Pseudo-static analysis of cantilever retaining walls using upper bound limit analysis approach

Given the extensive utilization of cantilever retaining walls in construction and development projects,their optimal design and analysis with proper attention to seismic loads is a typical engineering problem.This research presents a new algorithm for pseudo-static analysis of retaining walls employing upper bound method.The algorithm can be utilized to design and check the external and internal stability of the wall based on the proposed mechanism.One of the main features of this algorithm is its ability to determine the critical condition of failure wedges,the minimum safety factor and maximum force acting on the wall,as well as the minimum weight of the wall,simultaneously,by effectively using the multi-objective optimization.The results obtained by the proposed failure mechanisms show that,while using the upper bound limit analysis approach,the active force should be maximized concurrent with optimizing the direction of the plane passing through the back of the heel.The present study also applies the proposed algorithm to determine the critical direction of the earthquake acceleration coefficient.The critical direction of earthquake acceleration coefficient is defined as the direction that maximizes the active force exerted on the wall and minimizes the safety factor for wall stability.The results obtained in this study are in good agreement with those of similar studies carried out based on the limit equilibrium method and finite element analysis.The critical failure mechanisms were determined via optimization with genetic algorithm.

An improved pseudo-static method for seismic resistant design of underground structures

This paper describes a commonly used pseudo-static method in seismic resistant design of the cross section of underground structures. Based on dynamic theory and the vibration characteristics of underground structures, the sources of errors when using this method are analyzed. The traditional seismic motion loading approach is replaced by a method in which a one-dimensional soil layer response stress is differentiated and then converted into seismic live loads. To validate the improved method, a comparison of analytical results is conducted for internal forces under earthquake shaking of a typical shallow embedded box-shaped subway station structure using four methods： the response displacement method, finite element response acceleration method, the finite element dynamic analysis method and the improved pseudo-static calculation method. It is shown that the improved finite element pseudo-static method proposed in this paper provides an effective tool for the seismic design of underground structures. The evaluation yields results close to those obtained by the finite element dynamic analysis method, and shows that the improved finite element pseudo-static method provides a higher degree of precision.

Improvement of Pseudo-static Method for Slope Stability Analysis

traditional In this paper, two drawbacks pseudo-static method （vertical of the slice method） in the slope stability evaluation have been studied. First, the sliding mass is divided into vertical slices according to this method, which is irrational to some extent in the seismic design of slope. Second, only peak ground acceleration （PGA） is considered, and the effects of shaking frequency and duration on slope stability are neglected. And then, based on the theory of elastic wave and the summarized geological model, this paper put forwards an improved method of pseudo-method by using the theory of elastic wave and Hilbert-Huang transform. The improved pseudostatic method gives reasonable considerations to the time-frequency effects of seismic wave and its rationality has been verified by the shaking table test. This method can evaluate the safety of a slope, the happening time and the scale of landslides. At the same time, this method also can improve the high accuracy of the evaluation of the safety of the slope.

System reliability analysis of seismic pseudo-static stability of rock wedge based on nonlinear Barton–Bandis criterion

Based on the nonlinear Barton–Bandis(B–B)failure criterion,this study considers the system reliability of rock wedge stability under the pseudo-static seismic load.The failure probability(Pf)of the system is calculated based on the Monte−Carlo method when considering parameter correlation and variability.Parameter analysis and sensitivity analysis are carried out to explore the influence of parameters on reliability.The relationships among the failure probability,safety factor(Fs),and variation coefficient are explored,and then stability probability curves of the rock wedge under the pseudo-static seismic load are drawn.The results show that the parameter correlation of the B–B failure criterion has a significant influence on the failure probability,but correlation increases system reliability or decreases system reliability affected by other parameters.Under the pseudo-static seismic action,sliding on both planes is the main failure mode of wedge system.In addition,the parameters with relatively high sensitivity are two angles related to the joint dip.When the coefficient of variation is consistent,the probability of system failure is a function of the safety factor.

