Strip Footings Research Articles

Bearing capacity of rigid shallow footing on geogrid-reinforced fine sand—experimental modeling

The improvement of the bearing capacity and settlement characteristics of rigid shallow foundation on fine dune sands using geogrid reinforcement indicates a satisfactory behavior. In this research, an investigation evaluating the bearing capacity of (strip footing-geogrid-fine loose sand) system is carried out. The research main objective is to assess the influence of the reinforcement embedment ratio and the length ratio on the mobilized bearing capacity of the proposed system. The testing program includes 24 plate-loading tests on steel strip footing of varied width (B): 75, 100, and 120 mm rested on unreinforced sand as a reference to determine the obtained bearing capacity ratio (BCR). For reinforced dune sand, the studied parameters are the upper geogrid layer embedment ratio (u/B) and the geogrid length compared to the foundation element width (L/B). The increase of the mobilized bearing capacity of the footing could be monitored in comparison with the unreinforced dune sand bed. The increase of the geogrid reinforcing layers indicates a valuable increase in BCR, with an optimal value for the studied parameter. It is concluded that the gain in the mobilized bearing capacity (BCR) relative to that of the unreinforced case is found to be in range of 1.5 to 1.7 times, with optimal embedment ratio (u/B) and length ratio (L/B) of 0.25 and 7.5, respectively.

Seismic bearing capacity of surficial foundations on sloping cohesive ground

Engineers often assume undrained conditions in stability calculations of shallow foundations resting on soil with fine content as this assumption yields conservative results. Calculation of undrained bearing capacity of shallow foundations on level ground is a well-defined problem and when the footing is located on or near slopes, empirical equations or design charts produced based on limit equilibrium, upper bound plasticity calculations or finite element method (FEM) analyses are used. On the other hand, available studies that consider seismic bearing capacity of foundations on cohesive soils do not consider the influences of all influential parameters. Therefore, their use in design practice is rather limited. Accordingly, this study attempts to develop design charts that consider the influences of all parameters that affect the undrained bearing capacity factor of surficial strip footings under seismic conditions (Ncse). These influences are footing width, slope angle, slope height, footing position, undrained shear strength and pseudo-static acceleration coefficient. As the number of parameters to be considered is high, a parametric study is conducted using FEM models. Obtained results are consistent with the results of available studies in literature. Proposed design charts allow the selection of problem specific Ncse values. A design procedure is defined and two design examples are presented for the calculation of the magnitude of undrained bearing capacity under seismic conditions.

Effect of Load Eccentricity on the Bearing Capacity of Strip Footings on Non-homogenous Clay Overlying Bedrock

In underwater infrastructure design, foundations are embedded in soft clay seabeds that exhibited non-homogeneity of cohesion, and subjected to combined actions of vertical, inclined or eccentric loads due to the environmental conditions such as self-weight, wind and wave forces acting on substructure. This paper investigates the undrained bearing capacity for surface and embedded strip footings on non-homogenous clay overlying bedrock. Elasto-plastic finite element analyses are carried out for perfectly rough strip footings on Tresca soil under vertical eccentric loads. Meyerhof’s effective width rule is examined for the cases of surface and embedded footings in non-homogeneous clay. The effect of load eccentricity on the distribution of the normal stresses under strip footings is also investigated in this study. It is found that the effective width rule provides a conservative estimate of the bearing capacity. The elasto-plastic calculations predict that tensile stresses occur for surface footings because of the full bonding at the soil-footing interfaces, while for embedded footings, there is no tensile stresses.

A numerical upper bound formulation with sensibly-arranged velocity discontinuities and orthotropic material strength behaviour

