Strip Footings Research Articles

Seismic Bearing Capacity of a Strip Footing Over an Embankment of Anisotropic Clay

The present study adopts lower bound finite element limit analysis technique in association with non-linear optimization to compute the seismic bearing capacity of a strip footing placed over an embankment of anisotropic clay. The influence of seismic loading is incorporated in terms of a horizontal seismic acceleration coefficient. The bearing capacity factor Nc of the strip footing is obtained for various combinations of (i) slope angle, (ii) footing setback distance, (iii) horizontal seismic acceleration coefficient, and (iv) anisotropic strength ratio of clay. The bearing capacity factor of the strip footing increases with the increasing setback distances. However, beyond a certain setback distance, hardly any influence is found. For a particular footing position and constant value of horizontal seismic acceleration coefficient, the magnitude of bearing capacity factor increases with the increase in anisotropic strength ratio. However, the percentage increment in the bearing capacity reduces when the value of anisotropic strength ratio becomes greater than one. In addition, the bearing capacity reduces with the increasing slope angle and horizontal seismic acceleration coefficient. Failure patterns are obtained to understand the failure mechanism.

Interference of two closely spaced footings embedded in unreinforced and reinforced soil medium: a finite element approach using ABAQUS

The stress or the failure zone of footings placed at close proximity interfere altering the performance of the footings. The present study pertains finite element analysis of two closely spaced rough, rigid strip footings embedded in cohesion-less foundation soil medium using the commercially available software ABAQUS. The interfering footings are considered to be supported on homogeneous reinforced and unreinforced soil medium. The failure criterion of the soil is directed to follow Mohr–Coulomb criterion with the non-associated flow rule. The influence of interference phenomenon on the ultimate bearing capacity, settlement and load-settlement characteristics have been explored by considering and varying the various parameters such as depth of embedment, soil friction angle, depth of reinforcement (first layer and subsequent layer), number of reinforcement layers and length of reinforcement. The soil friction angle is one of the important factors to have an effect on bearing capacity, and the friction angle is varied between 20° to 40°. The ultimate bearing capacity of closely spaced footings over unreinforced and reinforced soils are represented by non-dimensionless efficiency factors (ξUR and ξR). The analyses results conclude that interference has a significant influence on bearing capacity and settlement of footings supported over unreinforced and reinforced soil medium. Although, soil friction angle affects the interference significantly (higher friction angle has the highest peak of efficiency factor), depth of footing embedment also has remarkable influence over the same. The peak of efficiency factor decreases with an increase in the depth of footing embedment for a specified soil friction angle; however, the same increases with increase in soil friction angle for a specified depth of footing embedment. The interference effect is found to be decreasing with increase in the embedment depth. The bearing capacity of interfering footings on reinforced soil is enhanced noticeably compared to that on unreinforced footings; however, the settlement is not predominant.

Ultimate seismic bearing capacities and failure mechanisms for strip footings placed adjacent to slopes

Assessment of the ultimate bearing capacity of foundations adjacent to slopes is complex as it is highly dependent on the slope geometry and soil properties. Seismic loading may impact both the critical failure mechanism and its associated bearing capacity. The existing approaches for analyzing the seismic bearing capacity of footings near slopes typically employ coefficients developed to fit the conventions of Terzaghi’s bearing capacity equation, herein referred to as the “superposition method.” In this study, a rigorous assessment of the seismic bearing capacity is performed using an upper-bound limit state plasticity framework known as discontinuity layout optimization (DLO), which makes few prior assumptions concerning the failure geometry. Results show that soil properties, slope configuration, and pseudostatic seismic loading all influence the realized failure mechanism and associated bearing capacity. The use of bearing capacity coefficients that fit within the conventional superposition method may underestimate limit loads when the underlying soil provides a relative increase in resistance, but may greatly overestimate bearing capacity when the self-weight of the soil is destabilizing in nature. A set of design charts using direct computational methods for a variety of geometric, geotechnical, and seismic conditions is provided.

