Strip Footings Research Articles

Upper bound solution for the bearing capacity of two adjacent footings on rock masses

In this paper, the effect of the adjacency of two strip footings on bearing capacity of rock masses was investigated using the upper bound analysis and finite element method. The modified Hoek-Brown nonlinear failure criterion was used for the rock mass. The effect of various parameters such as the distance between the two footings, Hoek-Brown parameters, surcharge pressure and unit weight of the rock mass on the ultimate bearing capacity of rock masses were also investigated. The results show that if the distance between the two footings is significant, the failure lines occur beneath each footing will not interfere with the failure lines beneath the other adjacent footing and each footing behaves as a single one. The maximum distance for which the two footings affect each other can be obtained from the charts presented in this paper. By reducing the distance between the two footings, the bearing capacity will increase firstly and then decrease. Finally, when the two footings touch each other, the ultimate bearing capacity of the two footings will be equal to the ultimate bearing capacity of a single isolated footing with a width twice the width of each footing.

Horizontal vibration of a rigid strip footing on viscoelastic half‐space

AbstractThis paper presented an analytical method for determining the response of a rigid strip foundation resting on the surface of a viscoelastic half‐space to horizontal dynamic loads, and the associated transient soil displacements resulting from the vibration of the footing. This mixed boundary value problem was solved by means of Jacobi orthogonal polynomials, a more efficient method compared to transforming the dual integral equations resulting from the boundary conditions to Fredholm integral equations. Displacements and stresses of the soil‐footing system were accordingly obtained by applying the inverse Fourier transform. Finally, we used the proposed solution to investigate the effects of material damping and Poisson's ratio of soil on the dynamic response of the strip footing, and the resulting soil displacements.

Study on Behaviour of Two Adjacent Strip Footings on Unreinforced/Reinforced Granular Bed Overlying Clay with Voids

This paper numerically studies the behaviour of two adjacent strip footings on unreinforced and reinforced granular bed (RGB) overlying clay having voids. The influence of different parameters such as granular bed thickness, length of reinforcement/s, number of layers of reinforcement, presence of void/s beneath the footing/s in the weak soil, on the behaviour of footings are carried out in this study. It is found that there is a certain optimum spacing between the two adjacent strip footings at which the footing/s carry the maximum load. The voids could be formed in weak soil due to various reasons and the presence of voids may affect the performance of footings. Such voids tend to reduce the load carrying capacity of the footing/s. However, providing a RGB over weak soil can be used as an effective method to maintain the good performance of footings, even when voids could be formed in future.

Model studies of bearing capacity of rectangular foundation subjected to eccentric and inclined loads

This study presents the behaviour of eccentrically inclined loaded rectangular foundation on unreinforced and geogrid reinforced sand carried out experimentally, theoretically and numerically. In the past, several works have been done relating to the estimate of the ultimate bearing capacity (UBC) of shallow foundations supported by geogrid reinforced sand. These researches are limited to strip, square and circular footings. It is found that the less attention was given to determine the UBC of the shallow rectangular foundation under eccentric and inclined load with different depth of embedment $${D}_{\rm f}$$ . Hence, the present study is based on the behaviour of eccentrically inclined loaded rectangular (surface and embedded) foundation on the unreinforced and geogrid reinforced sand bed. To determine the load–settlement behaviour and compare it with experimental observation, equally theoretical and numerical analysis (PLAXIS 3D) has also been conducted.

Comprehensive 3D numerical study on interaction between structure and dip-slip faulting

Investigations on the effects of fault permanent deformations on surface and subsurface engineering structures are important owing to their direct impact on the reduction of earthquake damage. This study presents the methodology and results of a comprehensive, three-dimensional, nonlinear numerical modeling of the interaction between dip-slip faulting in soil and a four-story steel moment frame structure founded on different types of shallow surface foundations. A modified Mohr–Coulomb constitutive model was implemented in the numerical modeling, where the softening/hardening behavior of soil and an elasto–plastic model that provided a more accurate description of the stress–strain response of steel elements were considered; both were adopted in a finite element program. The results demonstrate that modeling the structural elements, in comparison with only modeling the footing as a rigid plate and compromising the effect of the structure by applying its weight, significantly affects the soil–structure interaction and displacements of the footings. The results indicate that a strip footing oriented perpendicular to a fault strike yields results similar to a mat footing, whereas a strip footing parallel to a fault strike resembles a spread footing. This suggests that not only the stiffness of the footing to tolerate the vertical loads of the structure, but also its continuity or freedom to move in the direction of fault displacement is important. In the absence of rigid connection between structure footings, the excessive freedom of a footing to comply with the quasi-static deformation of soil due to fault-induced movements results in a considerable deformation and rotation of the columns, primarily in the columns between the footing and the first floor.