Pseudo-static/dynamic solutions of required reinforcement force for steep slopes using discretization-based kinematic analysis

This paper presents a procedure for assessing the reinforcement force of geosynthetics required for maintaining dynamic stability of a steep soil slope. Such a procedure is achieved with the use of the discretization technique and kinematic analysis of plasticity theory, i.e. discretization-based kinematic analysis. The discretization technique allows discretization of the analyzed slope into various components and generation of a kinematically admissible failure mechanism based on an associated flow rule.Accordingly, variations in soil properties including soil cohesion, internal friction angle and unit weight are accounted for with ease, while the conventional kinematic analysis fails to consider the changes in soil properties. The spatialetemporal effects of dynamic accelerations represented by primary and shear seismic waves are considered using the pseudo-dynamic approach. In the presence of geosynthetic reinforcement, tensile failure is discussed providing that the geosynthetics are installed with sufficient length. Equating the total rates of work done by external forces to the internal rates of work yields the upper bound solution of required reinforcement force, below which slopes fail. The reinforcement force is sought by optimizing the objective function with regard to independent variables, and presented in a normalized form. Pseudo-static analysis is a special case and hence readily transformed from pseudodynamic analysis. Comparisons of the pseudo-static/dynamic solutions calculated in this study are highlighted. Although the pseudo-static approach yields a conservative solution, its ability to give a reasonable result is substantiated for steep slopes. In order to provide a more meaningful solution to a stability analysis, the pseudo-dynamic approach is recommended due to considerations of spatial etemporal effect of earthquake input.

A comparative study of pseudo-static slope stability analysis using different design codes

Many researchers have developed new calculation methods to analyze seismic slope stability problems, but the conventional pseudo-static method is still widely used in engineering design due to its simplicity. Based on the Technical Code for Building Slope Engineering（GB 50330-2013） of China and the Guidelines for Evaluating and Mitigating Seismic Hazards in California（SP117）, a comparative study on the pseudo-static method was performed. The results indicate that the largest difference between these two design codes lies in determination of the seismic equivalence reduction factor( f;). The GB 50330-2013 code specifies a single value for f;of 0.25. In SP117, numerous factors,such as magnitude and distance, are considered in determining f;. Two case studies show that the types of slope stability status evaluated by SP117 are in agreement with those evaluated by the seismic time-history stability analysis and Newmark displacement analysis. The factors of safety evaluated by SP117 can be used in practice for safe design. However, the factors of safety evaluated by GB 50330-2013 are risky for slope seismic design.

Reliability analysis for seismic stability of tunnel faces in soft rock masses based on a 3D stochastic collapse model

A new horn failure mechanism was constructed for tunnel faces in the soft rock mass by means of the logarithmic spiral curve. The seismic action was incorporated into the horn failure mechanism using the pseudo-static method. Considering the randomness of rock mass parameters and loads, a three-dimensional (3D) stochastic collapse model was established. Reliability analysis of seismic stability of tunnel faces was presented via the kinematical approach and the response surface method. The results show that, the reliability of tunnel faces is significantly affected by the supporting pressure, geological strength index, uniaxial compressive strength, rock bulk density and seismic forces. It is worth noting that, if the effect of seismic force was not considered, the stability of tunnel faces would be obviously overestimated. However, the correlation between horizontal and vertical seismic forces can be ignored under the condition of low calculation accuracy.

Influence of non-dimensional strength parameters on the seismic stability of cracked slopes

Cracks in rock or soil slopes influence the stability and durability of the slopes. Seismic forces can trigger slope disasters, particularly in the cracked slopes. Considering the nonlinear characteristics of materials, the more generalized nonlinear failure criterion proposed by Baker is adopted. The influence of non-dimensional strength parameters on the stability of cracked slopes under earthquakes is performed using the upper bound limit analysis. The seismic displacement is calculated by adopting the logarithmic spiral failure surface according to the sliding rigid block model. Based on the existing studies, two methods for the stability analysis of cracked slopes under earthquakes are introduced: the pseudo-static method(with the factor of safety(Fs) as an evaluation index), and the displacement-based method(with the seismic displacement as an evaluation index). The pseudo-static method can only determine the instantaneous stability state of the cracked slope, yet the displacement-based methodreflects the stability variation of cracked slopes during earthquakes. The results indicate that the nondimensional strength parameters affect the factor of safety and seismic displacement of slopes significantly. The non-dimensional strength parameter(n) controlling the curvature of strength function shapes on the slope stability is affected by other parameters. Owing to cracks, the effect of non-dimensional strength parameters on seismic displacement becomes more significant.

