Geotechnics, Volume 2, Issue 3 (September 2022) – 15 articles

The objective of this study is to develop data-driven predictive models for peak rotation and factor of safety for tipping-over failure of rocking shallow foundations during earthquake loading using multiple nonlinear machine learning (ML) algorithms and a supervised learning technique. Centrifuge and shaking table experimental results on rocking foundations have been used for the development of k-nearest neighbors regression (KNN), support vector regression (SVR), and random forest regression (RFR) models. The input features to ML models include critical contact area ratio of foundation; slenderness ratio and rocking coefficient of rocking system; peak ground acceleration and Arias intensity of earthquake motion; and a categorical binary feature that separates sandy soil foundations from clayey soil foundations. Based on repeated k-fold cross validation tests of models, we found that the overall average mean absolute percentage errors (MAPE) in predictions of all three nonlinear ML models varied between 0.46 and 0.60, outperforming a baseline multivariate linear regression ML model with corresponding MAPE of 0.68 to 0.75. The input feature importance analysis reveals that the peak rotation and tipping-over stability of rocking foundations are more sensitive to ground motion demand parameters than to rocking foundation capacity parameters or type of soil. Full article

The variations of seismic velocity prior to the occurrence of major seismic events are an indicator of the rock mass performance subjected to mining-induced stress. There have been no prior field-scale studies to examine stress change within the rockmass volume immediately prior to potentially damaging mining-induced seismicity. Monitoring stress change is critical for mine stability and operation safety and eventually improves production by optimizing mine designs and mining practices. In this study, five major seismic events that occurred in a narrow-vein mine were used as case studies in order to investigate any significant changes in P-wave velocity distribution, on a daily basis, within a week of seismic events with Mw > 1; if observed, such changes could provide a warning to mine engineers and workers. It was observed there was no consistent significant velocity change of more than 1% within 200 m of the hypocenters within 6 days prior to the events. Additionally, the influence of blasting in the week of the occurrence of events was investigated however no recognizable trend was observed between blasting and changes in the seismic velocity distribution within the rock mass on the day of a blast or the following day. Full article

Saline conditions govern soil behavior during evaporation, thereby affecting the water budget in semi-arid regions. This research examined the effects of saline pore fluid on soil behavior during evaporation. The results indicated volumetric reductions of about 5% for silty sand and about 15% for lean clay. The evaporative flux for silty sand decreased from 26 mg/m²∙s to 22 mg/m²∙s in StageII, remained at a constant flux in StageIII, and decreased to 13 mg/m²∙s in StageIV. The air entry and residual suction values were found to be 5 kPa and 100 kPa, respectively, and the total suction of about 5000 kPa merged with matric suction near the Stage II/Stage III boundary. The swell–shrink curve (SSC) was J-shaped with the only void ratio decrease in Stage II. In contrast, the evaporative flux for lean clay decreased from 30 mg/m²∙s to 15 mg/m²∙s in StageII, to 10 mg/m²∙s in StageIII, and then to 5 mg/m²∙s in StageIV. The air entry and residual suction values were 5 kPa and 2000 kPa, respectively, and the total suction during Stage II and Stage III ranged from 1000 kPa to 6000 kPa, with an average value of 3500 kPa. The SSC showed a major void ratio decrease in Stage II, marginal decrease in Stage III, and no decrease in Stage IV. Under high demand, the evaporative flux for silty sand was constant at 180 mg/m²∙s in StageIII and decreased to 50 mg/m²∙s in Stage IV, whereas it decreased for the lean clay from 230 mg/m²∙s to 145 mg/m²∙s in StageII, to 95 mg/m²∙s in StageIII, and then to 25 mg/m²∙s in StageIV. For both soils, the total water loss was found to be six times higher than that under low demand. Full article

Buried continuous pipelines are prone to failure due to permanent ground deformation as a result of fault rupture. Since the failure mode is dependent on a number of factors, a probabilistic approach is necessary to correctly compute the seismic risk. In this study, a novel method to estimate regional seismic risk to buried continuous pipelines is presented. The seismic risk assessment method is thereafter illustrated for buried gas pipelines in the City of Victoria, British Columbia. The illustrated example considers seismic hazard from the Leech River Valley Fault Zone (LRVFZ). The risk assessment approach considers uncertainties of earthquake rupture, soil properties at the site concerned, geometric properties of pipes and operating conditions. Major improvements in this method over existing comparable studies include the use of stochastic earthquake source modeling and analytical Okada solutions to generate regional ground deformation, probabilistically. Previous studies used regression equations to define probabilistic ground deformations along a fault. Secondly, in the current study, experimentally evaluated 3D shell and continuum pipe–soil finite element models were used to compute pipeline responses. Earlier investigations used simple soil spring–beam element pipe models to evaluate the pipeline response. Finally, the current approach uses the multi-fidelity Gaussian process surrogate model to ensure efficiency and limit required computational resources. The developed multi-fidelity Gaussian process surrogate model was successfully cross-validated with high coefficients of determination of 0.92 and 0.96. A fragility curve was generated based on failure criteria from ALA strain limits. The seismic risks of pipeline failure due to compressive buckling and tensile rupture at the given site considered were computed to be 1.5 percent and 0.6 percent in 50 years, respectively. Full article