Study on Influence of Construction Process of Double-Line Shield Tunnels on Frame Structure

This paper presents a study of the influence on stress and deformation of the frame structure induced by double-line shield tunnels during tunneling. Using the finite element software MIDAS/GTS, the construction process of double-line shield tunnels passing through the adjacent frame structure with a strip foundation was simulated. By comparing the ground settlement monitoring data of a building passing through Changsha Metro Line 2 with the numerical simulation results, it is found that the Midas GTS/NX finite element analysis is reliable and can be used to predict the impact of shield tunneling on the frame. The location and construction sequence of double-line shield tunnels were varied to investigate the response of frame structure. The results of the analysis are as follows: (1) the position and value of the maximum stress of the frame structure are different in different excavation locations. Under the condition that the left tunnel passes under the frame structure and the right tunnel passes through from the side of the frame structure, the maximum stress of the frame structure has the minimum. (2) The frame structure inclined towards the tunnel when double-line tunnels pass-through from the side of the frame structure. Under the condition that the left tunnel passes under the frame structure and the right tunnel passes through from the side of the frame structure, the frame structure produced the longitudinal inclination. (3) The maximum settlement of the strip footings locates the ①-axis position when double-line tunnels pass-through from the side of the frame structure. The maximum settlement of the strip footings locates the ⑤-axis under the condition that the left tunnel passes under the frame structure and the right tunnel passes through from the side of the frame structure. The maximum settlement of the strip footings locates the ⑥-axis position when the double-line tunnels pass under the frame structure. (4) Under the condition that the double-line tunnels pass-through from the side of the frame structure, the impact of different construction sequences on the frame structure is slightly different. The construction sequence of the synchronous excavation of two lines in the opposite direction is more likely to cause that the frame structure inclines to the tunnel during tunneling.

Undrained seismic bearing capacity of strip footings horizontally embedded in two-layered slopes

This study investigated the undrained seismic bearing capacity of strip footings embedded in two-layered slopes by finite element limit analysis (FELA); in particular, a pseudostatic method was specified to seismic loads. Lower bound theory (LB), upper bound theory (UB), and adaptive meshing technique are employed for exploring the effect of the shear strength ratio of top layer and bottom layer, cu1/ cu2; the horizontal embedment depth of footings, b/ B; the footing locations (in bottom layer or top layer); seismic coefficient kh; and the slope gradient β on seismic bearing capacity. Results indicated that the seismic bearing capacity would increase with the growth of horizontal embedment depth of footings. The comparison between the predictions obtained from the proposed method and the existing method was presented, and the failure mechanisms are further summarized.

Ultimate bearing capacity of eccentrically loaded strip footings above voids in rock masses

Based on a self-developed adaptive finite element limit analysis (AFELA) code and generalized Hoek-Brown (GHB) failure criterion, the footing-void system subjected to eccentric load in rock masses is investigated. The research emphasis of this study is on quantifying the effect of the load eccentricity and voids on the ultimate bearing capacity of footings. Predictions of footing ultimate bearing capacity can be captured by the scope enclosed by upper bound (UB) results and lower bound (LB) results within 5% relative errors. All of independent variables including the void location, the void size, the void length-width ratio and the rock strength parameters are involved in parametric study in pairs. Furthermore, typical failure patterns which can cover nearly all cases are discussed for deeper insight into how the stability evolving with variations of above-mentioned variables.

