Spatiotemporal variations of sand hydraulic conductivity by microbial application methods

The spatiotemporal distributions of microbes in soil by different methods could affect the efficacy of the microbes to reduce the soil hydraulic conductivity.In this study,the specimens of bio-mediated sands were prepared using three different methods,i.e.injecting,mixing,and pouring a given microbial so-lution onto compacted sand specimens.The hydraulic conductivity was measured by constant-head tests,while any soil microstructural changes due to addition of the microbes were observed by scan-ning electron microscope(SEM)and mercury intrusion porosimetry(MIP)tests.The amount of dextran concentration produced by microbes in each type of specimen was quantified by a refractometer.Results show that dextran production increased exponentially after 5-7 d of microbial settling with the supply of culture medium.The injection and mixing methods resulted in a similar amount and uniform dis-tribution of dextran in the specimens.The pouring method,however,produced a nonuniform distri-bution,with a higher concentration near the specimen surface.As the supply of culture medium discontinued,the dextran content near the surface produced by the pouring method decreased dramatically due to high competition for nutrients with foreign colonies.Average dextran concentration was negatively and correlated with hydraulic conductivity of bio-mediated soils exponentially,due to the clogging of large soil pores by dextran.The hydraulic conductivity of the injection and mixing cases did not change significantly when the supply of culture medium was absent.

Rectangular tunnel heading stability in three dimensions and its predictive machine learning models

Tunnel heading stability in two dimensions(2D)has been extensively investigated by numerous scholars in the past decade.One significant limitation of 2D analysis is the absence of actual tunnel geometry modeling with a considerable degree of idealization.Nevertheless,it is possible to study the stability of tunnels in three dimensions(3D)with a rectangular shape using finite element limit analysis(FELA)and a nonlinear programming technique.This paper employs 3D FELA to generate rigorous solutions for stability numbers,failure mechanisms,and safety factors for rectangular-shaped tunnels.To further explore the usefulness of the produced results,multivariate adaptive regression spline(MARS)is used for machine learning of big dataset and development of design equations for practical design applications.The study should be of great benefit to tunnel design practices using the developed equations provided in the paper.

Limit load and failure mechanisms of a vertical Hoek-Brown rock slope

The problem considered in this short note is the limit load determination of a vertical rock slope.The classical limit theorem is employed with the use of adaptive finite elements and nonlinear programming to determine upper and lower bound limit loads of a Hoek-Brown vertical rock slope.The objective function of the mathematical programming problem is such as to optimize a boundary load,which is known as the limit load,resembling the ultimate bearing capacity of a strip footing.While focusing on the vertical slope,parametric studies are carried out for several dimensionless ratios such as the dimensionless footing distance ratio,the dimensionless height ratio,and the dimensionless rock strength ratio.A comprehensive set of design charts is presented,and failure envelopes shown with the results explained in terms of three identified failure mechanisms,i.e.the face,the toe,and the Prandtl-type failures.These novel results can be used with great confidence in design practice,in particularly noting that the current industry-based design procedures for the presented problem are rarely found.

Physics-based and data-driven modeling for stability evaluation of buried structures in natural clays

This study presents a hybrid framework to predict stability solutions of buried structures under active trapdoor conditions in natural clays with anisotropy and heterogeneity by combining physics-based and data-driven modeling.Finite-element limit analysis(FELA)with a newly developed anisotropic undrained shear(AUS)failure criterion is used to identify the underlying active failure mechanisms as well as to develop a numerical(physics-based)database of stability numbers for both planar and circular trapdoors.Practical considerations are given for natural clays to three linearly increasing shear strengths in compression,extension,and direct simple shear in the AUS material model.The obtained numerical solutions are compared and validated with published solutions in the literature.A multivariate adaptive regression splines(MARS)algorithm is further utilized to learn the numerical solutions to act as fast FELA data-driven surrogates for stability evaluation.The current MARS-based modeling provides both relative importance index and accurate design equations that can be used with confidence by practitioners.

Multivariate adaptive regression splines analysis for 3D slope stability in anisotropic and heterogenous clay

Little research can be found in relation to the stability of anisotropic and heterogenous soils in three dimensions.In this paper,we propose a study on the three-dimensional(3D)undrained slopes in anisotropic and heterogenous clay using advanced upper and lower bounds finite element limit analysis(FELA).The obtained stability solutions are normalized,and presented by a stability number that is a function of three geometrical ratios and two material ratios,i.e.depth ratio,length ratio,slope angle,shear strength gradient ratio and anisotropic strength ratio.Numerical results are compared with experimental data in the literature,and charts are presented to cover a wide range of design parameters.Using the multivariate adaptive regression splines(MARS)analysis,the respective influence and sensitivity of each design parameter on the stability number and the failure mechanism are investigated.An empirical equation is also developed to effectively estimate the stability number.

