Seismic Bearing Capacity Factors Research Articles

Seismic Bearing Capacity of Strip Footings Placed Adjacent to Rock Slopes

ABSTRACT The bearing capacity of strip footings placed adjacent to the rock slopes subjected to pseudo-static horizontal earthquake body forces has been investigated by using the upper bound (UB) finite element limit analysis (FELA) in combination with a mesh adaptive strategy. The generalized Hoek–Brown (GHB) failure criterion is applied to describe the strength properties of rock masses, which can be treated as its native form without the smoothing of the yield surface while employing the second-order cone and power cone programming to solve the optimization models. Based on the UB FELA method, the seismic bearing capacity factor is determined considering the effect of different governing parameters, namely the horizontal earthquake acceleration coefficient k h , the normalized slope height H/B, the rock strength ratio σ ci /γB, the geological strength index GSI and the material constant m i . For design purpose, a series of non-dimensional charts are provided, and typical failure mechanisms are also discussed in detail.

Soft-Computing Techniques for Predicting Seismic Bearing Capacity of Strip Footings in Slopes

In this study, various machine learning algorithms, including the minimax probability machine regression (MPMR), functional network (FN), convolutional neural network (CNN), recurrent neural network (RNN), and group method of data handling (GMDH) models, are proposed for the estimation of the seismic bearing capacity factor (Nc) of strip footings on sloping ground under seismic events. To train and test the proposed machine learning model, a total of 1296 samples were numerically obtained by performing a lower-bound (LB) and upper-bound (UB) finite element limit analysis (FELA) to evaluate the seismic bearing capacity factor (Nc) of strip footings. Sensitivity analysis was performed on all dimensionless input parameters (i.e., slope inclination (β); normalized depth (D/B); normalized distance (L/B); normalized slope height (H/B); the strength ratio (cu/γB); and the horizontal seismic acceleration (kh)) to determine the influence on the dimensionless output parameters (i.e., the seismic bearing capacity factor (Nc)). To assess the performance of the proposed models, various performance parameters—namely the coefficient of determination (R2), variance account factor (VAF), performance index (PI), Willmott’s index of agreement (WI), the mean absolute error (MAE), the weighted mean absolute percentage error (WMAPE), the mean bias error (MBE), and the root-mean-square error (RMSE)—were calculated. The predictive performance of all proposed models for a bearing capacity factor (Nc) prediction was compared by using the testing dataset, and it was found that the MPMR model achieved the highest R2 values of 1.000 and 0.957 and the lowest RMSE values of 0.000 and 0.038 in both the training and testing phases, respectively. The parametric analyses, rank analyses, REC curves, and the AIC showed that the proposed models were quite effective and reliable for the estimation of the bearing capacity factor (Nc).

Seismic bearing capacity factor [formula omitted] for a rough strip footing on sloping ground

By using the Mohr-Coulomb (MC) yield criterion, the method of stress characteristics (MOSC) has been employed to compute the bearing capacity factor Nγ in the presence of horizontal pseudo-static earthquake inertial forces for a rough strip footing over sloping ground surface. Two different types of failure mechanisms (M1 and M2) were employed. Due to rigorousness of the adopted failure mechanism, the present analysis overcomes the limitation of the existing MOSC formulation available in literature. The solutions in all the cases have also been determined based on the finite elements limit analysis (FELA). The results from the two different analyses, including the failure mechanisms, were found to be very close with each other.

Estimation of the Seismic Bearing Capacity of Shallow Strip Footings Based on a Pseudodynamic Approach

The bearing capacity of a shallow strip footing is investigated by a pseudodynamic method under earthquake conditions. A nonsymmetrical multiblock mechanism is herein adopted to describe the uplift failure of the foundations based on the kinematic theorem of limit analysis. This nonsymmetrical mechanism comprises a series of rigid triangular blocks that translate into the failure area. The seismic load, varying with time and space, is represented by a pseudodynamic method that considers the dynamic properties of earthquake waves. A slice method is proposed to adapt the variation in inertial force with time and depth for the convenience of calculating the earthquake-induced work rate. Then, equating the external work rate and the internal dissipation rate, the rigorous upper-bound solution of the seismic bearing capacity factors, which will be optimized by the sequential quadratic programming (SQP) in the MATLAB toolbox for searching for the optimal value, is explicitly derived. Comparisons between the present solution and previous works are made to validate the rationality and accuracy of the proposed methodology. A specific parametric analysis is conducted to reveal the influence of dynamic parameters on the bearing capacity of the strip footing. Numerical results are provided graphically as well as in the tabular form for reference in footing design.