Seismic Bearing Capacity of Strip Foundations on Fiber-Reinforced Granular Soil

The present study investigated the bearing capacity of strip footings on a bed of granular fiber-reinforced soils. Analyses were performed by the stress characteristics method (SCM). The failure criterion considers anisotropic distribution of fiber orientation and ignores the rupture of reinforcements. Seismic effects were included in the stress equilibrium equations as the horizontal and vertical pseudo-static coefficients. Stress equilibrium equations were solved by the finite difference method. A computer code was provided to solve the problem. Using the soil and reinforcement input parameters, the code determines the characteristics network and calculates the bearing capacity. The bearing capacity was expressed as the bearing capacity factors of the soil unit weight and surcharge. Parametric analysis was performed to investigate the effect of soil and reinforcement parameters on the bearing capacity and the shape of the failure zone. The outcomes indicated that the SCM results lower ultimate bearing capacity as compared with the upper bound method. Also, the depth of the failure zone increases with an increase in the amount of reinforcement or decrease in the horizontal seismic coefficient. Considering the anisotropic distribution of fiber orientations leads to more bearing capacity than the isotropic distribution.

Experimental and numerical studies of a strip footing on geosynthetic-reinforced sand

The behaviour of footings on geosynthetic-reinforced soils has been investigated by many researchers through experimental and numerical modelling under stress-controlled or strain-controlled conditions. A new experimental set-up was designed under a stress-controlled condition, with the application of the particle image velocimetry (PIV) technique. A series of model footing tests was carried out using this equipment to investigate the behaviour of the geosynthetic-reinforced soil below a strip footing. The deformation inside the soil mass below the strip footing was determined using the PIV technique. The reinforcing performances of single-layer and multi-layer geotextile and single-layer geogrid embedded at different depths were compared and discussed by analysing the load–settlement curves. It is found that there is a stepwise increase phenomenon in settlement under the stress-controlled condition. The ultimate bearing capacities were determined from the obtained stepwise load–settlement curves using three approaches: the tangent intersection method, the tail linear method and the allowable settlement method. The three approaches were coded in a Python program in order easily to determine and compare the results. In addition, the experimental model footing tests were simulated using the finite-element method under the same stress condition with good agreement for a settlement range within 0·1B.

Bearing capacity under increasing undrained shear strength

The undrained shear strength of naturally deposited, consolidated and saturated clay usually increases with depth due to the overburden pressure and the decreasing water content. Nonetheless, calculations of the bearing capacities of foundations under undrained conditions are usually done using the approach of Prandtl, which assumes constant values of the undrained shear strength. Analytical models using the kinematic element method show that the failure mechanism and the bearing capacity are both influenced by the increasing undrained shear strength; therefore, Prandtl's method might overestimate the bearing capacity of a shallow foundation assuming an average value of the undrained shear strength. Centrifuge tests of shallow strip footings on kaolin clay were conducted to validate the analytical model in terms of bearing capacity and failure mechanism. The estimated bearing capacity of the shallow foundation based on analytical models show good agreement with the centrifuge test results. However, the shape of the failure mechanisms is considerably different. In the analytical models, the development of the failure mechanism is estimated based on the assumption of a perfectly plastic behaviour, developing a rigid-body collapse. This behaviour was not observed in the physical models due to the development of the failure mechanism.

Bearing capacity of rigid strip footings near soil slopes

A reasonable combination of asymmetric foundation failure and whole slope failure is essential to solve the problem of the ultimate bearing capacity of a rigid strip footing near a soil slope. Based on a bilaterally admissible failure mechanism put forward to meet the requirement of the combination, a closed-form analytical solution to the ultimate bearing capacity is obtained in light of the upper-bound theorem of kinematical limit analysis. The proposed method can quantitatively illustrate that the failure mode of the footing-on-slope system varies from the slope side to the non-slope side with the increase in the horizontal distance ratio of the footing from the slope edge over the width of the footing. For some typical examples, the results calculated using the proposed method are in good agreement with those obtained using other analytical and numerical methods or laboratory model tests. The influences of the shear strength parameters of the soil and safety factor of the slope on the bearing capacity are also discussed in the examples.

