Circular Foundation Research Articles

Vertical vibration of a circular foundation in a transversely isotropic poroelastic soil

Abstract Analytical methods based on linear elasticity have been used to model the dynamic response of foundations. These solutions commonly assume that soils are isotropic and elastic. Incorporation of anisotropy and the two-phased nature of soils (solid skeleton with pores filled with water) is important in the study of dynamic response of foundations. This paper presents the explicit analytical solutions for a transversely isotropic poroelastic soil half-space under a buried time-harmonic vertical load and a time-harmonic pore pressure discontinuity. These versatile fundamental solutions are derived by using Hankel integral transforms. They can be used to analyze a variety of dynamic problems in geomechanics. The fundamental solutions are then applied to solve the time-harmonic vertical vibration of a flexible circular foundation by using variational methods. Selected numerical results are presented to demonstrate the influence of soil anisotropy, poroelasticity, foundation flexibility, depth of embedment and frequency of excitation on the vertical dynamic response of foundation and the force transmitted to soil.

Dynamic response of a footing adjacent to dynamically loaded footing on gypseous soil

This paper presents an experimental study on the dynamic response of a circular foundation, underneath the have an impact on of a dynamic load that outcomes from the placement of a neighbouring footing said as (vibration source), having square-shaped and excited by way of a known source of vibration placed on top of it. The cause is to evaluate the effect of dynamic motion closely by group called the second foundation. Both foundations were founded on collapsible soil (gypseous soil) with a content of gypsum 65%. The research is conducted in dry and soaked conditions with an oversized experimental programme. The first base (source vibration) and also the second base are made of steel, with the size of 80 × 80 × 40 and the circular shape of 80 mm diameter. Subsequently, the soil had been prepared in layers in steel containers with 1000 × 500 × 500 mm, then the two foundations positioned centrally over the underside. The first footing excited by the rotating mass type mechanical oscillator to come back up with vertical harmonic loading, produces a related have an impact on of dynamic loads and also the 2nd base is loaded with only static weight under dynamic excitement. The checks are conducted beneath dynamic response for 3 frequencies (12, 18, 24) Hz, Displacement amplitude and acceleration of the 2nd foundation are examined, at a special distance between the inspiration (2B, 4B, 6B). The results have shown that when the space between the inspiration increases, the amplitude and also the acceleration for the second foundation decreases. Furthermore, the value of these parameters at dry condition is larger than their value at soaked states.

The bearing capacity of a granular layer on clay

Granular layers are often placed over weaker clay soils to improve the bearing capacity of working platforms and spread foundations. Their design requires the calculation of a two-layer bearing capacity. The commonly used existing calculation models are quite empirical with imprecise input parameters and can err on the non-conservative side in some situations. Other proposed methods tend to involve multiple design charts and are suited only to either strip or circular foundations. In this paper a new and highly practical design method is proposed whose input parameters are derived directly from the shear strengths of the two layers without the need for empirical-based charts. The output can be obtained either from a single chart or a few equations that are straightforward to implement into a spreadsheet. It can be applied quite generally to both surface and shallow embedded foundations, circular and rectangular and with dry or saturated granular layers, and also to working platform design for tracked plant. The method was validated using three independent numerical studies and centrifuge testing. The results showed that, although errors can increase for foundation shapes towards square or circular and with increasing overburden, the errors are smaller than those of the commonly used existing methods and are also conservative.

Behavior of circular foundation on sand layer of limited thickness subjected to eccentrically inclined load

A numerical study on the behavior of an eccentrically inclined loaded circular foundation on a sand layer of limited thickness underlain by a rigid rough base is presented. Specific attention is given to simulating the effect of the rigid rough base, load eccentricity (e), load inclination (α) and failure mechanisms in the finite element (FE) analysis assuming axisymmetric conditions. Analyses are performed using two models, namely, (i) an elastic-perfectly plastic Mohr-Coulomb model (MCM) and (ii) an elasto-plastic hyperbolic model called the hardening soil model (HSM) using Plaxis 3D. The results of the numerical modeling indicate that the bearing capacity is modified when the rigid rough base is located at a shallow depth below the base of the foundation and the extent of the failure surface. The results of the FE analysis appear to be in good agreement with those obtained from the tests by Sethy et al. (2019) for all H/B ratios, except for H/B = 0.3. However, the results obtained by the hardening soil model are all close to the results obtained from the laboratory model tests by Sethy et al. (2019). Based on the results of the finite element (FE) analysis and the results of the laboratory model tests by Sethy et al. (2019), the modified ultimate inclined load per unit area is seen to be dependent on the H/B ratio and becomes constant beyond H/B′ ratios (where B′=B-2e) that equal about three.

