Variation Of Shear Strength Research Articles

Effects of anisotropy in correlation structure on reliability-based slope stability analysis of a landfill.

In this study, a reliability-based analysis of slope stability in a landfill considering the spatial variability of shear strength (c and φ) and unit weight (γ) of municipal solid waste was performed using the random finite difference method. The effect of the anisotropic correlation (AC) structure of random variables including c, φ, and γ on mean and coefficient of variation (CoV) of safety factor values was investigated using Monte Carlo simulation. Also, probability of failure was determined through probability distribution fitting to a series of safety factor data. The results showed that the AC of the random variables has a significant effect on the stochastic safety factor of landfill slope. In general, the mean of the stochastic safety factor decreases with increasing horizontal and vertical correlation lengths (CLs). Also, the CoV of the safety factor increased with increase in horizontal or vertical CLs or both. Moreover, it was found that failure probability increases with an increase in the horizontal and vertical CLs and assuming isotropic structure for the correlation of random variables leads to the underestimation of failure probability. Overall, the results indicate that assuming an AC structure results in different failure mechanisms in the landfill slope, which are different from the deterministic cases.

Effect of initial packing density, stress level and particle size ratio on the behavior of binary granular material: a micromechanical approach

The geo-mechanical behavior of granular materials rigorously depends on their initial packing density, stress level and particle size distribution. Moreover, the behavior of binary granular soil is affected by the quality and quantity of their small particles named the fines content (FC). The contribution mechanism of the FC to the load-bearing structure of the soil at various particle sizes, stress levels and densities is still pending. The present study aimed to use a micromechanical approach to simulate the behavior of binary mixtures with particle size ratios (α) of 2.5 to 7.1 and study the effect of stress level and initial packing density on the stress–strain behavior using discrete element method (DEM). Accordingly, the effect of FC on the internal friction angle, anisotropy parameters, coordination number and coarse–fine (C–F) contacts have been studied. The results indicate that the variation in peak shear strength versus FC is bell-shaped with a minimum for FC of 30% to 40% and this is independent of initial packing density and stress level, but depending on the value of α. The greater particle size ratios (α = 7.1) increase the tendency of fines particles to rotate during biaxial testing, reduced the shear strength in comparison with samples with small particle size ratios (α = 2.5). Exceeding the threshold FC (30–40%) led to formation of stronger force chains among the fines and increased the role of FC on the peak shear strength.

Effect of Contact Pad’s Roughness and Ni–P Plating Thickness on Leadless Packages’ Shear Strength Variation

Studies on shear strength of thin small leadless packages (TSLP) focused predominantly on solder and reflow factors. Contact pad’s surface roughness (Ra) and Ni–P thickness factors, though rather important, have not been reported widely. Thus, the current study investigates the effect of TSLP’s contact pad, in terms of Ra and Ni–P’s thickness, on shear strength variation of the TSLP after being soldered on PCB. The Ra was controlled by using different Cu alloy leadframes, etchant’s pH and etching conveyor speeds. A shear test was conducted on the soldered TSLP using the Dage Series-4000-Bond-Tester as per Infineon’s specifications. The shear test data was supported by failure mode results in the form of scanning electron microscopy images and energy-dispersive X-ray analysis. The present work revealed that TSLP with high contact pad’s Ra exhibited a wide shear strength variation. In addition, thicker Ni–P significantly enlarged the shear strength variation of TSLP when the etched surface of the contact pad’s Ra is low. After solder reflow, the contact pad’s high Ra and Ni–P thickness triggered the formation of more heterogeneous pores in the solder region of the solder joint between TSLP and PCB. This resulted in shear failure at the porous solder region and heterogeneous shear strength of the soldered TSLP.

Probabilistic analysis of tunnel face stability considering spatially variable undrained shear strength with linearly increasing mean trend

The inherent spatial variability of soil properties has been considered as one of the main sources of uncertainties in geotechnical problems. The need for probabilistic analysis of the tunnel face stability that takes into account the variability of soil properties has been acknowledged. This article employed a probabilistic-based method, called random finite difference method, for evaluating the stability of tunnel face under the influence of the variability of undrained shear strength in clays. The two-dimensional spatial variation in soil undrained shear strength is modeled by random fields, which are discretized by the Covariance Matrix Decomposition method. The procedure for random finite difference method is presented. An illustrative example is employed to investigate the effect of soil variability. Particular attention has been paid to the situation that undrained shear strength increases with depth. The results demonstrate that ignoring the variability of undrained shear strength will result in overestimates of the tunnel face stability if the support pressure of the tunnel face exceeds the deterministic value, especially for higher coefficient of variation of soil undrained shear strength. Minor differences in the failure mechanism are observed in comparison to the deterministic case, considering only the global failure of the tunnel face is observed. In addition, ignoring the increase of undrained shear strength with depth will lead to conservative designs. The random finite difference method can provide a practical tool for evaluating the stability of a tunnel face in variable soils.