Load-Deformation Behavior of Geosynthetic-Reinforced Retaining Walls with Limited Fill Space Under Static Footing Loading

Geosynthetic-reinforced retaining (GRR) walls have been increasingly built with limited fill space, which has posed challenges for designing such walls with satisfactory performance, especially under surface loading, such as bridge and building foundations. This study performed a series of laboratory model tests to investigate the performance of GRR walls constructed with limited fill space under strip footing loading. The devised experimental program consisted of constructing nine model tests with different retained medium distance, geosynthetic-reinforced fill width, and reinforcement layout. In each model test, a load was applied on the top of the wall through a 200 mm wide rigid plate to simulate a strip footing. Marks on facing units and the loading plate were installed to measure wall deformations and footing settlements, respectively. The test results show that limiting the size of the retained medium and the reinforced fill affected the internal stability of the wall, the wall deformation, and the footing settlement. Reduction of the reinforced fill width from 0.5H to 0.3H (H is the wall height) resulted in excessive wall deformation and footing settlement, and even sudden failure of the model wall. On the other hand, the test results reveal that connecting geosynthetic reinforcement to the stable retained medium resulted in substantial reduction in the deformation of the wall facing and the settlement of the footing. The test results also demonstrate that bending geosynthetic reinforcement upward along the back of the reinforced fill enhanced internal stability and resulted in considerable reduction in the lateral deformation of the wall facing and increase in the bearing capacity of the footing.

Effect of the Geotextile Arrangement on the Bearing Capacity of a Strip Footing

A series of laboratory tests were conducted to investigate the effect of the three-dimensional arrangement of geotextile strips on the load-bearing capacity of a strip foundation on sand reinforced by geotextile strips. The load-bearing capacity of a 24.5 × 7.5 × 1.5 cm strip foundation on a 90 × 25 × 30 cm sandbox reinforced with three different types of geotextiles in seven different forms of three-dimensional arrangement was studied. Geotextile arrangements consisted of one, two, and three layers of continuous strips with 1 cm vertical spacing, two and three strips of 5 cm wide reinforcements in 5 cm horizontal intervals beneath each other in the vertical plane, and 5 cm shifted in the horizontal plane. The results indicate that the improvement of the bearing capacity of the foundation on reinforced soil per unit width of the reinforcements is the maximum for one-layer continuous reinforcement. The bearing capability of the footing per unit width of the reinforcements decreases by increasing the number of reinforcements layers. For multi-layer reinforced models, using reinforcement strips in interval arrangements increases the effectiveness of the geotextile on the improvement of the bearing capacity of the footing. Using a proper three-dimensional arrangement of reinforcement strips results in a similar ultimate bearing capacity with approximately 50% less reinforcement when compared to continuous multi-layer reinforcement arrangement.

Effect of geosynthetic reinforcement on the bearing capacity of strip footing on sandy soil

Due to the increasing presence of problematic soils, expansive clays and highly compressive sand engineers are using a verity of soil improvement techniques to treat such soils. While geosynthetics are extensively used for improving soil characteristics in roads, pavements and embankments, it can also be used to increase the lack of bearing capacity of residential housing or lightweight structures constructed on sandy soils. In order to simulate site conditions in the laboratory environment, a laboratory-scale testing platform has been manufactured to assess the behaviour of geosynthetics reinforced and un-reinforced strip footing. The first group of tests were performed on the unreinforced compacted sandy soils with different densities where the other group of tests were carried out in the soil that has been reinforced individually with three different types of geosynthetic materials having distinct tensile strengths. Furthermore, interface direct shear tests and consolidated undrained triaxial tests have been carried out to determine the shear parameters which is directly influencing the bearing capacity a strip footing. Geosynthetic reinforcement has considerably enhanced the mechanical behaviour of sandy soil in regarding the type of geosynthetic. Furthermore, it was observed that coir geosynthetic has provided increased interfacial friction when compared to other geosynthetic types and improved bearing capacity. Moreover, the adopted testing method found to represent well the behaviour of such materials in the laboratory environment.

Bearing Capacity of Strip Footing on Hoek-Brown Rock Mass Subjected to Eccentric and Inclined Loading

This paper presents the numerical solutions for the bearing capacity of strip footing under inclined and eccentric loads on rock mass obeying the Hoek-Brown yield criterion. This study applies the lower and upper bound finite element limit analysis to evaluate the numerical solutions. The dimensionless parameters including the geological strength index and the yield parameter of rock as well as the inclined angle and eccentricity of load are considered. The influences of all considered dimensionless parameters on the bearing capacity factors are demonstrated and discussed. Finally, the failure mechanisms of strip footing subjected to inclined and eccentric load on Hoek-Brown rock mass are illustrated to portray the effects of all considered dimensionless parameters.