Model tests on jacking installation and lateral loading performance of a new skirted foundation in sand

A new type of caisson, composed of two skirted side semicircles and a skirted middle rectangle, was used as a breakwater foundation in Xuyu Port, China. In this study, large-scale laboratory model tests were carried out on jacking installations and lateral loading of this new skirted foundation in sand. Test results showed that the soil pressure acting on the caisson's inner skirt was larger than the outer soil pressure during jacking installation; whilst the tip resistance was greater than skirt friction. Penetration resistance was well predicted with the jacked pile theory and cone resistance. Overturning failure of the foundation occurred under the lateral loading. Ultimate lateral loads displayed a descending trend with increasing loading position height, whereas the corresponding moments exhibited an increasing trend. Parameters were suggested to calibrate the expression of circular foundation for purpose of estimating the combined capacity of the new skirted foundation. Passive soil pressure zones occurred on the outer surface of the new skirted foundation in the loading direction. In contrast, active soil pressure zones were found in the area with opposite loading direction. The net incremental soil pressure was positive in the loading direction, suggesting that the rotation center was beneath the model base.

Experimental Study on Connected and Non-connected Piled Raft Foundations Subjected to Eccentric Loading

Piled raft foundations are sometimes used when the supporting soil has no adequate bearing capacity and the raft settlements exceed allowable values. This research investigates the bearing capacity of a foundation subjected to eccentric loads in both connected and non-connected piled raft foundations under 1 g. The load-settlement curves of a strip, square and circular raft are compared. The results illustrate that piled raft behavior is influenced by various factors such as pile length, spacing, shape, and eccentricity ratio in connected and non-connected cases. Test results indicate that connected foundations have greater bearing capacities and lesser settlements in larger pile spacing (S/D = 6), while non-connected foundations have higher bearing capacities and lesser settlements in lesser pile spacing (S/D = 3). Moreover, both the pile length in a connected piled raft system and pile spacing in a non-connected system affected the bearing capacity remarkably. The bearing capacity of the square and circular foundations at S/D = 3 was greater for the non-connected pile (19.8 and 15.8 kg/cm2 receptivity) than the connected pile (18 and 14.1 kg/cm2), while at S/D = 6, the bearing capacity of the foundations was greater for the connected pile than the non-connected pile. However, in both cases, the bearing capacity was enhanced and the settlements were reduced. The effect of various parameters is also evaluated and discussed in this study.

Simple discrete models for dynamic structure-soil-structure interaction analysis

Simple models are presented for dynamic analyses of Structure-Soil-Structure Interaction (SSSI). Structures built on rigid, circular surface foundations resting on a homogeneous, elastic soil half-space are considered. The proposed models consist of discrete mass and spring elements that represent inertial, stiffness, and damping characteristics of an SSSI system. Frequency-dependent springs are developed to simulate Foundation-Soil Interaction (FSI) and Cross-Interaction (CI) between adjacent foundations, both being affected by the number and arrangement of neighbouring foundations. The stated springs are developed using a novel approach that approximates the through-the-soil interaction between adjacent footings using existing solutions to soil-structure interaction (SSI) analyses. Static stiffness matrices are obtained by means of compliance matrices using well known analytical solutions of surface displacement field to a ‘single-disk’ problem and a suggested displacement averaging rule. Dynamic stiffness matrices are created by applying modification factors to their static counterparts. To this end, a practical expression for dynamic modification factors that relate static and dynamic amplitudes of surface displacement field is provided. Equations of motion are formulated and solved in both time and frequency domains, taking into account time-lagging effects on input motion at separate foundations due to their vibration and wave passage. Validation results against more advanced numerical models prove the effectiveness of the proposed models. Finally, the limitations and potential improvements on the models are discussed.