A New Representative Sampling Method for Series Size Rock Joint Surfaces

The greatest variability in both shear strength and roughness exists for joint samples with smaller size, which underscores the necessity of performing representative sampling. This study aims to provide a representative sampling method for series size joint surfaces. The progressive coverage statistical method is introduced to provide the sufficient sample capacity for series sampling sizes by setting different propulsion spaces. The statistical law of the joint surface morphology at different sampling sizes is measured by the 3D roughness parameter with {{theta }}_{max }^{ast }/({C}+1). Through an application in nine natural large-scale rock joints, nine consecutive sampling sizes from 100 mm × 100 mm to 900 mm × 900 mm are selected and 121 samples are successfully acquired from each sampling size. According to the frequency distribution of roughness statistics, a new sampling method combining the layering principle and K-medoids clustering algorithm is proposed to screen representative joint samples for each sampling size. The sampling results that meet the test accuracy requirements suggest the possibility of realizing an intelligent sampling method. In addition, the representative of the interlayer cluster center is validated. Finally, the comparison results with the traditional stratified sampling method prove that the proposed method has better stability.

On determining the undrained bearing capacity coefficients of variation for foundations embedded on spatially variable soil

Abstract This paper presents an efficient method and its usage for the three-dimensional random bearing capacity evaluation for square and rectangular footings. One of the objectives of the study is to deliver graphs that can be used to easily estimate the approximated values of coefficients of variations of undrained bearing capacity. The numerical calculations were based on the proposed method that connects three-dimensional failure mechanism, simulated annealing optimization scheme and spatial averaging. The random field is used for describing the spatial variability of undrained shear strength. The proposed approach is in accordance with a constant covariance matrix concept, that results in a highly efficient tool for estimating the probabilistic characteristics of bearing capacity. As a result, numerous three-dimensional simulations were performed to create the graphs. The considered covariance matrix is a result of Vanmarcke’s spatial averaging discretization of a random field in the dissipation regions to the single random variables. The matrix describes mutual correlation between each dissipation region (or between those random variables). However, in the presented approach, the matrix was obtained for the expected value of undrained shear strength and keep constant during Monte Carlo simulations. The graphs were established in dimensionless coordinates that vary in the observable in practice ranges of parameters (i.e., values of fluctuation scales, foundation sizes and shapes). Examples of usage were given in the study to illustrate the application possibility of the graphs. Moreover, the comparison with the approach that uses individually determined covariance matrix is shown.

Bearing capacity and reliability analysis of spudcan foundations embedded at various depths based on the non-stationary random finite element method

Spudcan foundations for mobile jack-up units are large diameter conical foundations that can penetrate into the seabed to a maximum depth of three times the diameter of the spudcan. As a deeply penetrated foundation, the bearing capacity of a spudcan is highly dependent on the failure mechanism and the strength distribution of the seabed soil, which exhibits strong spatial variability. While many recent studies have explored the failure mechanism and bearing capacity of spudcan foundations, these studies have commonly deterministically described the soil in which the spudcan is embedded. Therefore, this paper aimed to investigate the probabilistic bearing capacity of spudcan foundations embedded in the seabed at various depths, under the condition of spatially variable undrained shear strength that increased linearly with depth. The random finite element method was used to study this problem, where nonlinear finite element analysis was combined with random field theory within a Monte Carlo framework. The variability in undrained shear strength was modelled as a random field and characterised by a log-normal distribution with anisotropic autocorrelation distances. The influence of autocorrelation distance on the mean bearing capacity and the failure mechanism was discussed for each embedment depth. A correlation between the probability of failure and the factor of safety was established based on the obtained results. These findings can provide guidance for reliability-based design of spudcan foundations embedded in spatially variable soil.