Numerical limit analysis allows for fast estimates of the collapse load of structures exhibiting ideal plastic material behaviour. In numerical upper bound formulations, the description of the unknown velocity field can be extended by introducing velocity discontinuities between finite elements. Through these additional degrees of freedom, localised failure modes may be approximated more accurately and better upper bounds can be obtained. In the existing formulations, such discontinuities are typically introduced between all elements and the description is restricted to isotropic failure behaviour. In this work, a general 3D upper bound formulation is briefly proposed, allowing the consideration of both isotropic and orthotropic yield functions within finite elements as well as at velocity discontinuities. The concept of “projecting” a stress-based orthotropic yield function onto a certain discontinuity is presented, giving a traction-based yield function which allows for a consistent description of the material strength behaviour across the interface. The formulation is verified by means of two classical examples, the rigid strip footing and the block with asymmetric holes. Furthermore, based on the computation of potential orientations of plastic flow localisation, a simple concept for a sensible arrangement of velocity discontinuities is proposed. It is shown that this concept performs very well for isotropic as well as anisotropic material strength behaviour. A feature of the present work is that, velocity jumps are allowed only across the prescribed finite element interfaces determined from the sensible discontinuity arrangement. Good upper bounds similar to those in the existing works are obtained with far fewer degrees of freedom.

Bearing Capacity of Strip Footing on Clay Slope Reinforced with Stone Columns

Bearing capacity is very important in geotechnical engineering, which depends on factors such as footing shape, stress distribution under footing and failure mechanism of soil. One of the methods for improving the bearing capacity and reducing settlement in soft and fine soils is adding column like elements to soil which called stone column. In this research using model tests and numerical modeling, the effect of existence and location of stone column on bearing capacity of strip footing near soft clay slope is studied. In fact, reinforced and unreinforced stone columns in different locations are added to slope and the effect of them on load-settlement behavior of strip footing rested on top of the slope was investigated. Group stone columns are also studied, and efficiency of them is investigated. Also numerical modeling is carried out with Plaxis 3D Foundation program, and finally the results of experimental and numerical modeling were compared. Results show that reinforcing clay slope with stone column in all situations leads to increase in bearing capacity of strip footing. Moreover, reinforcing stone columns with encasing cause better performance of stone columns and increase in bearing capacity of footing compared with the same unreinforced stone columns. The maximum effect of stone column on bearing capacity of strip footing occurs when the stone column is located beneath the footing, and with increase in distance between the column and footing, the bearing capacity of footing is decreased.

Rate of Subsidence Due to Primary Consolidation on Cileles Village, Jatinangor Subdistrict

Jatinangor is an area of education in Sumedang Regency. Because many educational institutions established in this area, Jatinangor had a high level of infrastructure development. Soil plays an important role in determining the security level of infrastructure built on it. Imposition on the surface due to building load can have an impact on land subsidence. This study aims to determine the engineering properties of soil in research area, so that can know the rate of subsidence due to primary consolidation because of building load. The engineering properties of soil obtained from laboratory tests, such as unit weight, moisture content, void ratio, porosity, specific gravity, coefficient of permeability, angle of internal friction, cohesion, preconsolidation pressure, coefficient of consolidation, compression index, and swelling index. Based on the calculation bearing capacity of soil for general shear failure condition with strip footings type, the value of allowable bearing capacity ranges from 0.433 kg/cm2 – 12.064 kg/cm2. Assuming the building load addition is equal to the value of allowable bearing capacity, within 1 year the land subsidence is about 0.43 cm - 11.37 cm.

Yield criteria for glaciotectonically deformed deposits

Most glaciotectonically deformed deposits, including varved clays and glacial tills, are characterised by cracks and fissures. This paper presents a method for describing the yield criteria for glacitectonically deformed cohesive deposits using a model of cracked geomaterial with isotropic or anisotropic matrix. The general representation of the limit conditions for anisotropic materials in plane-strain is used to determine the yield criterion. The yield criterion represents a convex, piece-wise surface in the three-dimensional stress space revealing explicitly global, plastic properties of the materials considered. An example of using proposed yield criteria to solve a bearing capacity problem of a strip foundation constructed on a glaciotectonically cracked layer is presented. The lower and upper-bound estimates of limit loads on the strip footing are given. The limit state analysis presented in this paper can be used to solve many other geotechnical engineering problems, for example, the stability of slopes and reinforced walls or the bearing capacity of pile foundations.