Assessment of numerical procedures for determining shallow foundation failure envelopes

The failure envelope approach is commonly used to assess the capacity of shallow foundations under combined loading, but there is limited published work that compares the performance of various numerical procedures for determining failure envelopes. This paper addresses this issue by carrying out a detailed numerical study to evaluate the accuracy, computational efficiency and resolution of these numerical procedures. The procedures evaluated are the displacement probe test, the load probe test, the swipe test (referred to in this paper as the single swipe test) and a less widely used procedure called the sequential swipe test. Each procedure is used to determine failure envelopes for a circular surface foundation and a circular suction caisson foundation under planar vertical, horizontal and moment (VHM) loading for a linear elastic, perfectly plastic von Mises soil. The calculations use conventional, incremental-iterative finite-element analysis (FEA) except for the load probe tests, which are performed using finite-element limit analysis (FELA). The results demonstrate that the procedures are similarly accurate, except for the single swipe test, which gives a load path that under-predicts the failure envelope in many of the examples considered. For determining a complete VHM failure envelope, the FEA-based sequential swipe test is shown to be more efficient and to provide better resolution than the displacement probe test, while the FELA-based load probe test is found to offer a good balance of efficiency and accuracy.

Earthquake and Wave Analysis of Circular Cylinder considering Water‐Structure‐Soil Interaction

Offshore structures in zones of active seismicity are under a potential threat caused by the combined action of earthquakes and waves. Taking a submerged circular cylinder as the prototype and considering water‐structure‐soil interaction, the present study is devoted to the investigation of the combined action of earthquakes and waves. Water‐cylinder interaction and soil‐structure interaction are simulated by added mass and rigid circular massless foundations, respectively. Based on the radiation and diffraction wave theory, the scaled boundary finite element method is utilized to determine the earthquake‐induced and wave‐induced pressure on a circular cylinder. Then, a closed‐form expression for the natural frequencies and mode shapes of the system is derived by using the transfer matrix method, where the transfer matrix is obtained based on Euler–Bernoulli’s beam differential equation. Furthermore, the dynamic response of the system under the combined action of earthquakes and waves is derived by using the mode superposition method. Finally, the effects of the hydrodynamic force, wave force, and soil‐structure interaction on the dynamic response of the submerged cylinder are investigated. The results indicate that the wave forces can substantially increase the dynamic responses of the cylinder and that the influence increases as the stiffness ratio increases and the width‐depth ratio decreases. It is necessary to consider the combined action of earthquakes and waves in the seismic design of offshore structures.

H-M Bearing Capacity of Cone-Shaped Foundation for Onshore Wind Turbine under Monotonic Horizontal Loading

In this paper, monotonic horizontal loading tests were carried out to study the bearing capacity of the cone-shaped foundation in marine fine sand. With load-controlled methods, the horizontal load was applied to the rod of cone-shaped foundation at loading eccentricity ratios of 5.0, 6.0, and 7.0. In addition, theoretical analysis was used to investigate the horizontal ultimate bearing capacity, and finite element analysis was also used in this paper to investigate the influence factors of the bearing capacity of cone-shaped foundation. Based on the theoretical analysis, the formula for horizontal ultimate bearing capacity was deduced. Test results show that, at the same loading eccentricity, cone-shaped foundation can provide higher H-M bearing capacity as well as lower lateral deflection compared to regular circular foundation for wind turbines. In addition, the deflection-hardening behavior of load-deflection curve for cone-shaped foundation is also observed. Numerical analysis results show that the H-M bearing capacity of the cone-shaped foundation increases with increasing aspect ratio and buried depth, however, and decreases with increasing loading eccentricity. Based on the results from finite element analyses, several equations to calculate the maximum moment bearing capacities are put forward, which take the aspect ratio, loading eccentricity, and embedded depth into account.

Применение кольцевых фундаментов при возведении телевизионных башен и дымовых труб

Приведены результаты наблюдения за осадками фундаментов телебашен и дымовых труб. Доказана эффективность использования кольцевого фундамента в сравнении с круглым со сплошной фундаментной плитой.

Progressive failure and scale effect of anchor foundations in sand

Progressive failure is considered one of the least understood classical problems in geomechanics, gaining considerable attention in foundation related problems. However, the transformation of model test results to prototype is so much complex (scale effect). This paper highlights a FE ideology for evaluation of the response of shallow circular anchor foundations in sands with sophisticated strain hardening-softening behaviour. In these soils, the progressive failure can occur because of the non-mobilization of pinnacle strength of soil on potential failure surface and softening behaviour of soils. The presented paradigm allows this failure phenomenon to be properly evaluated by using a non-associated elastoplastic constitutive model coupled with explicit dynamic relaxation method considering yield surface as the MC material model and the potential surface is the smooth DP model having shear band effect. The FE results are compared with experimental outcomes to assess the reliability. Numerical model well-predicted the experimental stress-strain data points from element tests very closely. The scale effect is deliberated due to the progressive failure with shear banding phenomenon, which is remarkable with the increase of embedment and predominant in the sand of higher density. The peak resistance factor and settlement are presenting a decreasing trend with the increase of foundation width.