The use of the node-based smoothed finite element method to estimate static and seismic bearing capacities of shallow strip footings

The node-based smoothed finite element method (NS-FEM) is shortly presented for calculations of the static and seismic bearing capacities of shallow strip footings. A series of computations has been performed to assess variations in seismic bearing capacity factors with both horizontal and vertical seismic accelerations. Numerical results obtained agree very well with those using the slip-line method, revealing that the magnitude of the seismic bearing capacity is highly dependent upon the combinations of various directions of both components of the seismic acceleration. An upward vertical seismic acceleration reduces the seismic bearing capacity compared to the downward vertical seismic acceleration in calculations. In addition, particular emphasis is placed on a separate estimation of the effects of soil and superstructure inertia on each seismic bearing capacity component. While the effect of inertia forces arising in the soil on the seismic bearing capacity is non-trivial, and the superstructure inertia is the major contributor to reductions in the seismic bearing capacity. Both tables and charts are given for practical application to the seismic design of the foundations.

Seismic bearing capacity of strip footing over spatially random soil using modified pseudo-dynamic approach

This paper explores the influence of dynamic behaviour under earthquake loading and soil heterogeneity on the bearing capacity of the strip footing over a horizontal ground of cohesionless soil. A finite element lower bound limit analysis formulation with second-order conic optimisation is used for the analysis. Dynamic behaviour of seismic waves is incorporated using a modified pseudo-dynamic approach. Spatial distribution of soil is generated by discretising the random field of internal friction angle using Karhunen-Loéve (KL) expansion method. The stochastic response is determined using Monte Carlo Simulation technique. Design charts for mean seismic bearing capacity factor and probability of failure of the footing are provided for practical cases of soil heterogeneity and seismic acceleration. It is found that the consideration of high factor of safety, such as 3, also does not ensure that the structure is safe against failure. The dynamic effect of seismic waves is studied by comparing the plastic yielding of soil at various intervals of time per period of lateral shaking (t/T). It is observed that the failure pattern changes with respect to t/T interval and attains maximum yielding at the t/T ratio corresponding to the least magnitude of seismic bearing capacity factor.

Influence of failure mechanism on seismic bearing capacity factors for shallow foundations near slopes

The bearing capacity of shallow foundations may decrease when located near slopes, particularly under seismic conditions. However, there is limited work that isolates the destabilising influences of seismicity and finite slope geometry on ultimate bearing capacity in terms of conventional bearing capacity factors. Herein, analytical solutions based on upper-bound kinematic limit analysis are used to isolate both the mechanism of failure and bearing capacity factors (Nc, Nγ and Nq) for shallow foundations near slopes subject to seismic action without using principles of superposition. The analytical solutions of ultimate seismic bearing capacity show good agreement and accuracy compared with numerical results. Seismic bearing capacity factors are assessed considering transitions in failure mechanism, soil properties and finite configurations of slope and footing geometry. The results presented demonstrate significant non-linearity in bearing capacity factors that have not been previously demonstrated, primarily owing to the transition in governing mechanism with geometry, shear strength or seismic loading. This study shows that the isolation of bearing capacity factors without superposition is possible considering slope and footing geometry, and is greatly influenced by the failure mechanism.

Seismic bearing capacity of strip footings placed near c-φ soil slopes

Seismic bearing capacity of strip footings placed near c-φ soil slopes is investigated in this work using finite element limit analysis combined with an adaptive remeshing procedure. In the analysis, the so-called pseudo-static approach is employed to quantitatively describe the seismic effects. Based on the method, the upper and lower bounds of the normalized seismic bearing capacity factor p/γB are calculated and summarized in design tables/charts for practitioner's use. Parametric studies are performed to illustrate the variation of the normalized seismic bearing capacity factor p/γB with respect to all of the problem variables defined in section 2. In addition, graphical results from upper bound analyses are also provided to display the potential failure mechanisms of the footing-slope bearing system under seismic conditions.