Probabilistic stability analysis of embankment slopes considering the spatial variability of soil properties and seismic randomness

The safety of embankments under seismic conditions is a primary concern for geotechnical engineering societies.The reliability analysis approach offers an effective tool to quantify the safety margin of geotechnical structures from a probabilistic perspective and has gained increasing popularity in geotechnical engineering.This study presents an approach for probabilistic stability analysis of embankment slopes under transient seepage considering both the spatial variability of soil parameters and seismic randomness.The spatial varying soil parameters are firstly characterized by the random field theory,where a large number of random field samples of the soil parameters can be readily generated.Then,the factor of safety(FS)of the embankment slope under seismic conditions corresponding to each random field sample is evaluated through performing seismic stability analysis based on the pseudo-static method.A hypothetical embankment example is adopted in this study for illustration,and the influences of shear strength parameters,seismic coefficient,and the external water level on the embankment slope failure probability are systematically investigated.Results show that the coefficient of variation of the friction angle and the horizontal scale of fluctuation have more significant effects on the embankment slope failure probability.Besides,the seismic coefficient also affects the embankment slope failure probability considerably.For a given external water level,the failure probability corresponding to the downstream slope of the embankment is larger than that in the upstream slope.

Lateral response of pile foundations in liquefiable soils

Liquefaction has b e e n a m ain cause o f dam ag e to civil en g in eerin g stru ctu res in seism ically active areas.The effects o f dam ag e o f liquefaction o n d eep foundations are v ery d estructive. Seism ic beh av io r o f pilefoundations is w idely discussed by m any researchers for safer an d m ore econom ic design purposes. Thisp a p e r p resen ts a p se u d o -static m eth o d for analysis o f piles in liquefiable soil u n d e r seism ic loads. A freefieldsite resp o n se analysis using th ree-d im en sio n al （3D） num erical m odeling w as p erfo rm ed to d e te rmine kin em atic loads from lateral g ro u n d disp lacem en ts an d inertial loads from vib ratio n o f th e supe rstru ctu re . The effects o f various p aram eters, such as soil layering, k in em atic and inertial forces,b o u n d ary con d itio n o f pile h ead an d gro u n d slope, o n pile resp o n se w e re studied. By com paring th enum erical results w ith th e centrifuge te s t results, it can be concluded th a t th e use o f th e p-y curves w ithvarious d eg rad atio n factors in liquefiable sand gives reasonable results.

A simplified approach to assess seismic stability of tailings dams

In the zones of high seismic activity, tailings dam should be assessed for the stability against earthquake forces. In the present paper, a simplified method is proposed to compute the factor of safety of tailings dams. The strain-dependent dynamic properties are used to assess the stability of tailings dams under seismic conditions. The effect of foundation soil properties on the seismic stability of tailings dams is studied using the proposed method. For the given input parameters, the factor of safety for lowfrequency input motions is nearly 26% lower than that for high-frequency input excitations. The impedance ratio and the depth of foundation have significant effect on the seismic factor of safety of tailings dams. The results from the proposed method are well compared with the existing pseudo-static method of analysis. Tailings dams are vulnerable to damage for low-frequency input motions.

Elastic-plastic study on high building with SRC transferring story

A new type of transferring structure for steel reinforced concrete (SRC) beams is used in high building. The pushover analysis method was used to study the failure mechanism and ductility of SRC transferring structure through consulting pseudo-static test results for the structure. And, the occurrence order and position of the plastic hinge, the weak story and seismic capacity of high building with SRC transferring story were also studied through consulting shaking table test results for the high building, showing that the seismic behavior of high building with SRC transferring story is good.