A new design equation for drained stability of conical slopes in cohesive-frictional soils

New plasticity solutions to the drained stability of conical slopes in homogeneous cohesive-frictional soils were investigated by axisymmetric finite element limit analysis. Three parameters were studied,i.e. excavated height ratios, slope inclination angles, and soil friction angles. The influences of these parameters on the stability factor and predicted failure mechanism of conical slopes were discussed. A new design equation developed from a nonlinear regression of the lower bound solution was proposed for drained stability analyses of a conical slope in practice. Numerical examples were given to demonstrate a practical application of the proposed equation to stability evaluations of conical slopes with both associated and non-associated flow rules.

Undrained stability of a spherical cavity in cohesive soils using finite element limit analysis

A parametric study of undrained stability of a spherical cavity in clays is investigated by finite elementlimit analysis with an axisymmetric condition. Influences of cover depth ratio of cavity and dimensionlessoverburden factor on predicted failure mechanisms and dimensionless load factor are examined.It is found that a previously recommended and up-to-date lower bound solution to the problem wassignificantly inaccurate for practice use. Thus, an accurate approximate solution to the problem is proposedfrom nonlinear regression analysis of the computed average bound solutions. New cavity stabilityfactors for the soil cohesion and soil unit weight are proposed. New findings are revealed for the threedimensionaleffect of the cavity shape on these factors between the axisymmetric and plane strainconditions, and their applications to the undrained stability evaluation of cavity problems in practice aredescribed.

Axisymmetric loading on nanoscale multilayered media

Multilayered nanoscale structures are used in several applications.Because the effect of surface energy becomes nontrivial at such a small scale,a modified continuum theory is required to accurately predict their mechanical behaviors.A Gurtin–Murdoch continuum model of surface elasticity is implemented to establish a computational scheme for investigating an elastic multilayered system under axisymmetric loads with the incorporation of surface/interface energy.Each layer stiffness matrix is derived based on the general solutions of stresses and displacements obtained in the form of the Hankel integral transform.Numerical solutions to the global equation,which are formulated based on the continuity conditions of tractions and displacements across interfaces between layers,yield the displacements at each layer interface and on the top surface of the multilayered medium.The numerical solutions indicate that the elastic responses of multilayered structures are affected significantly by the surface material properties of both the top surface and interfaces,and that they become size dependent.In addition,the indentation problem of a multilayered nanoscale elastic medium under a rigid frictionless cylindrical punch is investigated to demonstrate the application of the proposed solution scheme.

Underground storage tank blowout analysis:Stability prediction using an artificial neural network

Most geotechnical stability research is linked to“active”failures,in which soil instability occurs due to soil self-weight and external surcharge applications.In contrast,research on passive failure is not common,as it is predominately caused by external loads that act against the soil self-weight.An earlier active trapdoor stability investigation using the Terzaghi’s three stability factor approach was shown to be a feasible method for evaluating cohesive-frictional soil stability.Therefore,this technical note aims to expand“active”trapdoor research to assess drained circular trapdoor passive stability(blowout condition)in cohesive-frictional soil under axisymmetric conditions.Using numerical finite element limit analysis(FELA)simulations,soil cohesion,surcharge,and soil unit weight effects are considered using three stability factors(Fc,Fs,and Fγ),which are all associated with the cover-depth ratio and soil internal friction angle.Both upper-bound(UB)and lower-bound(LB)results are presented in design charts and tables,and the large dataset is further studied using an artificial neural network(ANN)as a predictive model to produce accurate design equations.The proposed passive trapdoor problem under axisymmetric conditions is significant when considering soil blowout stability owing to faulty underground storage tanks or pipelines with high internal pressures.

Developing soft-computing regression model for predicting bearing capacity of eccentrically loaded footings on anisotropic clay

In this investigation,the bearing capacity solution of a strip footing in anisotropic clay under inclined and eccentric load is analyzed using the numerical simulation model.The lower and upper bound finite element limit analysis(FELA)approaches are utilized to establish precise modeling and derive the numerical outcomes of a strip footing’s bearing capacity.All analyses use effective automated adaptive meshes with three iteration stages to enhance the accuracy of the outcomes.The parametric analysis is performed to examine the influence of four dimensionless parameters which are taken into account in this study,namely the anisotropic strength ratio,the dimensionless eccentricity,the load inclination angle,and the adhesion factor to the bearing capacity factor.Furthermore,a new model has been proposed to predict the bearing capacity factor for the calculation of the undrained bearing capacity for footings resting on an anisotropic clay using an advanced data-driven method(MOGA-EPR).The new model takes into account the anisotropy,eccentricity,and inclination of the applied load and could be used with confidence in routine designs of shallow foundations in undrained conditions with the consideration of the anisotropic strengths of clays.