Probabilistic bearing capacity analysis of spudcan foundation in soil with linearly increasing mean undrained shear strength

Spudcan foundations have been widely used in offshore oil and gas engineering for jack-up rigs. During penetration into seabed soil, spudcan foundations may encounter large uncertainties in soil properties, which have a strong impact on its bearing capacity. A large number of studies have been conducted to demonstrate the failure mechanisms and the bearing capacity of spudcan foundations in soils with deterministic properties, but the influence of spatially variable soil properties on spudcan foundations remains unclear and should be accounted for. In this study, we aimed to investigate the failure mechanisms and the bearing capacity of a spudcan foundation embedded in soils where the mean undrained shear strength increased linearly with depth. The spectral representation method (SRM) was used to generate a non-stationary non-Gaussian random field. The random finite element method (RFEM) in conjunction with Monte Carlo simulations was carried out to evaluate the statistical characteristics of the bearing capacity for spudcan foundations, followed by a series of comparisons and discussion. The results indicated that the mean bearing capacity for the spatial variability of undrained shear strength was smaller than that obtained from the corresponding deterministic case. The probability of failure decreased slightly with an increase in the degree of non-stationarity under the constant coefficient of variation (COV) condition. Upon comparing the results obtained from different random field models, we found that the probability of failure under the non-constant condition was smaller than that under the stationary and constant COV conditions.

Improved nonlinear Burgers shear creep model based on the time-dependent shear strength for rock

Shear strength is an important mechanical index of rock. The adjustment and reorganization of rock structure can be reflected by the variation of shear strength. During rock rheology, the shear strength decreases with time due to rock damage. Therefore, from the point of difference of shear strength, the mechanical properties of rock can be effectively studied. In this paper, for the state of direct shear test, the Kachanov creep damage law was adopted to describe the time characteristics of the rock shear strength during the accelerated creep stage. A nonlinear viscoplastic element on the basis of time-dependent shear strength was established by connecting the plastic element representing shear strength with the viscous element in parallel. After introducing the nonlinear viscoplastic element into the classic Burgers model, the rationality of the model was verified by the shear creep test results of rock discontinuity. Results showed that the modified Burgers model can reflect the mechanical properties of rock in three creep stages. In addition, the model parameter δ can also reflect the evolution of internal cracks in rock during creep.

Hydromechanical properties of 3D printed fractures with controlled surface roughness: Insights into shear-permeability coupling processes

We explore the potentials of three-dimensional (3D) printing to explore hydromechanical processes in laboratory-scale fractures. 3D printing enables replication of designer fractures with quantified and repeatable roughness to examine the interdependencies between mechanical and hydraulic response including, for example, the Barton-Bandis model. The present study successfully probes subtle variations of shear strength and dilation behavior in 3D printed fractures controlled by surface roughness. For constant materials and basic frictional characteristics, shear strength increases with increasing the standard deviation of the surface height with dilation rate principally controlled by the average amplitude of the long period wavelength of the fracture surface and insensitive the secondary (minor amplitude) roughness. Importantly, these sensitivities are manifest in the permeability response. With increasing shear displacement, the fracture permeability first decreases and then increases with oscillations resulting from step changes in fracture-fracture contact architectures. As these distinctive behaviors are consistent with those of real rock fractures, we conclude that 3D printed fractures provide a useful analog to real rock fractures when constraining slip-permeability coupling during shear slip.

Stabilisation of a clay soil by ion injection using an electrical field

A programme of experiments was conducted to study the use of the electro-kinetic technique to transport a stabilising chemical agent through a clay soil. The experimental tests were undertaken on a clay soil in a special apparatus by applying a constant voltage gradient across the sample to introduce a solution of calcium chloride (CaCl2) with different concentrations in the soil. The variations of shear strength across the sample resulting from the electro-kinetic process were determined. The experiments were conducted in two groups. In the first group, the electro-osmosis method was used for soil samples with distilled water. In the second group, the electro-kinetic technique was applied to the soil to transport the solution of calcium chloride with varying concentrations through the pores in the soil. The results showed that the strength of soil increased for both groups and the amount of increase in the second group was dependent on the concentration of calcium chloride injected into the soil. The injection of this stabiliser also increased the electric current and electro-osmotic permeability.

Combined Effect of Rainfall and Shear Strength on the Stability of Highway Embankments Made of Yazoo Clay in Mississippi