3–storey building subjected to reverse faulting: Analysis and experiments

The paper studies the response of a 3-storey building subjected to reverse faulting. 1 g physical model tests are conducted using a 3m long split-box, modelling the nonlinear response of structural members with artificial plastic hinges. The experimental results are used to validate the numerical modelling technique, which is subsequently employed to conduct a parametric study on sand density, foundation type (isolated footings, strip and slab foundations), and the location and angle of fault crossing. It is shown that the response of the structure is sensitive to the relative location of the fault rupture. In the case of isolated footings, complex interaction mechanisms develop, including fault rupture diversion, bifurcation, or diffusion. While the rigid-body rotation of the structure θr is crucial in terms of serviceability, the footing rotations θfare responsible for superstructure distress. Such distress is directly related to differential footing rotations and displacements. Looser soil may act as a cushion, but its effect is not always beneficial. Bifurcation of the fault rupture may lead to outcropping of a secondary branch between the footings, with obvious detrimental consequences. Strip footings or a slab foundation offer substantial improvement. Such rigid and continuous foundation systems prohibit differential displacements between columns, forcing the entire structure to rotate as a rigid body. The interaction mechanisms are complicated further when the fault rupture crosses the structure at an oblique angle. The distress of the structure is reduced with strip footings, which should be installed in both directions.

Effect of inclined and eccentric loading on the bearing capacity of strip footing placed on the reinforced slope

The present study considers the influence of inclined and eccentric loading on the bearing capacity of a strip footing placed on the reinforced cohesionless soil slope by using lower bound finite element limit analysis technique. The effects of other parameters such as soil friction angle, embedment depth of reinforcement layer below the footing, interface friction angle between soil and reinforcement, and vertical spacing between two reinforcement layers are also investigated. Results are presented as the variation between reinforcing efficiency and various combinations of above-mentioned parameters. The bearing capacity of strip footing reduces under combined effects of inclined and eccentric loading. However, with the inclusion of reinforcement layers at the optimum depth, the bearing capacity enhances significantly. The reinforcing efficacy increases with the increasing value of load inclination. The reinforcing efficiency reduces with the consideration of partial roughness between soil and reinforcement layer. Stress contours are also plotted in the two-dimensional object space to understand the failure mechanism of slopes.

Study on Behaviour of Two Adjacent Strip Footings on Granular Bed Overlying Clay with a Void

This paper numerically examines the behaviour of two adjacent strip footings on granular bed over weak soil having a void. Voids could be formed in weak soil strata due to various reasons such as due to water leakage from the water supplying lines or sewer lines, poor drainage and erosion of soil, animal burrows, etc. A parametric study is carried out to understand the influence of granular bed thickness, width of footings, spacing between the footings, and the presence of a void beneath the footing in the weak soil, on the behaviour of footings. To understand the failure mechanism, shear strain contours, for different cases, are being studied. It is observed that there is a certain critical spacing between the two adjacent footings at which the footing/s carry the maximum load. This critical spacing depends on the type of loading, whether equal and simultaneous loading or unequal and sequential loading. The presence of voids also affects the performance of footings. Such voids tend to reduce the load carrying capacity of the footing/s and alter failure pattern.

Probabilistic analysis of strip footings on spatially variable soils with linearly increasing shear strength

Abstract This paper presents a probabilistic approach to obtain bearing capacities of strip footings resting on spatially variable marine clay deposits of increasing undrained shear strength with depth. A spatially variable feature is generated with a non-stationary random field where the ratio of the mean and standard deviation of undrained shear strength is maintained. The sparse polynomial chaos expansion is adopted to improve the calculation efficiency of random numerical simulation. Similar to the deterministic case, for a given degree of soil heterogeneity κ, the dimensionless vertical capacity is independent of the change in the slope of undrained shear strength in the stochastic case. The probability density function (PDF) and cumulative distribution function (CDF) curves of normalised bearing capacity for varying κ are constructed and the effect of soil parameters, such as κ, coefficient of variations and autocorrelation distances, on the probabilistic bearing capacity is discussed. Results show a remarkable improvement in efficiency in computation with a minimal number of realisations. Parametric studies obtained demonstrate that κ has the lowest effect on the normalised bearing capacity among the above parameters. In addition, for an anisotropic autocorrelation distance of δh/δv = 5, the greatest reduction in the random vertical capacity vu,p at a low p occurs when the dimensionless vertical autocorrelation distance δv/B = 0.5, which offers a guide in the design of offshore shallow foundations.