Numerical analysis of bearing capacity of multiple strip footing on unreinforced and reinforced sand beds

In this paper, the ultimate bearing capacity of multiple strip footings on reinforced and unreinforced sand beds is investigated using finite element method. The study utilizes efficiency factor to assess the change in the ultimate bearing capacity due to footing interference. The impacts of angle of internal friction, clear footing spacing and number of reinforcement layers on the efficiency factor are presented and evaluated. In addition, the effect of dilatancy angle and stress distribution in soil-reinforcement system is examined. The developed numerical model was verified against available theoretical and experimental data from literature prior to its use in this study. It is noted that for both reinforced and unreinforced sand, the ultimate bearing capacity of strip footings in a group is always greater than that of a single footing when the footing spacing is less than twice the footing width. Furthermore, the efficiency factor was found to increase as the footing spacing decreased and as the number of reinforcement layers increased. The degree of enhancement in ultimate capacity is, therefore, dependent on the angle of internal friction and number of reinforcement layers. The paper also proposes and assesses the use of alternative approach to modelling the effect of reinforcement using an apparent cohesion to reflect the addition of reinforcement layer. The use of apparent cohesion seems reasonable but further investigations would be required.

Shape Effects on Bearing Capacity of Footings on Two-Layered Clay

The undrained vertical bearing capacity on a two-layered clay of centrally loaded rigid strip, rectangular and ring footings is studied parametrically with 2D, 3D and axisymmetric finite-element analyses. The shear strength ratio of the two layers and the relative thickness of the uppermost layer with respect to pertinent foundation dimension are the key parameters investigated. In addition, for rectangles and rings the length-to-width (“aspect”) ratio and the ring width to external radius ratio are reported. The results are portrayed in diagrams of bearing capacity and shape modification factors, in the familiar soil mechanics form, along with fitted algebraic expressions to facilitate their numerical use. The failure mechanisms are presented for a number of characteristic cases and are being contrasted with the classical Prandtl failure mechanism, giving additional insight into the mechanics of the problem. The results of the paper can be directly used in practical applications.

An Upper Bound Solution to Undrained Bearing Capacity of Rigid Strip Footings Near Slopes

The undrained ultimate bearing capacity of rigid strip footings near slopes is one of important problems in practical foundation engineering in soft clay. To solve the bearing capacity conveniently and easily, a calculation method for the undrained bearing capacity is proposed using the upper bound limit analysis. A bilateral failure mechanism is provided and involved in the analysis, and two failure modes including slope face failure and below-toe failure are pointed out considering the location relationship between the critical slip surface and the slope toe. The upper bound solution of the undrained bearing capacity based on the failure mechanism is carried specifically out via the optimization algorithm. Analysis of some typical examples shows that the results calculated by the proposed method agree well with those obtained using other analytical and numerical methods. The maximum error is about 10%. Cohesion of slope soil, slope angle, horizontal setback distance of strip footing from the slope crest, slope height, surcharge on the slope top level, and the footing depth have great influence on the undrained bearing capacity.

Implementation of Fuzzy Reliability Analysis for Elastic Settlement of Strip Footing on Sand Considering Spatial Variability

AbstractThis paper deals with the reliability analysis for the elastic settlement of the surface strip footing resting on cohesionless soil using the concept of fuzzy set theory in conjunction with...

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.

Experimental Verification of Seismic Bearing Capacity of Near-slope Footings Using Shaking Table Tests

ABSTRACT Monotonic and shaking table tests are performed using strip footings placed near a model slope. Test results indicate that footing restraint conditions affect the seismic response of near-slope footings, in terms of amplification factor and critical peak ground acceleration (PGA). The theoretical seismic bearing capacity correction factor (ηγe ) vs. seismic coefficient (kh ) relationships based on pseudo-static methods are in good agreement with the experimental values of ηγe provided that correction factors for load inclination, load eccentricity, footing set-back are accounted for. Furthermore, a correct empirical relationship between kh and PGA is vital in applying theoretical ηγe in earthquake engineering practices.

Experimental evaluation of analytical methods to assess building response to tunnelling subsidence

AbstractThis paper evaluates the performance of currently available analytical procedures to assess building response to tunnelling‐induced ground displacements. The focus is on methods that account for the interaction between the soil and the structure during tunnelling. These methods relate the soil to the building stiffness and are often called Relative Stiffness Methods (RSMs). Results from centrifuge model tests are used to evaluate the ability of these RSMs to predict building deformations. This evaluation benefits from detailed building models including facade openings, intermediate walls and strip footings. The range of RSM predictions was large, and the accuracy of each RSM was quantified. It was found that no RSM accurately predicts flexural building deformations. Recommendations that consider the building‐to‐tunnel position to achieve accurate predictions are indicated. This contribution provides a better understanding of the performance of currently available criteria to assess the risk of urban tunnelling.

