‐ to 25‐km diameter complex crater on Earth using the new method to those from simulations that explicitly resolve multiple thin weak layers. We show that our approach allows for a reduction in computational cost, negating the need for an increase in spatial resolution to resolve thin layers in the target, while replicating crater formation and final morphology from the high‐resolution models. In keeping with field observations, we also find that anisotropic layers may be responsible for a lack of central uplift expression observed at many craters formed in targets with thick sedimentary layers (e.g., the Haughton and Ries impact structures).

Probabilistic size effect law for mode II fracture from critical lengths in snow slab avalanche weak layers

ABSTRACTFrom field observations, dry snow slab avalanche initiation is associated with fracture within relatively thin weak layers under stronger, cohesive slabs. For risk-based avalanche prediction, it is important to understand the fracture properties of alpine snow. Alpine snow is a quasi-brittle material with a fracture mechanical size effect on nominal shear strength meaning that strength decreases with increasing specimen size. A related size effect is the critical length required for rapid propagation of a shear fracture. In that case, the probability of fracture increases with increasing crack length. In this paper, 45 sets of field-measured critical lengths are presented based on 591 individual tests. From analysis, a probabilistic size effect law based on critical lengths is derived analogous to the deterministic size effect law for nominal shear strength related to fracture mechanics. The new size effect law may be useful in applications, particularly since the critical length is easily measured in the field and it is a principal component of weak layer fracture toughness.

The bearing capacity of footings on sand with a weak layer

Minor details of the ground, such as thin weak layers, shear bands and slickensided surfaces, can substantially affect the behaviour of soil–footing and other geotechnical systems, despite their seeming insignificance. In this paper, the influence of the presence of a thin horizontal weak layer on the ultimate bearing capacity of a strip footing on dense sand is investigated by single-gravity tests on small-scale physical models of the soil–footing system. The test results show that the weak layer strongly influences both the failure mechanism and the ultimate bearing capacity if its depth is lower than about four times the footing width. It is found that the presence of a thin weak layer can cause decreases of the ultimate bearing capacity of up to 80%. Numerical simulations, by finite-element analysis, of the behaviour of the reduced-scale models are able to capture the failure mechanism and the ultimate bearing capacity correctly, only if the mean equivalent constant value of the secant angle of shearing resistance used in calculations is selected, taking into account the curvature of the shear strength envelope of the sand within the very low normal stress range existing in the tested models.

Centrifuge tests on strip footings on sand with a weak layer

Tests on small-scale physical models of a strip footing resting on a dense sand bed containing a thin horizontal weak soil layer were carried out at normal gravity (1 g ). The results, reported in a companion paper, point out that the weak layer plays an important role in the failure mechanism and the ultimate bearing capacity of the footing if it falls within the ground volume relevant to the behaviour of the sand–footing system. The same problem was also investigated by means of centrifuge tests on reduced-scale models at 25 g and 40 g . The results of these tests, reported and discussed in this paper, confirm that failure mechanisms are governed substantially by the presence of the weak layer if its depth does not exceed a critical value and highlight marked scale effects involving the ultimate bearing capacity related essentially to the mean equivalent stress level in the soil beneath and around the footing. Equivalent bearing capacity factors, [Formula: see text], for footings on a dense sand bed containing a thin weak layer are derived from experimental results and are proposed in the paper.

Dynamics of the Wulong landslide revealed by broadband seismic records

The catastrophic Wulong landslide occurred at 14:51 (Beijing time, UTC+8) on 5 June 2009, in Wulong Prefecture, Southwest China. This rockslide occurred in a complex topographic environment. Seismic signals generated by this event were recorded by the seismic network deployed in the surrounding area, and long-period signals were extracted from 8 broadband seismic stations within 250 km to obtain source time functions by inversion. The location of this event was simultaneously acquired using a stepwise refined grid search approach, with an error of ~2.2 km. The estimated source time functions reveal that, according to the movement parameters, this landslide could be divided into three stages with different movement directions, velocities, and increasing inertial forces. The sliding mass moved northward, northeastward and northward in the three stages, with average velocities of 6.5, 20.3, and 13.8 m/s, respectively. The maximum movement velocity of the mass reached 35 m/s before the end of the second stage. The basal friction coefficients were relatively small in the first stage and gradually increasing; large in the second stage, accompanied by the largest variability; and oscillating and gradually decreasing to a stable value, in the third stage. Analysis shows that the movement characteristics of these three stages are consistent with the topography of the sliding zone, corresponding to the northward initiation, eastward sliding after being stopped by the west wall, and northward debris flowing after collision with the east slope of the Tiejianggou valley. The maximum movement velocity of the sliding mass results from the largest height difference of the west slope of the Tiejianggou valley. The basal friction coefficients of the three stages represent the thin weak layer in the source zone, the dramatically varying topography of the west slope of the Tiejianggou valley, and characteristics of the debris flow along the Tiejianggou valley. Based on the above results, it is recognized that the inverted source time functions are consistent with the topography of the sliding zone. Special geological and topographic conditions can have a focusing effect on landslides and are key factors in inducing the major disasters, which may follow from them. This landslide was of an unusual nature, and it will be worthwhile to pursue research into its dynamic characteristics more deeply.Graphical abstractIn order to trace the dynamic process of the Wulong landslide, we estimate its source time functions (lower panel of the following image) using long-period seismic signals extracted from 8 broadband seismic stations within 250 km of the landslide. The topography in landslide area varies dramatically, enhancing the complexity in its movement characteristics. The moving direction of the sliding mass changed twice during the event (upper panel of the following image), leaving a Scouring Zone, a Main Depositional Zone and a Debris Depositional Zone. Our inversion results can perfectly characterize its movement features, including three stages of the landslide divided by two major collisions. Additionally, kinematic parameters of the sliding mass, such as velocities, are provided, with the maximum velocity of 35 m/s resulting from the height difference between the cliff and the Tiejianggou valley. Basal friction coefficients are also estimated and are consistent with the topography in the landslide area.