Shallow slope failure repeatedly occurs in many highway slopes in Mississippi due to the abundance of expansive Yazoo Clay. The highly plastic clay soil undergoes repetitive wet–dry cycles, which reduces the shear strength to fully soften state. The current study focused on the progressive change in shear strength and the safety factor of slopes constructed out of Yazoo Clay. Undisturbed and remolded specimens were used to determine the peak, fully softened and residual shear strength, with effective normal stresses of 25, 50, and 100 kPa. The variations in shear strength were investigated with the 2D slope stability analysis software, which uses the Finite Element Method, Plaxis 2D. A highway slope in Jackson, MS was considered as the reference slope. Different rainfall volumes, 70.8 mm (2.78 in.) to 312.4 mm (12.29 in.), with a rainfall duration (30 min–7 days) based on 100-year return periods of Jackson, MS were utilized. Furthermore, three slope ratios 2H:1V, 3H:1V and, 4H:1V were selected for this study. The safety factor of the slope was determined based on peak shear strength soil test data. Later, the topsoil layer, which gets weathered within the active zone due to the repeated wet–dry cycle, was varied to fully softened and residual shear strengths. The slope stability analysis results showed that the safety factor reduces progressively from peak to residual shear strength. In addition, the factor of safety was critical when the soil reached its fully softened shear strength for 2H:1V and 3H:1V slopes with progressive rainfall. On the other hand, the 4H:1V slope reached failure at the residual phase with the presence of rainfall.

Undrained cylindrical cavity expansion in clays with fabric anisotropy and structure: Theoretical solution

Abstract This paper presents a novel, exact, semi-analytical solution for the quasi-static undrained expansion of a cylindrical cavity in soft soils with fabric anisotropy and structure. The assumed constitutive model is the S-CLAY1S model, which is a Cam clay type model that considers fabric anisotropy that evolves with plastic strains, structure and gradual degradation of bonding (destructuration) due to plastic straining. The solution involves the numerical integration of a system of seven first-order ordinary differential equations, three of them corresponding to the effective stresses in cylindrical coordinates, other three corresponding to the components of the fabric tensor and one corresponding to the amount of bonding. The solution is validated against finite element analyses and analytical limit asymptotic values of the effective stresses at the cavity wall are established. When destructuration is considered, the solution provides lower values of the effective radial stresses near the cavity wall, which are partially compensated by larger values of the excess pore pressures. Parametric analyses and discussion of the influence of soil overconsolidation, initial amount of bonding and rate of destructuration are presented. Finally, the theoretical solution is compared with experimental data of undrained shear strength variation immediately after pile driving in a sensitive clay.

Discussion of “Reclaimed Lignin-Stabilized Silty Soil: Undrained Shear Strength, Atterberg Limits, and Microstructure Characteristics” by Tao Zhang, Guojun Cai, and Songyu Liu

The discussers read with interest the recent paper by Zhang et al. (2018), which reports on the investigation of the effects of 0–12% lignin additive on some index and shear strength properties of a silty soil material. The use of the fall-cone device to study undrained shear strength variation with moisture content is pleasing to see and shows how the approach is useful for this purpose: namely the study of undrained strength variation. We wish to make the following comments regarding some of the underlying assumptions in the paper by way of offering some other explanations and interpretations for the results obtained.

Slope Stability of Embankments on Soft Soil Improved with Vertical Drains

The overloads of structures or embankments built on clayey soft ground are generally applied gradually, respecting a specific phasing. This phasing on construction allows the undrained shear strength of clay increasing over consolidation in order to avoid the risk of collapse during loading. In this work, the undrained shear strength of clay over the consolidation was estimated following SHANSEP method of which parameters proposed by eight researchers have been employed, as well as the slope stability analysis of embankments on soft soils during staged construction. Assessment of factor of safety for slope stability was conducted basing on the Bishop method. Additionally, the variations of undrained shear strength and factor of safety were presented. In order to validate the methods discussed in this study, slope stability analysis of five embankments constructed on clayey soft soils improved by the vertical drain technique in a high-speed railway construction project in Morocco was performed. For these embankments, field measurements about lateral displacement are presented. It was found that some of the adopted methods is in a good agreement with field measurements. Hence, generalization of these methods to many soft ground cases can be proposed.

Calculation model for the shear strength of unsaturated soil under nonlinear strength theory

The shear strength of unsaturated soils, a research hotspot in geotechnical engineering, has great guiding significance for geotechnical engineering design. Although kinds of calculation models for the shear strength of unsaturated soil have been put forward by predecessors, there is still need for new models to extensively consider the nonlinear variation of shear strength, particularly for the nonlinear effect of the net normal stress on the shear strength of unsaturated soil. Here, the shear strength of unsaturated soils is explored to study the nonlinear effects of net normal stress with the introduction of a general nonlinear Mohr-Coulomb (M-C) strength criterion, and the relationship between the matric suction (or suction stress) and degree of saturation (DOS) constructed by the soil-water characteristics curve (SWCC) of van Genuchten is also applied for unsaturated soil. Then, two calculation models (i.e., an envelope shell model and an effective stress model) are established for the shear strength of unsaturated soils under the nonlinear strength theory. In these two models, the curve of the shear strength of unsaturated soils versus the net normal stress exhibits a tendency to gently. Moreover, the proposed formulas have flexibility and convenience with five parameters (for the effective stress model) or six parameters (for the envelope shell model), which are from the M-C strength parameters of the saturated soil and fitting parameters of SWCC of van Genuchten. Thereafter, by comparison with the classical theory of the shear strength of unsaturated soils from some actual cases, the rationality and accuracy of the present models were verified.