Embedded strip footing in a geotextile-reinforced sand slope

This paper presents experimental and numerical investigations of dense sand slopes supporting an embedded strip footing, considering both unreinforced and geotextile-reinforced cases. The effect of footing location, defined in terms of embedment depth D and edge distance e, on the bearing capacity of the footing was investigated. The results show that the bearing capacity of the footing increased with an increase in D and e. The inclusion of one layer of geotextile reinforcement in the dense sand slope further increased the bearing capacity. This benefit was expressed in terms of BCRu, which is defined as the ratio of the ultimate bearing capacity for the reinforced case to the ultimate bearing capacity for the unreinforced case. The maximum value of BCRu( ≈ 2·5 − 3) was observed for D/B = 0 and e/B = 0 where B is the width of the footing, while the minimum value of BCRu( ≈ 1·5) was obtained for D/B = 1 and e/B = 3.

Finite element analysis of two nearby interfering asymmetric footings embedded in cohesionless foundation medium

ABSTRACT The present study encompasses the behaviour of two closely spaced rigid, rough asymmetrical strip footings embedded in homogenous, semi-infinite cohesionless foundation soil medium. The geometry of the interfering footings with respect to their width is considered to be asymmetric. The analyses have been carried out using finite element software ABAQUS following the Mohr-Coulomb failure criterion obeying non-associated flow rule for foundation medium. The interference effect on the characteristic behaviour of the footing such as load-settlement (p-δ) behaviour, ultimate bearing capacity (UBC) and settlement have been evaluated. The UBC and settlement have been represented in terms of non-dimensional interaction factors defined as the ratio of UBC/settlement of left/right footing in presence of adjacent footing to that of the same considered for an isolated footing under identical condition. The results of the analyses reveal that the interaction factors with respect to UBC (ξL/ξR ) and settlement (ζL/ζR ) are affected significantly by the variation of clear spacing between the footings, embedment depth, soil friction angle and the width of adjacent footings. The interference effect is more prominent in the case of smaller footing having lesser embedment depth on the soil with higher friction angle in comparison with the footing of larger dimension.

Discussion of “Bearing Capacity of Strip Footings on Anisotropic Soils by the Finite Elements and Linear Programming” by Mehdi Veiskarami, Reza Jamshidi Chenari, and Amir Arsalan Jameei

Discussion of “Bearing Capacity of Strip Footings on Anisotropic Soils by the Finite Elements and Linear Programming” by Mehdi Veiskarami, Reza Jamshidi Chenari, and Amir Arsalan Jameei

Closure to “Bearing Capacity of Strip Footings on Anisotropic Soils by the Finite Elements and Linear Programming” by Mehdi Veiskarami, Reza Jamshidi Chenari, and Amir Arsalan Jameei

Closure to “Bearing Capacity of Strip Footings on Anisotropic Soils by the Finite Elements and Linear Programming” by Mehdi Veiskarami, Reza Jamshidi Chenari, and Amir Arsalan Jameei

Numerical Investigation of the Behavior of Strip Footings under Large Eccentric Loads

Abstract In this paper, numerical computations using the FLAC code are carried out to investigate of the behavior the bearing capacity of strip footings embedded in sandy soil and under large eccentric vertical load conditions. The study focuses on an evaluation of the non-dimensional reduction factor (RF), which is the ratio between the average bearing capacity of an eccentric footing and its bearing capacity when subjected to a central load. The results indicate a significant decrease in RF when the eccentricity increases and the curve of the decrease is parabolic, even in large eccentricity cases. Based on the numerical results obtained, a new formula of the RF is proposed, and the reasons for the discrepancy between the RF proposed by several authors are identified. The values provided by the proposed formula are in close agreement with some experimental results available in the literature.

Centrifuge model study on settlement of strip footing subject to rising water table in loess

Owing to man-made activities and natural conditions, the groundwater table experiences considerable changes in Lanzhou. Centrifugal model tests were performed to investigate the settlement of strip footings on loess subject to rising water table under different foundation pressures. The air-fall method was employed to reconstitute the artificial loess samples. The applicability of the air-fall prepared samples was evaluated against the parameters of the undisturbed loess samples obtained from the same location. The results of centrifuge tests reveal that the footing settlement increases significantly with increasing foundation loading pressure or increasing rising water table. However, the rate of increase in ultimate footing settlement under combined rising water level and footing pressure is established to be more intriguing. A simplified method for predicting the ultimate footing settlement on collapsible loess due to rising water table height is proposed. The proposed formulation is verified, as there is a good agreement between the test results under various loading pressures and rising water heights and the predicted ultimate footing settlements. A discussion on the ultimate settlement of strip footings subjected to rising water table against conventional bearing capacity safety factors is presented to provide some basis for the foundation design consideration under rising water scenario.