Stability of Slopes Reinforced with Truncated Piles

Piles are extensively used as a means of slope stabilization. A novel engineering technique of truncated piles that are unlike traditional piles is introduced in this paper. A simplified numerical method is proposed to analyze the stability of slopes stabilized with truncated piles based on the shear strength reduction method. The influential factors, which include pile diameter, pile spacing, depth of truncation, and existence of a weak layer, are systematically investigated from a practical point of view. The results show that an optimum ratio exists between the depth of truncation and the pile length above a slip surface, below which truncating behavior has no influence on the piled slope stability. This optimum ratio is bigger for slopes stabilized with more flexible piles and piles with larger spacing. Besides, truncated piles are more suitable for slopes with a thin weak layer than homogenous slopes. In practical engineering, the piles could be truncated reasonably while ensuring the reinforcement effect. The truncated part of piles can be filled with the surrounding soil and compacted to reduce costs by using fewer materials.

Mode II fracture parameters of dry snow slab avalanche weak layers calculated from the cohesive crack model

Release of dry snow slab avalanches starts with shear failure within a thin weak layer beneath a stronger, cohesive slab. The propagating fracture is within the weak layer as mode II. The fundamental fracture properties include the weak layer critical mode II fracture energy and stress intensity factors. In this paper, mode II fracture energy was calculated from the cohesive crack model from dry slab avalanche fracture line data and in-situ shear fracture tests. One advantage of the cohesive crack model is that it does not require the effective elastic modulus which is highly rate dependent and largely unknown in avalanche release. The results gave weak layer mode II fracture toughness less than mode I fracture toughness for the cohesive slab and fracture energy about one order of magnitude less than for solid ice. From the fracture energy and the mode II stress intensity factor, Irwin’s relation enables calculation of the effective elastic modulus. Calculations of the effective modulus for mode II initiation were compared with other estimates and they were shown to be consistent.

Numerical Study of Slope-Stabilizing Piles in Undrained Clayey Slopes with a Weak Thin Layer

AbstractThis paper presents a numerical study using three-dimensional (3D) finite-element (FE) analyses for slopes that contain a weak thin layer and are reinforced with piles. The presence of a thin weak layer usually has a negative effect on slope stability. In the FE analysis, a strength reduction technique is employed using FE software. In the numerical model, an elastic-perfectly plastic with Mohr-Coulomb failure criterion is used for the soils. The pile is assumed to be an elastic member, without considering failure. Some of the effective factors, such as the optimal pile location and pile length, were verified beforehand using two-dimensional (2D) FE analysis. The spacing effect of the pile, S/D=4.0 (S is on-center spacing; D is diameter), is found to be comparable for the 3D model in relation to the 2D model. The appropriate length of the pile used in the 3D analysis is based on the length of piles typically used in engineering practice. It is concluded that proper stabilization can be provided if...

Influence of lithospheric mantle stratification on craton extension: Insight from two-dimensional thermo-mechanical modeling

Lithospheric mantle stratification is a common feature in cratonic areas which has been demonstrated by geophysical and geochemical studies. The influence of lithospheric mantle stratification during craton evolution remains poorly understood. We use a 2D thermo-mechanical coupled numerical model to study the influence of stratified lithospheric mantle on craton extension. A rheologically weak layer representing hydrated and/or metasomatized composition is implemented in the lithospheric mantle. Our results show that the weak mantle layer changes the dynamics of lithospheric extension by enhancing the deformation of the overlying mantle and crust and inhibiting deformation of the underlying mantle. The thickness and depth of the weak layer determines two deformation patterns: 1) narrow mantle necking favored by shallow and thin weak layer, and 2) widespread mantle necking favored by deep and thick weak layer. High Moho temperatures also promote the formation of widespread mantle necking in the model with a weak mantle layer. Both shear heating and plastic strain weakening can enhance deformation and promote asymmetric extension. Modeling results are compared with North China and North Atlantic cratons. Our work indicates that although the presence of a weak layer may not be sufficient to initiate craton deformation, it enhances deformation by lowering the required extensional plate boundary force.