A smooth hyperbolic approximation to the Generalised Classical yield function, including a true inner rounding of the Mohr-Coulomb deviatoric section

A new yield function recently introduced by Lagioia and Panteghini (2016), herein referred to as the Generalised Classical (GC) yield function, combines a series of criteria commonly used in geotechnical analysis into a single equation, including those of Tresca, Mohr-Coulomb and Matsuoka-Nakai. This makes for efficient implementation of multiple criteria into finite element software, and in this paper two key improvements are made to further enhance the usefulness of the GC yield function. The first is the development of a new expression for the shape parameter γ, corresponding to the so-called ‘Inner Mohr-Coulomb’ option, which ensures that a true inner rounding of the hexagonal Mohr-Coulomb deviatoric section is always obtained. The second is the introduction of a hyperbolic rounding to eliminate a discontinuity which can occur at the tip in the meridional section of the GC yield surface. The resulting yield surface is at least C2 continuous everywhere, provided a rounded criterion is selected, and can thus be used in consistent tangent finite element formulations. The results of finite element analyses carried out for two benchmark problems (a thick cylinder and a rigid strip footing) demonstrate the benefits of the rounding techniques in the new yield surface. Comparisons are made with the original yield surface and also the Hyperbolic Rounded Mohr-Coulomb (HRMC) yield surface originally developed by Abbo and Sloan (1995).

Ultimate Bearing Capacity Prediction of Eccentrically Inclined Loaded Strip Footings

Extensive laboratory model tests have been carried out on a strip footing resting over dry sand bed subjected to eccentrically inclined load to determine the ultimate bearing capacity (Patra et al. in Int J Geotech Eng 6(3):343–352, 2012a. https://doi.org/10.3328/IJGE.2012.06.03.343-352 , Int J Geotech Eng 6(4):507–514, b. https://doi.org/10.3328/IJGE.2012.06.04.507-514 ). Similarly, lower bound calculations based on finite element method were performed to compute the bearing capacity of a strip footing subjected to an eccentric and inclined load lying over a cohesionless soil with varying embedment depth and relative density (Krabbenhoft et al. in Int J Geomech ASCE, 2014. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000332 ). The load may be applied in two ways namely, towards the center line and away from the center line of the footing. Based on the results (both experimental and numerical analyses), a neural network model is developed to predict the reduction factor that will be used in computing the ultimate bearing capacity of an eccentrically inclined loaded strip footing. This reduction factor (RF) is the ratio of the ultimate bearing capacity of the footing subjected to an eccentrically inclined load to the ultimate bearing capacity of the footing subjected to a centric vertical load. A thorough sensitivity analysis is carried out to evaluate the parameters affecting the reduction factor. Based on the weights of the developed neural network model, a neural interpretation diagram is developed to find out whether the input parameters have direct or inverse effect on the output. A prediction model equation is framed with the trained weights of the neural network as the model parameters. The predictions from ANN, and those from other approaches, are compared with the results computed from both experimentation and FEM analyses. The ANN model results are found to be more accurate and well matched with other results.

The use of generalized finite difference method in perfectly matched layer analysis

• GFDM is extended to general form, which includes complex and real situations as special cases. • GFDM is implemented in perfectly matched layer (PML) analysis. • GFDM assessed through the use of compliance analysis of a rigid strip footing. • The comparisons with other methods show that GFDM can be used effectively and reliably in PML analysis. This study deals with the use of Generalized Finite Difference Method (GFDM) in Perfectly Matched Layer (PML) analysis. There are two options for performing PML analysis. First option is to express PML equations in terms of real coordinates of the points in actual (real) PML region; the second is to use governing equations (expressed in terms of complex stretching coordinates) as they are in complex PML region. The first option is implemented in this study; the implementation of the second option is under way and will be reported in another study. For the integration of PML equations, the use of GFDM is proposed. Finally, the suggested procedure is assessed computationally by considering the compliance functions of surface and embedded rigid strip foundations. GFDM with PML results are compared to those obtained by using Finite Element Method (FEM) with PML and Boundary Element Method (BEM). Excellent matches in results showed the reliability of the proposed procedure in PML analysis.

Non-coaxial soil model with an anisotropic yield criterion and its application to the analysis of strip footing problems

This paper presents numerical applications of a non-coaxial soil model, in which an anisotropic yield criterion is incorporated, to analyze two-dimensional strip-footing problems. Semi-analytical solutions of the bearing capacity for a strip footing that rests on anisotropic, weightless, cohesive-frictional soils are developed based on the slip line method. The degrees of influences of soil anisotropy and non-coaxiality on the bearing capacity of the strip footing are examined. From the viewpoint of strength and stiffness, it is necessary to incorporate both the strength anisotropy and non-coaxiality into numerical simulations and practical designs of geotechnical problems.