Surface-active solutes that exist in the subsurface either naturally (humic acid) or as a result of anthropogenic activities (alcohols, surfactants, PFAS) alter the hydraulic and geotechnical properties of the unsaturated porous media. The alteration of properties is the result of concentration-dependent surface tension, and/or density, and the contact angle effects. These effects are manifested in the form of changes in water retention and conduction and changes in the suction component of the shear strength. Differences in the spatial distribution of these solutes in the subsurface result in capillary pressure gradients causing flow perturbations. Conceptual and numerical models to understand the effects of these solutes require concentration-dependent consideration of surface tension, density, and the contact angle effects on hydraulic and geotechnical properties of porous media. Capillary rise experiments have been carried out to either quantify the effect of surface-active solutes on the height of capillary rise or to determine the concentration-dependent contact angle changes due to salinity of the pore water. This paper provides a comprehensive review of the literature on capillary rise experiments and how they can potentially be used to characterize the hydraulic and geotechnical properties of unsaturated porous media affected by surface-active solutes. Full article

In highway slopes (HWS) constructed on high expansive clay soil (HECS), in situ moisture variation is an environmentally driven variable that can significantly impact the safety of the constructed soil. Electrical resistivity imaging (ERI) is a non-destructive method with a considerable potential for subsurface soil moisture mapping, which can be correlated with volumetric soil moisture content (VSMC) and soil matric suction (SMS) of HECS to remarkably enhance the evaluation of the performance of the HWS. However, limited datasets are available to evaluate the accuracy and feasibility of the available correlative field-based models for the HECS under various field conditions. The objective of the current study is to develop a field-based model of VSMC and SMS using real-time field monitoring and ERI data. Six HWS located in the Jackson metro area in Mississippi (MS), USA were considered as reference slopes in this study. Comprehensive field instrumentation was executed at the six HWS to monitor the VSMC, SMS and rainfall intensity. The sensors were installed at the crest, middle and toe of the slope. The 2D ERI test was conducted using a dipole–dipole array with multiple electrodes at 5 ft (1.5 m) spacing. The ERI survey was conducted at the crest and middle of the six HWS to image the continuous soil subsurface profile in terms of moisture variation. The developed models indicated a good agreement between instrumented and ERI data. The developed models will facilitate the estimation of VSMC and SMS variations and aid in performance monitoring of the HWS built on HECS such as Yazoo clay. Full article

The classical Neumann boundary value problem of an isotropic, homogeneous elastic half-plane under plane strain conditions is readdressed as the limiting case of the fully three-dimensional problem. Analytical solutions of the stress and strain tensors are obtained by taking the limit from known three-dimensional solutions. It is shown that the displacement fields for the plane strain problem are not well defined. A small number of simple expressions are developed, which provide a general solution for linearly-varying traction over arbitrary regions on the boundary. A simple, efficient, and rapidly convergent algorithm is developed which uses these solutions as analytic elements and provides a solution approach to the general boundary value problem. The method is verified against known solutions for Hertzian contact between parallel cylinders. Two numerical examples are presented for the analysis of shallow foundation systems. In the first, the boundary conditions are informed by analytical elastoplastic calculations and a strain influence analysis is performed and compared with the Schmertmann method. Subsequently, empirical laboratory contact traction distributions measured by Bauer et al., in both the normal and tangential directions are employed as boundary conditions for an analysis of the underlying stress field. Full article

Prime materials involved in a problem such as underground structures are concrete, reinforcement steel, and geo-material surrounding the tunnel. Among these three materials, concrete and steel are manufactured materials and their properties can be controlled up to a certain extent. However, geo-material is a naturally occurring material whose constitutive properties vary from region to region, making it highly unpredictable. Findings from one study cannot be applied to other geotechnical problems directly, especially in the case of tunnels subjected to surface explosions. The blast wave generated has to travel through the geo-material before it interacts with the tunnel. As the shock wave propagates radially, its characteristics are likely to be altered by the geo-material. Limited study has been carried out considering this problem. In the present study, the effect of various types of geo-material on the blast response of tunnels subjected to surface explosions is investigated. Finite element analysis has been carried out using LS-DYNA^®, wherein the problem has been modeled using the multi-material arbitrary Lagrangian–Eulerian (MM-ALE) method. Materials with fluid behavior such as air, explosives, and soil are modeled using ALE formulation. Other materials including tunnel lining, reinforcement steel, and rock are modeled using Lagrangian formulation. Blast loading is simulated using the Jones–Wilkins–Lee (JWL) equation of state. Geo-materials considered for the comparative study are sandy loam, saturated clayey soil, sandstone, and granite. Vertical displacement measured at the crown of the tunnel is used to determine the response of the tunnel. Sandy loam soil, being a highly compressible soil, exhibits non-linear and fluid-like behavior under high-strain loading such as explosions. Tunnels undergo extreme deformation in the case of sandy loam soil and clayey soil compared to rock cases. Further, the effect of saturation in sandy loam on tunnel stability is studied. It is observed that with the increase in saturation of soil, more blast energy is transmitted to the structure, which results in higher deformation. Lastly, the effect of the weathering of rock on the tunnel’s response is investigated in the case of sandstone and granite. It was observed that weathering in rock led to more displacement of tunnel crown when compared to intact rock. Full article