Seismic bearing capacity factor N γe for dry sand beneath strip footing using modified pseudo-dynamic method with composite failure surface

ABSTRACT An important aspect of studying soil behaviour under seismic loading is the accurate modelling of time-dependent and random seismic forces. The pseudo-static method of analysis is very approximate and although the pseudo-dynamic method considers phase difference and amplification effects, it has certain limitations. The modified pseudo-dynamic method considers the time-dependent behaviour of seismic forces and inherently accounts for the amplification of acceleration, thus making it more realistic. This newly developed method is applied to determine seismic inertia forces for estimating the seismic bearing capacity factor (N γ e) of dry sand underlying shallow strip footings. Limit equilibrium approach is used and a one-sided composite failure surface is considered to be developed under seismic load. The focus of the log-spiral is iteratively determined to give the least value of N γe. The results are presented graphically in non-dimensional form which may be used by geotechnical practitioners for design in seismically active regions.

Spectral bearing capacity analysis of strip footings under pseudo-dynamic excitation

ABSTRACT Spectral seismic bearing capacity of strip foundations is evaluated by the limit equilibrium method (LEM). In this study, the pseudo-dynamic approach is followed to take into account seismic accelerations. The formulation of spectral pseudo-dynamic bearing capacity of strip foundations is presented for the Coulomb failure mechanism. The results are reported in the form of joint bearing capacity considering the contributions of cohesion, surcharge, and soil weight, simultaneously. A parametric study is conducted to evaluate the influence of soil friction angle, interface wall friction angle, dimensionless ratio of cohesion, depth factor, primary and shear wavelength values, amplification factor as well as the frequency on the seismic bearing capacity factor. The results of this study are shown in the form of design aids and tabular for the sake of simplicity to be used by engineers. The consistency of the results with those reported in literature shows the ability and efficiency of the methodology presented herein. It is shown that both the seismic loading characteristics and shear strength parameters affect the bearing capacity of shallow footings.

Seismic bearing capacity of shallow foundations rested on anisotropic deposits

ABSTRACT This paper investigated the effect of the anisotropy of the internal friction angle on the seismic bearing capacity factor of shallow foundations placed over a frictional soil deposit with the adoption of pseudo-static and pseudo-dynamic seismic loading approaches. The simplified Coulomb failure mechanism was assumed, and the method of analysis was limit equilibrium formulation. The results of the two approaches showed that the seismic bearing capacity factor decreases with increase in the degree of anisotropy and seismic accelerations. However, the pseudo-dynamic seismic loading approach was shown to return higher bearing capacity predictions for the footings rested over the anisotropic soil deposits in comparison to the pseudo-static approach. For the both approaches, the bearing capacity of the overlying shallow footing is lost after a certain base excitation. The results of this study were presented in charts and tabular forms and were compared well with findings of other researchers.

Seismic Bearing Capacity of Strip Footings on Cohesive Soil Slopes by Using Adaptive Finite Element Limit Analysis

By employing adaptive finite element limit analysis (AFELA), the seismic bearing capacity of strip footing on cohesive soil slopes are investigated. To consider the earthquake effects, the pseudostatic method is used. The upper and lower bounds for the seismic bearing capacity factor (Nce) are calculated, and the relative errors between them are found within 3% or better by adopting the adaptive mesh strategy. Based on the obtained results, design tables and charts are provided to facilitate engineers use, and the effects of footing position, undrained shear strength, slope angle, slope height, and pseudostatic acceleration coefficient are studied in detail. The collapse mechanisms are also discussed, including overall slope failure and foundation failure.