Bearing capacity of strip footings on c–φ soils with square voids

The presence of underground voids has an adverse influence on the performance of shallow foundations. In this study, the bearing capacity and failure mechanism of footings placed on cohesive-frictional soils with voids are evaluated using discontinuity layout optimization. By introducing a reduction coefficient, a set of design charts that can be directly applied to the classical bearing capacity formulation is presented. The results indicate that the undrained bearing capacity with voids is sensitive to soil weight and cohesion, as both the bearing capacity and stability issues exist in the problem. The failure mechanism is directly related to a variety of soil properties, the locations of single voids, and the horizontal distance between two voids. The presence of voids has a more dominant effect on c–φ soils compared to that on undrained soil. An interpretation of the critical and adverse locations for single-void and dual-void cases with various soil strengths is presented.

Bearing Capacity and Uneven Settlement of Consecutively Constructed Adjacent Footings Rested on Saturated Sand Using Model Tests

The interference of two nearby footings has been challenging due to the lack of suitable construction sites. Therefore, engineers are often forced to place footings at close spacing, which results changing of the ultimate bearing capacity, the settlement, and the tilt based on the considered spacing. In this study, two series of 1 g model test were conducted on two interfering parallel strip footings rested on the Babolsar saturated sand with different safety factors considered for the previously constructed footing (named as the old footing). The footings are loaded unequally and non-simultaneously to simulate mechanism of the new and the old footing with different surcharge and construction orders. The results are presented in the form of non-dimensional interference factors for ultimate bearing capacity and settlement of interfering footings versus isolated footings. It is demonstrated that the interference effect on the performance of isolated footings is considerable. Moreover, by decreasing the S/B ratio (i.e., spacing divided by footing width) from 1 to 0, the settlement ratio increases more than five times. Furthermore, in both series of tests, more than 300% increase in the tilting degree of the old footing was resulted due to the interference with the new footing in the ratio of S/B = 0 compared with S/B = 1. It demonstrates the perilous effect of the old footing tilting caused by the new footing adjacency. Moreover, applying different safety factors for the old footing has no dramatic effect on the tilting of the old footing enforced by the adjacent new footing.

The Effect of Rigidity of Reinforced Stone Columns on Bearing Capacity of Strip Footings on the Stabilized Slopes

The effect of slope-stabilizing stone columns on the bearing capacity of a rigid strip footing placed on a sand slope has experimentally and numerically investigated in this paper. A broad series of conditions has been tested by varying parameters such as the rigidity of stone columns and their spacing in a row. Different types of stone columns were studied including ordinary stone columns, encased stone columns, and concrete piles. Soil displacement fields were obtained via particle image velocimetry method. The results were analyzed to find qualitative and quantitative relationships among bearing capacity and various parameters. A series of finite-element analyses was additionally carried out on a prototype slope and the findings were compared with the results from the laboratory model tests. They were also used to complement the results of the model tests. The agreement between observed and computed results is found to be reasonably good in terms of load–settlement behavior and optimum parameters. Findings of the study showed that increasing rigidity and decreasing the stone columns spaces result in increasing bearing capacity of footing. This enhancement in bearing capacity is attributed to arching effect of soil between stone columns. The rigidity and spacing of stone columns had a significant effect on soil arching. Moreover, the load–settlement behavior of rigid footing is improved.

Bubble-enhanced quadrilateral finite element formulation for nonlinear analysis of geotechnical problems

We investigate a new numerical procedure based on a bubble-enriched finite element formulation in combination with the implicit backward Euler scheme for nonlinear analysis of strip footings and stability of slopes. The soil body is modeled as a perfect plastic Mohr–Coulomb material. The displacement field is approximated by a 4-node quadrilateral element discretization enhanced with bubble modes. Collapse loads and failure mechanisms in cohesive frictional soil are determined by solving a few Newton–Raphson iterations. Numerical results of the present approach are verified by both analytical solutions and other numerical solutions available in the literature.