This study focuses on the stability analysis of slopes reinforced by soil nailing. The effects of slope geometry and nail parameters on slope stability are investigated using PLAXIS 2D. Four different slope angles and three different backslope angles are considered for assessing the effect of slope geometry on the stability of a nailed slope. The factor of safety (FS) was found to decrease with the increasing values of the slope angle as well as the backslope angle. The influence of different nail parameters (nail inclination, nail length, and nail spacing) was also investigated. With the increase in nail inclination, FS was found to increase initially and thereafter, reaching a peak value followed by a drop in FS. The optimum nail inclination was found between 0 and 25° at a horizontal angle, depending on the different slope geometries, which is evident from observation of the slip surface as well. With the increase of nail length, FS increases; however, the increase was small after L/H (length of nail/height of slope) reached a value of 0.9. Moreover, increasing the length of the nail was found to be effective in reducing the lateral movement of the slope. The maximum nail forces are observed in the bottom-most row of nails and increase with the depth. The inclusion of soil nailing with optimum nail parameters can increase FS by 29–75% depending on the slope geometry, signifying the effectiveness of nailing. Full article

A new method for implicit integration of the Mohr-Coulomb non-smooth multisurface plasticity models is presented, and Koiter’s requirements are incorporated exactly within the proposed algorithm. Algorithmic and numerical complexities are identified and introduced by the nonsmooth intersections of the Mohr-Coulomb surfaces; then, a projection contraction algorithm is applied to solve the classical Kuhn–Tucker complementary equations which provide the only characterization of possible active yield surfaces as a special class of variational inequalities, and the actual active yield surface is further determined by iteration. The basic idea is to calculate derivatives of the yield and potential functions with the expressions in the principal stresses and perform the return manipulations in the general stress space. Based on the principal stress characteristic equation, partial derivatives of principal stresses are calculated. The proposed algorithm eliminates the error caused by smoothing the corner of Mohr-Coulomb surfaces, avoids the numerical singularity at the intersections in the general stress space, and does not require the stress transformation needed in the principal stress space method. Lastly, several numerical examples are given to verify the validity of the proposed method. Full article

Several studies have been reported in published literature on analytical solutions for a laterally loaded pile installed in a homogeneous single soil layer. However, piles are rarely installed in an ideal homogeneous single soil layer. The present study describes a new continuum-based analysis or energy-based approach for predicting the pile displacement responses subjected to static lateral loads and moments considering the soil non-linearity. This analytical analysis treats the pile as an elastic Euler–Bernoulli beam and the soil as a three-dimensional (3D) continuum in which the non-linear elastic properties are described by a modulus degradation relationship. The principle of virtual work was applied to the energy equation of a pile–soil system in order to obtain the governing differential equation for the pile and soil displacements. An iterative procedure was adopted to solve the equations numerically using a finite difference method (FDM). The pile displacement response was obtained using the software MATLAB R2021a, and the results from the energy-based method were compared with those obtained from the field test data as well as the finite element analysis (FEA) based on the software ANSYS Workbench 2021R1. The present study investigated the effect of explicit incorporation of soil properties and layering through a parametric study in order to understand the importance of predicting appropriate pile displacement responses in a linear elastic soil system. The responses indicated that the effect of soil layers and their thicknesses, pile properties and the variation in soil moduli have a direct impact on the displacements of piles subjected to lateral loading. Hence, a proper emphasis has to be given to account for the soil non-linearity. Considering the effect of soil non-linearity, it is observed that the results obtained from the energy-based method agreed well with the field measured values and those obtained from the FEA. The results indicated a difference of approximately less than 7% between the proposed method and the FEA. The approach presented in this study can be further extended to piles embedded in multi-layered soil strata subjected to the combined action of axial loads, lateral loads and moments. Furthermore, the same approach can be extended to study the response of the soil to group piles. Full article