The ARMR Classification System and the Modified Hoek-Brown Failure Criterion Compared to Directional Shear Strength Models for Anisotropic Rock Masses

The anisotropic rock mass rating classification system, ARMR, has been developed in conjunction with the Modified Hoek-Brown failure to deal with varying shear strength with respect to the orientation and degree of anisotropy within an anisotropic rock mass. Conventionally, ubiquitous-joint or directional shear strength models have assumed a general rock mass strength, typically estimated using the Hoek-Brown failure criterion, and applied a directional weakness in a given orientation depending on the anisotropic nature of the rock mass. Shear strength of the directional weakness is typically estimated using the Barton-Bandis failure criterion, or on occasion, the Mohr-Coulomb failure criteria. Directional shear strength models such as these often formed the basis of continuum models for slopes and underground excavations in anisotropic rock masses. This paper compares ARMR and the Modified Hoek-Brown failure criterion to the conventional directional shear strength models using a case study from Western Australia.

Effect of spatial variability of block-type cement-treated ground on the bearing capacity of foundation under inclined load

Deep mixing methods are widely used for stabilizing soft clayey soils and improving their bearing capacity. However, spatial variability in the shear strength of the cement-treated ground introduces uncertainties in estimating the bearing capacity for design. This paper evaluates the reliability of, block-type, cement-treated foundation under inclined load conditions using random field numerical limit analyses. The undrained shear strength is modelled as a random field which is characterized by a log-normal distribution and a spatial correlation length. Monte Carlo simulations are then used to interpret the stochastic bearing capacity factor and failure mechanisms for inclined concentric loading conditions at selected ratios of the shear strength ratio of cement-treated ground to original clay, the coefficient of variation in undrained shear strength and correlation length of the cement-treated zone. Variability of the undrained shear strength can reduce the expected bearing capacity of the cement-treated ground by 50–70% compared to homogeneously mixed clay.

Fine roots benefit soil physical properties key to mitigate soil detachment capacity following the restoration of eroded land

Trait-based approaches are increasingly used to improve ecological restoration in degraded ecosystems. The aim of this study was to evaluate how vegetation controls soil detachment capacity (Dc) by concentrated flow based on the linkages between root traits and soil physics. We selected 60 plots along a land degradation gradient caused by long-term water erosion in a small catchment, central China. These plots consisted of woodlands, scrublands, grasslands and bare lands. And soil physical properties, root traits and Dc were measured in each plot. Fine roots (0.2 mm < diameter < 2 mm) accounted for 51–93% of total root length in topsoil. Roots explained most of the soil variations in noncapillary porosity, aggregate stability and shear strength. Furthermore, our prediction model (R2 = 0.88, NSE = 0.85) showed that fine roots length density and soil shear strength were the primary factors reducing Dc. Vegetation restoration improves multiple soil physical properties key to mitigating Dc, and the root functional traits play a substantial role in this relationship. These findings could provide the basis for soil conservation, and for expanding the pool of species of interest, which can be used to provide erosion mitigation services in degraded ecosystems.

Parameter variability of undrained shear strength and strain using a database of reconstituted soil tests

During construction, the mobilization of undrained shear strength must be limited to avoid soil failure. Soil strains must be controlled to avoid compromising structural serviceability. To assess foundation performance by strength mobilization, an understanding of soil strains at various levels of strength mobilization is required. In practice, ground investigation data are often limited, and assessment of the expected variation of stress–strain and undrained shear strength is improved with empirical correlations calibrated with a database. The new database RFG/TXCU-278 contains data of 278 consolidated–undrained triaxial tests on reconstituted fine-grained soil samples compiled from the literature. Analysis of the database to evaluate the variability of undrained strength ratio (cu/[Formula: see text]) and a reference shear strain with shear mode is undertaken in this paper. The new database provides evidence that shear strain (like undrained shear strength) is sensitive to the consolidation (isotropic or K0) and shear mode (triaxial compression or extension) applied in the test. For the materials included in the database, the strength mobilization parameters obtained from a triaxial compression test can be used to predict the corresponding triaxial extension parameters to a reasonable accuracy.