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.

Strength reduction and step-loading finite element approaches in geotechnical engineering

The finite element limit analysis method has the advantages of both numerical and traditional limit equilibrium techniques and it is particularly useful to geotechnical engineering.This method has been developed in China,following well-accepted international procedures,to enhance understanding of stability issues in a number of geotechnical settings.Great advancements have been made in basic theory,the improvement of computational precision,and the broadening of practical applications.This paper presents the results of research on（1） the efficient design of embedded anti-slide piles,（2） the stability analysis of reservoir slopes with strength reduction theory,and（3） the determination of the ultimate bearing capacity of foundations using step-loading FEM（overloading）.These three applications are evidence of the design improvements and benefits made possible in geotechnical engineering by finite element modeling.

Finite element analyses of slope stability problems using non-associated plasticity

In recent years, finite element analyses have increasingly been utilized for slope stability problems. In comparison to limit equilibrium methods, numerical analyses do not require any definition of the failure mechanism a priori and enable the determination of the safety level more accurately. The paper compares the performances of strength reduction finite element analysis(SRFEA) with finite element limit analysis(FELA), whereby the focus is related to non-associated plasticity. Displacement-based finite element analyses using a strength reduction technique suffer from numerical instabilities when using non-associated plasticity, especially when dealing with high friction angles but moderate dilatancy angles. The FELA on the other hand provides rigorous upper and lower bounds of the factor of safety(FoS) but is restricted to associated flow rules. Suggestions to overcome this problem, proposed by Davis(1968), lead to conservative FoSs; therefore, an enhanced procedure has been investigated. When using the modified approach, both the SRFEA and the FELA provide very similar results. Further studies highlight the advantages of using an adaptive mesh refinement to determine FoSs. Additionally, it is shown that the initial stress field does not affect the FoS when using a Mohr-Coulomb failure criterion.

Effects of cement-enhanced soil on the ultimate lateral resistance of composite pile in clayey soil

The composite pile consisting of core-pile and surrounding cement-enhanced soil is a promising pile foundation in recent years.However,how and to what extent the cement-enhanced soil influences the ultimate lateral resistance has not been fully investigated.In this paper,the ultimate lateral resistance of the composite pile was studied by finite element limit analysis(FELA)and theoretical upper-bound analysis.The results of FELA and theoretical analysis revealed three failure modes of laterally loaded composite piles.The effects of the enhanced soil thickness,strength,and pile-enhanced soil interface characteristics on the ultimate lateral resistance were studied.The results show that increasing the enhanced soil thickness leads to a significant improvement on ultimate lateral resistance factor(N P),and there is a critical thickness beyond which the thickness no longer affects the N P.Increasing the enhanced soil strength induced 6.2%-232.6%increase of N P.However,no noticeable impact was detected when the enhanced soil strength was eight times higher than that of the natural soil.The maximum increment of N P is only 30.5%caused by the increase of interface adhesion factor(a).An empirical model was developed to calculate the N P of the composite pile,and the results show excellent agreement with the analytical results.

Developing a novel big dataset and a deep neural network to predict the bearing capacity of a ring footing

The accurate prediction of the bearing capacity of ring footings,which is crucial for civil engineering projects,has historically posed significant challenges.Previous research in this area has been constrained by considering only a limited number of parameters or utilizing relatively small datasets.To overcome these limitations,a comprehensive finite element limit analysis(FELA)was conducted to predict the bearing capacity of ring footings.The study considered a range of effective parameters,including clay undrained shear strength,heterogeneity factor of clay,soil friction angle of the sand layer,radius ratio of the ring footing,sand layer thickness,and the interface between the ring footing and the soil.An extensive dataset comprising 80,000 samples was assembled,exceeding the limitations of previous research.The availability of this dataset enabled more robust and statistically significant analyses and predictions of ring footing bearing capacity.In light of the time-intensive nature of gathering a substantial dataset,a customized deep neural network(DNN)was developed specifically to predict the bearing capacity of the dataset rapidly.Both computational and comparative results indicate that the proposed DNN(i.e.DNN-4)can accurately predict the bearing capacity of a soil with an R2 value greater than 0.99 and a mean squared error(MSE)below 0.009 in a fraction of 1 s,reflecting the effectiveness and efficiency of the proposed method.

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.

An efficient probabilistic design approach for tunnel face stability by inverse reliability analysis

In order to maintain the safety of underground constructions that significantly involve geo-material uncertainties,this paper delivers a new computation framework for conducting reliability-based design(RBD)of shallow tunnel face stability,utilizing a simplified inverse first-order reliability method(FORM).The limit state functions defining tunnel face stability are established for both collapse and blow-out modes of the tunnel face failure,respectively,and the deterministic results of the tunnel face support pressure are obtained through three-dimensional finite element limit analysis(FELA).Because the inverse reliability method can directly capture the design support pressure according to prescribed target reliability index,the computational cost for probabilistic design of tunnel face stability is greatly reduced.By comparison with Monte Carlo simulation results,the accuracy and feasibility of the proposed method are verified.Further,this study presents a series of reliability-based design charts for vividly understanding the limit support pressure on tunnel face in both cohesionless(sandy)soil and cohesive soil stratums,and their optimal support pressure ranges are highlighted.The results show that in the case of sandy soil stratum,the blowout failure of tunnel face is extremely unlikely,whereas the collapse is the only possible failure mode.The parametric study of various geotechnical uncertainties also reveals that ignoring the potential correlation between soil shear strength parameters will lead to over-designed support pressure,and the coefficient of variation of internal friction angle has a greater influence on the tunnel face failure probability than that of the cohesion.

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.

Undrained seismic bearing capacity of strip footing adjacent to a heterogeneous excavation

The analysis of the bearing capacity of strip footings sited near an excavation is critical in geotechnics.In this study,the effects of the geometrical features of the excavation and the soil strength properties on the seismic bearing capacity of a strip footing resting on an excavation were evaluated using the lower and upper bounds of the finite element limit analysis method.The effects of the setback distance ratio(L/B),excavation height ratio(H/B),soil strength heterogeneity(kB/cu),and horizontal earthquake coefficient(kh)were analyzed.Design charts and tables were produced to clarify the relationship between the undrained seismic bearing capacity and the selected parameters.

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.

Three-dimensional seismic face stability of shield tunnels inundrained clay

Tunnel face stability has received increasing research interest over the past few decades. However, computing time-efficient and safethree-dimensional solutions under seismic loading is still an unsolved problem, while case studies indicate that seismic loading can be onecritical destabilizing factor affecting tunnel stability. The primary objective of this work is to fill this gap in knowledge by providing compromisingand computationally efficient solutions, along with their respective lower and upper bounds, to compute face stability underseismic conditions. The analyses employ the finite element limit analysis method to evaluate the limit support pressure in undrained clay,considering horizontal pseudo-static seismic forces pointing outwards from the face. Moreover, the analyses employ both constant andlinearly increasing shear strengths with depth. The results are summarized as dimensionless stability charts and tables to facilitate theirinterpretation and future use for tunnel design. A new design equation has been developed to evaluate the stability of the tunnel faceconsidering the effect of seismic forces. Additionally, the effects of different parameters on the shape of the failure mechanism have beeninvestigated by analysing the distribution of shear dissipation.