Numerous studies have been reported in the published literature on analytical solutions for a vertically loaded pile installed in a homogeneous single soil layer. However, piles are rarely installed in an ideal homogeneous single soil layer. This study presents an analytical model based on the energy-based approach to obtain displacements in an axially loaded pile embedded in multi-layered soil considering soil non-linearity. The developed analytical model incorporating Euler-Bernoulli beam theory proved to be an effective way in estimating the load-displacement responses of piles embedded in multi-layered non-linear elastic soil strata. The differential equations are solved analytically and numerically using the variational principle of mechanics. A parametric study investigated the effect of explicit incorporation of soil properties and layering in order to understand the importance of predicting appropriate pile displacement responses in linear elastic soil system. It is clear from the results that the analyses which consider the soil as a single homogeneous layer will not be able to produce an accurate estimation of the pile stiffnesses. Therefore, it is highly important to account for the effect of soil layering and the non-linear response. The pile displacement response is obtained using the software MATLAB R2019a and the results from the energy-based method are compared with those obtained from the field test data as well as the Finite Element Analysis (FEA) based on the software ANSYS 2019R3. The non-linear elastic constitutive relationship which described the variation of secant shear modulus with strain through a power law has shown reasonably accurate predictions when compared to the published field test data and the FEA. The developed mathematical framework is also more computationally efficient than the three-dimensional (3D) FEA. Full article

Circular/spherical rigid particle models that were initially applied to rock fracture studies were not able to match the ratio of the compressive strength to tensile strength that occurs in rock. In addition, the predicted macroscopic friction angle was much lower than the known hard rock experimental values. Several enhancements have been proposed to address these issues, namely the use of a clumped particle logic or the adoption of polygonal/polyhedral grain structures, either rigid or flexible. In this work, a flexible 2D DEM based particle model (PM) that allows deformable particles to interact in a simplified way is presented. The proposed flexible PM model keeps the contact interaction simplicity and the reduced computational costs characteristic of circular rigid particle models. The PM model is tested using biaxial tests and Brazilian tests. A discussion regarding the influence of the grain deformability on the macroscopic elastic and strength response is presented. It is shown that, when compared with a rigid model, the proposed flexible PM model predicts more reasonable indirect tensile strength to direct tensile strength ratio and requires a smaller value of contact fracture energy to give a good agreement with known experimental data. It is also shown that the proposed flexible PM model can predict a behaviour similar to that obtained using a flexible PM model through inner particle discretization that is more computationally demanding. Full article

Gravity-driven mass flows are typically large-scale complex multi-phase phenomena involving multiple interacting phases. Various types of mass flows usually exhibit distinct behaviors in their formation, propagation and deposition. In such large-scale geological systems, many uncertainties may arise from the variations in material composition and phase behavior. The present study aims to investigate the important characteristics of some common types of mass flows including debris flows, mudflows and earth flows, based on a recently developed multi-phase computational framework, r.avaflow for flow simulation. Fractions of different phases are varied to reflect different characteristics of material composition of various mass flows and simulate the resulting flow behavior. The evolution of the critical entities during the flow motion, such as velocity, peak discharge, flow height, kinetic energy, run-out distance and deposition is examined; considerable differences among various flows are identified and discussed. Overall, the simulated mudflow cases develop higher velocity, peak discharge, kinetic energy, and longer run-out distance than the debris flow cases. The fluid fraction has a significant influence on the flow dynamics; a higher fluid fraction often leads to higher velocities and long run-out distances, but lower kinetic energy, and it also affects the final deposition and deposition pattern considerably. The present study shows promising potential of a quantitative approach to the physics and mechanics of mass flows that may assist in the risk assessment of such large-scale destructive geological hazards or disasters. Full article

Over the conventional limit equilibrium method and limit analysis method, the finite element method is advantageous, especially for slopes involving complex failure mechanisms where the critical slip surfaces cannot be represented by log spirals and other similarities. In the presence of tension cracks at slope crests, however, the finite element method encounters difficulties in convergence while handling Mohr–Coulomb’s yielding surfaces with tensile strength cut-off. Meanwhile, the commonly used load-controlled method for the system of nonlinear equilibrium equations is hard to bring the slope into the limit equilibrium state. The two drawbacks drag down the finite element method in more extensive applications. By reducing the constitutive integration of plasticity with non-smooth yielding surfaces to the mixed complementarity problem, the convergence in numerical constitutive integration is established for arbitrarily large incremental strains. In order to bring the slope to the limit equilibrium state, a new displacement-controlled algorithm is designed for the system of nonlinear equilibrium equations, which is far more efficient than the load-controlled method. A procedure is proposed to locate tension cracks. Corresponding to the Mohr–Coulomb failure criterion with and without tensile strength cut-off, the failure mechanisms differ significantly, while the difference in the factor of safety might be ignorable. Full article