Sliding response of gravity dams including vertical seismic accelerations

Seismic safety assessment of gravity dams has become a major concern in many regions of the world while the effects of vertical seismic accelerations on the response of structures remain poorly understood.This paper first investigates the effect of including vertical accelerations in the sliding response analysis of gravity dams subjected to a range of historical ground motion records separated in two groups according to their source-to-site distance.Analyses showed that the incidence of vertical accelerations on the sliding response of gravity dams is significantly higher for near-source records than for far- source records.The pseudo-static 30% load combination rule,commonly used in practice to account for the non-simultaneous occurrence of the peak horizontal and vertical accelerations,yielded good approximations of the minimum safety factors against sliding computed from time-history analyses.A method for empirically estimating the vertical response spectra based on horizontal spectra,accounting for the difference in frequency content and amplitudes between the two components is investigated.Results from analyses using spectrum compatible horizontal and vertical synthetic records also approximated well the sliding response of a gravity dam subjected to series of simultaneous horizontal and vertical historical earthquake records.

Experiment study on RC frame retrofitted by the external structure

A new retrofitting method is proposed herein for reinforced concrete （RC） structures through attachment of an external structure. The external structure consists of a fiber concrete encased steel frame, connection slab and transverse beams. The external structure is connected to the existing structure through a connection slab and transverse beams. Pseudo- static experiments were carried out on one unretrofitted specimen and three retrofitted frame specimens. The characteristics, including failure mode, crack pattern, hysteresis loops behavior, relationship of strain and displacement of the concrete slab, are demonstrated. The results show that the load carrying capacity is obviously increased, and the extension length of the slab and the number of columns within the external frame are important influence factors on the working performance of the existing structure. In addition, the displacement difference between the existing structure and the outer structure was caused mainly by three factors： shear deformation of the slab, extraction of transverse beams, and drift of the conjunction part between the slab and the existing frame. Furthermore, the total deformation determined by the first two factors accounted for approximately 80% of the damage, therefore these factors should be carefully considered in engineering practice to enhance the effects of this new retrofitting method.

Experimental Research on Seismic Performance of Storey-Adding Frame Structures

The seismic behaviors of an integral concreting frame, a light steel storey-adding frame and a storeyadding frame strengthened with carbon fiber reinforced polymer(CFRP)were investigated under low-cycle and repeated load(scale 1∶3). The failure characteristics, hysteretic behavior, rigidity degeneracy, deflection ductility and energy-dissipation capacity of the three specimens were compared. The test results reveal that chemicallybonded rebar technique can meet the requirements of storey-adding engineering. The carrying capacity, the deflection ductility, the energy-dissipating capacity and seismic performance of the light steel storey-adding frame are higher than those of the integral concreting frame, and they are the highest in the storey-adding frame strengthened with CFRP.

Numerical and analytical studies on the coupling effects of unloading and cutterhead vibration on tunnel face in dry sandy ground

When tunnelling in difficult ground conditions,shield machine would inevitably produce significant ground loss and vibration,which may disturb the ground ahead of the tunnel face.In this paper,discrete element models calibrated by model tests were established to investigate the response of tunnel face under the coupling effects of unloading and cutterhead vibrations.The results show that the friction angle reduction under cyclic loading and vibration attenuation in the sandy ground are significant and can be estimated by the fitted exponential functions.Under cutterhead vibration,the tunnel face stability is undermined and the limit support pressure(LSP)increases to 1.4 times as that in the static case with the growth of frequency and amplitude.Meanwhile,the loosening zone becomes wider and the arching effect is weakened with the reduction of peak horizontal stress and the increase of vertical stress above the tunnel.Based on the numerical results,a pseudo-static method was introduced into the limit equilibrium analysis of the wedge-prism model for calculating the LSP under vibration.With an error rate less than 5.2%,the proposed analytical method is well validated.Further analytical calculation reveals that the LSP would increase with the growth of vibration amplitude,vibration frequency and covered depth but decrease with the increase of friction angle.This study can not only lay a solid foundation for the further investigation of ground loss,ground water and soft-hard heterogeneous ground under cutterhead vibration,but also provide meaningful references for the control of environmental disturbance in practice.