Interference of Strip Footings Resting on Nonlinearly Elastic Foundation Bed: A Finite Element Analysis

The study pertains to finite element analysis of two interfering strip footings (symmetrical and asymmetrical with respect to footing size) resting on the surface of a nonlinearly elastic soil (dense/loose sand) medium obeying Duncan and Chang’s hyperbolic constitutive relationship. Predicted pressure–settlement behavior, bearing pressure and settlement characteristics of the interfering footings are then compared with the same for isolated footing, expressing the interference effects in terms of non-dimensional interaction factors. It is found that the characteristic behavior of an isolated footing is greatly influenced due to interference of a nearby footing. Studies have shown that for dense sand, interference affects the response of isolated footing much more compared to loose sand and for asymmetrical footings at very close spacing, the effect is more pronounced for footing with small size. The variation of pressure-interaction factors measured in working/allowable range is found to be similar to that measured at the ultimate failure, but on the contrary, the settlement-interaction factors are found to be different.

Finite element evaluation of ultimate capacity of strip footing: assessment using various constitutive models and sensitivity analysis

Finite element method can be used for computing bearing capacity of shallow foundation with irregular geometry resting on variable subsoil. It is necessary to quantify the parameters affecting the ultimate capacity of footing. This paper presents the results of finite element (FE) analysis of the ultimate failure load of a rough base rigid strip footing resting on c-ϕ soil. The soil is assumed as linear elastic perfectly plastic with Mohr–Coulomb failure criterion and non-associative flow rule. Sensitivity analysis is carried out to examine the ultimate capacity of strip footing considering the strength parameters (c′, ϕ′, and ψ), width of strip footing (B), unit weight of soil (γ), surcharge (q) at the base level of footing, and the deformation parameters (E and ν) as the variables. The study also examines the effect of different material models on the ultimate capacity of the strip footing. The material models considered are Mohr–Coulomb (MC) model, Hardening Soil (HS) model, Hardening Soil model with small-strain stiffness (HSsmall), and Soft Soil (SS) mode-l. It is found from the results of FE analysis that the ultimate load of the strip footing is dependent on the strength parameters, width of footing, unit weight of soil, and surcharge at the base level of the footing. The ultimate capacity is independent of the deformation parameters and will remain almost same corresponding to the material models like MC, HS, HSsmall, and SS. The FE results are compared with the analytical solutions of Terzaghi and Meyerhof. Based on the study, a few suggestions are given in regard to the FE analysis of geotechnical stability problems to obtain the quick results.

Bearing Capacity of Interfering Strip Footings

AbstractIn this paper, the ultimate bearing capacity of two closely spaced rigid strip footings with rough base on granular soil is examined based on enhanced limit equilibrium, plastic limit analy...

A Simple Model for Vertical Dynamic Interactions among a Group of Strip Footings Rested on Homogeneous Half‐Space

A simple model for vertical dynamic interactions among a group of strip footings rested on half‐space is presented in this paper. An analytical method is presented to obtain the contact pressures and the impedance matrix for a group of surface strip footings. In order to conveniently solve the unknown contact pressures between the soil and footings, the soil‐footing interfaces are discretized into a series of strip elements. The Green function for each element under uniform harmonic force is derived and calculated by the piecewise integration and Cauchy principal value integral. The influences of footing and soil parameters on contact pressures and vertical dynamic impedances of footing groups are discussed in detail. The SSSI effect between adjacent footings increases with the decrease of the distance ratio S/L. For three footings in a group, the middle footing experiences greater cross‐interactional effect than the side ones. The present method has high accuracy, which is not only simple but also suitable for the high‐frequency analysis.

Behavior of a strip footing on reinforced soil subjected to inclined load

This study investigates the behavior of a strip footing under inclined load on reinforced sandy soil by using experimental model. The effect of the load inclination angle (α), number of geogrid layers (N) and the relative density (RD) on the bearing capacity, settlement and horizontal displacement were studied. The results showed that by increasing the number of reinforcement layers (N), the bearing capacity increased, but there is an optimum value (N=4-5) depending on relative density of supporting soil. Also the settlement and horizontal displacement of footing decreasing with increase number of reinforcement layers.