Stability of active trapdoors in axisymmetry

Trapdoor stability has been widely studied by many researchers in the field of tunneling engineering.A general question being fre-quently asked is that why most sinkholes have a near-perfect circular shape on the ground surface.This could be possibly explained by the current numerical study using finite element limit analysis under axisymmetric condition,where upper and lower bound solutions of active circular trapdoors are determined.The failure study of sinkholes and the associated failure mechanisms in this paper are for non-homogeneous clay with a linear increase of strength with depth under various cover depth ratios and dimensionless strength gra-dients.A design equation for predicting the stability solutions is also developed based on the novel three dimensional solutions using axisymmetry.

Design equation for stability of a circular tunnel in anisotropic and heterogeneous clay

The safety assessment of tunnel stability is critical to tunnel construction and requires accurate analysis to obtain a reliable prediction.Strength anisotropy is an important aspect of clay behavior,but it is mostly neglected in practical stability analyses.In this study,the effects of undrained strength anisotropy and strength nonhomogeneity on the stability of unlined circular tunnels in clays are investi-gated.The static approach of lower-bound(LB)analysis using finite-element and second-order cone programming is employed to exam-ine the aforementioned effects.The anisotropic shear strength of clay is modeled by employing an elliptical yield function under plane strain conditions.A complete set of dimensionless parameters covering the cover depth ratios of tunnels,normalized overburden pressure ratios,normalized strength gradient ratios of clays,and anisotropic strength ratios,are systematically investigated.The new LB solutions indicate that the stability load factor of the problem has a nonlinear relationship with the cover depth ratio and the anisotropic strength ratio,and there exists a linear relationship with the normalized overburden pressure and the normalized strength gradient.Their influ-ence on the predicted failure mechanism is parametrically evaluated.A statistically approximate stability equation of unlined circular tunnels in anisotropic and non-homogeneous clay is proposed for the first time,which contains four new stability factors,namely,con-stant undrained strength,linearly increasing strength gradient,undrained strength anisotropy,and soil unit weight,and it can serve as a fast and accurate tool for predicting the undrained stability of this problem in practice.

Undrained stability of pit-in-pit braced excavations under hydraulic uplift

Pit-in-pit(PIP)excavations in an aquifer–aquitard system likely undergo catastrophic failures under the hydraulic uplift,the associated undrained stability problem,however,has not been well analyzed in the past.To this end,a hypothetical model of PIP braced excavation in typical soil layers of Shanghai,China is developed using the finite element limit analysis(FELA)tool.The FELA solutions of safety factors(FSs)against hydraulic uplift are verified with the results from the finite element analysis with strength reduction technique(SRFEA)and existing design approaches.Subsequently,FELA is employed to identify the triggering and failure mechanisms of PIP braced excavations subjected to hydraulic uplift.A series of parametric studies considering the various geometric configurations of the PIP excavation,undrained shear strengths of aquitard,and artesian pressures are carried out.The sensitivities of relevant design parameters are further assessed using a multivariate adaptive regression splines(MARS)model that is capable of accurately capturing the nonlinear relationships between a set of input variables and output variables in multi-dimensions.A MARS-based design equation used for predicting FS is finally presented using the artificial dataset from FELA for practical design uses.

Undrained stability of active trapdoors in two-layered clays

Several environmental changes can induce an underground hole,leading to failures of non-ground infrastructure,such as pavements.Under a continued overload of traffic action on the pavement,the hole can potentially collapse,leading to creation of potholes.This phenomenon is commonly known as a trapdoor problem.Even though there are several previous works considering this problem,the stability solutions of trapdoors in two-layered soils have not yet been studied.To estimate the undrained stability of active trapdoors in two-layered clays under plane strain conditions,numerical solutions based on the finite element method have been developed.The influence parameters include the coverage depth of the trapdoor,and the thickness and undrained shear strength of the clay layers.The effects of these parameters on the stability of active trapdoors as well as their associated failure mechanisms are examined and discussed in this paper.The solutions are presented in the form of dimensionless charts that can be used for the design of trapdoor systems in two-layered clays with different thicknesses and undrained shear strengths.