Evaluation of the Seismic Bearing Capacity of Shallow Foundations Located on the Two-Layered Clayey Soils

The seismic bearing capacity of shallow strip footings located on homogeneous soils is studied extensively. But the effect of building height and layering is not included in those studies. In this paper two-layered cohesive soils are studied along with building height effect. The formulation of the problem is derived by extending the limit equilibrium method developed by Merlos and Romo (J Soil Dyn Earthq Eng 26(2):103–114, 2006) for two-layered soils. A log-spiral potential failure surface is assumed, and the inertia forces are applied directly to the building and the failure block soil mass. The position of the failure surface is obtained by a minimization process for every earthquake shaking acceleration. Results show that the potential failure surface moves upward and its length shortens as the peak ground acceleration (PGA) increases, reducing the bearing capacity. Also, the effects of building height, PGA, ratio of cohesion of the layers and the thickness of the top layer on seismic bearing capacity factor (Nce) are studied.

Seismic Bearing Capacity Factor Considering Composite Failure Mechanism

This article describes how the design of shallow foundation needs complete knowledge about bearing capacity. During earthquakes additional lateral force acts at the foundation bed which reduces the bearing capacity. Most of the literature present either the pseudo static analysis or assume a planar failure surface to estimate seismic bearing capacity factors. Here, a pseudo dynamic approach that considers the time dependent effect of earthquake loading is employed. A composite failure surface has been considered for a more realistic estimation of seismic bearing capacity. New expressions were formulated to arrive at the seismic bearing capacity factor, considering the forces acting on the failure wedge based on the limit equilibrium approach. The effect of soil friction angles and the seismic peak of horizontal ground accelerations on the seismic bearing capacity were studied using the proposed method. It was observed that present pseudo-dynamic analysis with a composite failure mechanism gives lower values of seismic bearing capacity factors when compared to pseud- static analysis.

Critical setback distance for a footing resting on slopes under seismic loading

A footing located on slopes possess relatively lower bearing capacity as compared to the footing located on the level ground. The bearing capacity further reduces under seismic loading. The adverse effect of slope inclination and seismic loading on bearing capacity can be minimized by proving sufficient setback distance. Though few earlier studies considered setback distance in their analysis, the range of considered setback distance was very narrow. No study has explored the critical setback distance. An attempt has been made in the present study to comprehensively investigate the effect of setback distance on footing under seismic loading conditions. The pseudo-static method has been incorporated to study the influence of seismic loading. The rate of decrease in seismic bearing capacity with slope inclination become more evident with the increase in embedment depth of footing and angle of shearing resistance of soil. The increase in bearing capacity with setback distance relative to level ground reduces with slope inclination, soil density, embedment depth of footing and seismic acceleration. The critical value of setback distance is found to increase with slope inclination, embedment depth of footing and density of soil. The critical setback distance in seismic case is found to be more than those observed in the static case. The failure mechanisms of footing under seismic loading is presented in detail. The statistical analysis was also performed to develop three equations to predict the critical setback distance, seismic bearing capacity factor (Nrqs) and change in seismic bearing capacity (BCR) with slope geometry, footing depth and seismic loading.

Static and seismic bearing capacity of shallow strip footings

In this study, the evaluation of static and seismic bearing capacity factors for a shallow strip footing was carried out by using the method of characteristics, which was extended to the seismic condition by means of the pseudo-static approach. The results, for both smooth and rough foundations, were checked against those obtained through finite element analyses.Under seismic conditions the three bearing capacity problems for Nc, Nq and Nγ were solved independently and the seismic bearing capacity factors were evaluated accounting separately for the effect of horizontal and vertical inertia forces arising in the soil, in the lateral surcharge and in the superstructure.Empirical formulae approximating the extensive numerical results are proposed to compute the static values of Nγ and the corrective coefficients that can be introduced in the well-known Terzaghi׳s formula of the bearing capacity to extend its applicability to seismic design of foundations.

The Static and Seismic Bearing Capacity Factor Nγ for Footings Adjacent to Slopes

Foundations resting adjacent to the crest of a slope exhibit a smaller bearing capacity respect to the case of horizontal ground. In this paper the static and seismic values of the bearing capacity factor Nγg for shallow strip foundations adjacent to slopes were evaluated using the method of characteristics, extended to the seismic case by means of the pseudo-static approach. Nγg was evaluated for different values of the slope angle and, under seismic conditions, accounting only for the effect of horizontal and vertical inertia forces arising in the foundation soil. The results, for both smooth and rough foundations, are presented and checked against those obtained through finite element analyses.