Probabilistic analysis of strip footings based on enhanced Kriging metamodeling

SummaryTwo advanced Kriging metamodeling techniques were used to compute the failure probability of geotechnical structures involving spatially varying soil properties. These methods are based on a Kriging metamodel combined with a global sensitivity analysis that is called in literature Global Sensitivity Analysis‐enhanced Surrogate (GSAS) modeling for reliability analysis. The GSAS methodology may be used in combination with either the Monte Carlo simulation (MCS) or importance sampling (IS) method. The resulting Kriging metamodeling techniques are called GSAS‐MCS or GSAS‐IS. The objective of these techniques is to reduce the number of calls of the mechanical model as compared with the classical Kriging‐based metamodeling techniques (called AK‐MCS and AK‐IS) combining Kriging with MCS or IS. The soil uncertain parameters were assumed as non‐Gaussian random fields. EOLE methodology was used to discretize these random fields. The mechanical models were based on numerical simulations. Some probabilistic numerical results are presented and discussed.

Numerical Analysis of Shallow Foundations in a Soil Mass under Various Behavior Laws

This paper proposes to study the soil-structure interaction (SSI) applied to shallow foundations. To conduct the study, a characterization of the foundation soils is carried out. The finite element study is conducted using the Optum G2 software that allows taking into account the various soil mass behavior. Two types of superficial foundations (individual footing and strip footing) embedded in a homogeneous and stratified soil mass are modeled. The method proceeds to a parametric study of the soil mass by varying the modulus of elasticity, the angle of internal friction, the cohesion, the Poisson’s ratio and the failure criteria to study their influences on the mechanical behavior of the foundation. The results obtained show that with the increasing variation of the modulus of elasticity (E), the clay becomes more and more stiff and ductile. For a given stress value, there is a decrease in deformations as the ductility of the clay increases. During the consolidation analysis, it is found that the lower the Young's modulus, more the material is compressible. This shows that the modulus of elasticity of the soil mass depends on its state of consolidation. The study reveals that the constitutive law, the intrinsic properties and the lithology of the soil mass condition the mode of ruin of the structure.

Load-settlement mechanism of strip footings rested on saturated loose sand and improved by zeolite–cement pads

This study aims to investigate the performance of cemented sand pads after being incorporated with zeolite. Therefore, mechanical properties of the prepared zeolite–cemented sand pads were measured by a series of unconfined compressive strength (UCS) tests. Also, several small 1 g model tests were conducted to evaluate the behavior of shallow foundations rested on the prepared pads. The results demonstrated a remarkable increase in the UCS of the 14 and 28 days cured pads containing 40 wt% zeolite. In addition, incorporating 40 wt% zeolite into the cemented sand pads improved both their strength improvement ratio (SIR) and settlement reduction ratio (SRR). In particular, the SIR and SRR of the pads containing 40 wt% zeolite improved up to 323% and 86% respectively compared to that of the pristine cemented sand pads. As such, adding zeolite to the cemented sand is one of the most promising candidate to overcome the shortcomings of sandy soils in backfills, roadbeds, embankments, and etc. It is notable that this method taking the advantages of easy fabrication, low cost, and absence of environmentally deleterious wastes.

On vertical bearing capacity of ring footings: finite element analysis, observations and recommendations

ABSTRACT Ring footing is defined by a radius ratio (ri /ro ) which is the ratio of the inner radius (ri ) to outer radius (ro ) of the ring footing. The behaviour of ring footings (ri /ro = 0 to 1) lies in-between the behaviour of circular (ri /ro = 0) and strip footings (ri /ro = 1). In this study, the variation of bearing capacity factors N’c, N’q and N’γ of smooth and rough base ring footings from axisymmetric solutions (ri /ro = 0 to 0.95) to the plane strain solutions (ri /ro = 1) is examined using finite element (FE) analysis. The bearing capacity factors of ring footings for the ri /ro = 0 to 0.75 are taken from Chavda and Dodagoudar (2019) and the same solution technique is adopted to evaluate the bearing capacity factors for ri /ro = 0.75 to 1. Based on the observations from the FE results, the guidelines are provided in regard to the following points: (a) the proper choice of the equation for ultimate bearing capacity of ring footing (b) the effect of variation of the Young’s modulus and Poisson’s ratio on the ultimate bearing capacity and (c) the dependency of N’γ on the width of ring footing. An example problem is considered to illustrate the pattern of variability in the bearing capacity of ring footing for ri /ro = 0 to 1. Based on the pattern, the ultimate bearing capacity equation for the ring footing is proposed using the bearing capacity expressions of the circular and strip footings.