General variational solution for seismic and static active earth pressure on rigid walls considering soil tensile strength cut-off

According to the limit equilibrium state of soils behind rigid walls and the pseudo-static approach,a general closed-form solution to seismic and static active earth pressure on the walls,which considers shear and tension failure of the retained soil,is put forward using a variational calculus method.The application point of the active resultant force specified in the proposed method is explained with a clear physical meaning related to possible movement modes of the walls.In respect of the derived nine dependent equations reflecting the functional characteristics of the earth pressure,the proposed method can be performed easily via an implicit strategy.There are 13 basic factors related to the retained soils,walls,and external loads to be involved in the proposed method.The tension crack segment of the slip surface is obviously influenced by these parameters,apart from vertical seismic coefficient and geometric bounds of the surcharge,but the shear slip segment maintains an approximately planar shape almost uninfluenced by these parameters.Noticeably,the proposed method quantitatively reflects that the resultant of the active earth pressure is always within a limited range under different possible movements of the same wall.

Limit analysis on seismic stability of anisotropic and nonhomogeneous slopes with anti-slide piles

This study employs the limit analysis method to evaluate the seismic stability of anisotropic and nonhomogeneous slopes stabilized with anti-slide piles. The pseudo-static approach is used to simplify the earthquake load. The yield seismic acceleration factor is obtained from the optimization procedure and the results are verified with the published data. Then, the seismically-unstable slope is reinforced with anti-slide piles, and the seismic stability of the reinforced slope is explored. The results show that the anisotropy and nonhomogeneity of soils have significant effects on the stabilizing force required from the anti-slide piles and the optimal location of the pile is near the toe of the slope.

Stability Analysis of Rainfall-Triggered Toe-Cut Slopes and Effectiveness Evaluation of Pile-Anchor Structures

Slope toe excavation strongly influences the stress balance of natural slopes and redistributes the stress of the slope body. Consequently, the sliding failure of toe-cut slopes is increasingly becoming more frequent, particularly in regions with persistent rainfall. The effects of external factors, namely, toe excavation and persistent rainfall, which lead to toe-cut slope failure were investigated through the numerical analysis of typical toe-cut slopes in the southeastern coastal region of China. Based on the grey relational theory, sensitivity analysis was carried out on the controlling factors to determine the degree of influence exerted by the external factors on the stability of toe-cut slopes. The stability analysis of toe-cut slopes reinforced by pileanchor structures under earthquake conditions was carried out using pseudo-static analysis. The safety factor of toe-cut slopes significantly decreases as the excavation height, rainfall duration, and rainfall intensity increase. The slope stability is more sensitive to the excavation height of a toe-cut slope than it is to rainfall. The stability of a toe-cut slope reinforced by a pile-anchor structure was also analyzed under rainfall and earthquake conditions using the limit equilibrium method and pseudo-static analysis, respectively. The slope stability significantly improved when the slope was reinforced by a pile-anchor structure, even when the slope was subjected to persistent rainfall and earthquakes. The findings of this study can provide important guidance for the prevention of geological disasters in mountainous areas.

Prediction of the seismic behavior of an underground railway station and a tunnel in Napoli(Italy)

The assessment of the seismic safety of underground structures,either tunnels or large station boxes,should not be overlooked especially in densely populated areas,even with low to moderate seismicity.For underground structures,an important issue is the estimation of the seismic actions acting on the structure;only few experimental evidences are available for multi-level propped walls.For tunnels,it is generally assumed that their seismic behavior in soft ground is governed by the surrounding soil,while the inertial load contribution of the underground structure itself is negligible.In both cases,recent numerical studies proved that advanced dynamic analyses can provide satisfactory interpretation of non-linear soil-structure interaction during earthquakes.In this paper,a real case study,represented by a large open multi-propped excavation and a circular segmented tunnel in a densely urbanized area of the city center in Napoli,has been used to investigate some of the mentioned aspects.Accurate geotechnical characterization and choice of the reference input motions lead to a first estimate of the free-field ground motion,which was subsequently used for pseudo-static decoupled analyses.For the complexity of both excavation geometry and staged construction,a full dynamic analysis was considered neither affordable nor reliable for the multi-propped station box;thus two conventional pseudo-static analyses,applying either a displacement-based or a force-based approach,were carried out.In the case of the tunnel,the seismic increments of internal forces in the lining could be calculated through both a simplified pseudostatic analysis and a full dynamic analysis,showing a satisfying agreement.Overall,the results of the study demonstrated that the seismic increments of internal forces in the diaphragm walls of the station and in the segmented lining of the tunnel were quite significant.The case study encourages improving the reliability of simplified methods based on the more advanced dynamic approaches.