Seismic Bearing Capacity Factors for Strip Footings on an Embankment by Using Lower-Bound Limit Analysis

AbstractBy using the lower-bound finite-element limit-analysis technique, the bearing capacity of a strip footing placed over an embankment was determined with the incorporation of pseudostatic horizontal seismic body forces. The variation of the bearing capacity factors Nc, Nq, and Nγ were calculated as the function of the friction angle of soil ϕ, slope angle β, horizontal seismic acceleration coefficient kh, and setback distance S. On the basis of the magnitude of ϕ, the S values were varied from 0B to 15B. From the results, it can be understood that the bearing capacity factors decrease with the increase in β and kh. With the increase in ϕ and S, the bearing capacity factors were found to increase. After a particular setback distance, the effect of the embankment slopes was found to be negligible. Failure patterns were also studied.

Seismic bearing capacity of shallow foundations on partially liquefiable saturated sand

The seismic bearing capacity of partially liquefiable saturated sand is investigated by numerical analysis. An empirical correlation in the literature assumes a punching shear mechanism, which underestimates the seismic bearing capacity due to omission of the q-term. In this paper, the effects of the footing width, soil relative density, foundation depth, and maximum seismic acceleration on the seismic bearing capacity of partially liquefiable saturated sands are investigated. The results show that the foundation depth has a remarkable effect on the seismic bearing capacity. Hence, the failure mode is not likely punching. The seismic bearing capacity of partially liquefiable saturated sands is redefined with new seismic bearing capacity factors, Nq and Nγ. The paper presents also a guideline to estimate the allowable seismic bearing capacity considering both the ultimate and serviceability limit states.

Considerations about Load Inclination Effect on Seismic Bearing Capacity Factors of Strip Foundations

Assessment of seismic bearing capacity of strip foundations has been the concern of only few researchers in the field of geotechnical earthquake engineering during the last decades. The previous works have mostly assumed that in the presence of a horizontal earthquake acceleration (kh.g) besides the body force due to gravity, the ratio of the shear stresses to the normal stresses along the ground surface is equal to kh and the load inclination beneath the footing with respect to vertical equals to tan-1(kh). But this assumption does not seem to be always correct. For example in the case of multi span frames where only some spans may be braced and the support conditions at the end of the columns may not be uniform, the load inclination beneath some footings may not be equal to tan-1(kh). This paper presents the seismic bearing capacity factors Nγ, Nq and Nc of a rigid strip foundation resting on a horizontal ground surface, when the load inclination beneath the footing is not equal to tan-1(kh). All calculations are executed by the well known stress characteristic method, commonly referred to as the slip-line method. It is assumed that the soil behaves rigid perfectly plastic and obeys the well known Mohr-Coulomb failure criteria under plane strain conditions. It is assumed that the state of the stress everywhere in the neighborhood of the foundation is at failure. It is also assumed that everywhere along the surface of the foundation, the ratio of the shear to the normal stress is equal to the horizontal earthquake acceleration coefficient (kh). The Nγ parameter was calculated based on the both-sides failure mechanism, whereas the Nq and Nc parameters were calculates based on the single-side failure mechanism. The Nc parameter for cohesive media was calculated using the rule of equivalent states. Some graphs and tables are presented that could be used in order to assess the seismic bearing capacity factors of rigid strip foundations obtained by the stress characteristic method for various load inclinations. It is shown that the seismic bearing capacity factors, just like the static bearing capacity factors, increase considerably with reduction in the load inclination and vice versa. Further, this important outcome of some previous research works has been confirmed once again that the earthquake's effect on each of the body force as well as the overburden is as important as the earthquake's effect on the load inclination which should not be neglected. It is also shown that because of the non-symmetric nature of the seismic loading, the disposal of the characteristic lines as well as the pressure distribution below the foundation is non-symmetric. In other words, the foundation would be subjected to a moment in addition to the vertical and horizontal reactions, as a result of the non-symmetric soil pressure distribution during earthquakes.