Experimental study of behaviour of circular footing on geogrid-reinforced sand

ABSTRACT Load tests were carried out with a circular foundation of diameter, B = 100 mm, supported on geogrid-sand reinforced contained in a circular-steel tank with diameter of 600 mm and depth of 450 mm, to determine the increase produced in the bearing capacity by including geogrid layers in the sand. Two types of geogrid, uniaxial and biaxial, were used as reinforcement material. Besides, a parametric study was carried out to verify the effect of several factors on the behaviour of reinforced soil. The parameters considered in the study include the depth of the first geogrid layer, vertical separation between layers of geogrid, diameter of the geogrid, number of reinforcement layers, deep of the foundation, geogrid type, and relative density of the sand. Moreover, the effect of folding the edges of the geogrid layer was studied. Finally, regression models will be developed from the laboratory model test to perform an initial calculation of the bearing capacity of the reinforced sand. Results showed that the parameters studied have a significant influence on the performance of the footing in terms of bearing capacity. The proposed regression models presented an adequate approximation to the experimental results.

Load recovery mechanism of arching within piled embankments using discrete element method and small scale tests

In this paper, small scale tests and 3D discrete element method (DEM) simulations are proposed to explore the load recovery mechanism of arching within unreinforced piled embankments. Comparisons between numerical and physical samples in regards to efficiency response, volumetric deformation and displacement characteristics are conducted to verify the DEM which is an effective way to capture the load transfer mechanism of piled embankments. The validation of the numerical tool is performed for different sand densities and pile patterns with small scale tests. Experimental tests results confirm that the load recovery stage in dense sand for equivocal triangular patterns reaches at a low value of displacement in comparison with square patterns. The results also show that the load recovery phases can be accurately modeled with DEM. The peak efficiency of the equilateral triangular sample is sharper and its strain-softening behavior is more significant. Also, the results show that the failure mechanism above pile heads is analogous to that of a circular shallow foundation, although vertically mirrored and similar to shallow foundations, the failure mechanism is dependent on the soil state, including relative density and mean stress. The discrete nature of the utilized numerical model for soil allows a good description of the evolution of the load recovery stage and contact forces within the granular material considering the kinematic of the arching process.

Bearing capacity of embedded foundations using quasi-kinematic limit analysis

Bearing capacity of rectangular foundations, with varying aspect ratios (1 ≤ L/B ≤ 5) and embedded at shallow to medium depths (D/B ≤ 5), has been evaluated by using the three-dimensional cell-based smoothed finite elements quasi-kinematic limit analysis. The results have also been obtained for circular and strip foundations by performing exclusively the axisymmetric and plane strain analyses. The associated optimization problem has been solved by employing the semidefinite programming (SDP). Shape factors (sc, sq and sγ) and depth factors (dc, dq and dγ) are given as a function of soil internal friction angle (ϕ). The shape factors have been expressed as a function of L/B, on the other hand, the depth factors have been given as a function of D/B and L/B. A thorough comparison of the results has been made with the different solutions available in literature. The variations of (i) power dissipation function, (ii) maximum plastic shear strain rates, and (iii) the nodal velocities patterns, have also been examined to interpret the failure mechanism.

Simplified frequency-independent model for vertical vibrations of surface circular foundations

PurposeThis paper aims to simplify a new frequency-independent model to calculate vertical vibration of rigid circular foundation resting on homogenous half-space and subjected to vertical harmonic excitation is presented in this paper.Design/methodology/approachThe proposed model is an oscillator of single degree of freedom, which comprises a mass, a spring and a dashpot. In addition, a fictitious mass is added to the foundation. All coefficients are frequency-independent. The spring is equal to the static stiffness. Damping coefficient and fictitious mass are first calculated at resonance frequency where the response is maximal. Then, using a curve fitting technique the general formulas of damping and fictitious mass frequency-independent are established.FindingsThe validity of the proposed method is checked by comparing the predicted response with those obtained by the half-space theory. The dynamic responses of the new simplified model are also compared with those obtained by some existing lumped-parameter models.Originality/valueUsing this new method, to calculate the dynamic response of foundations, the engineer only needs the geometrical and mechanical characteristics of the foundation (mass and radius) and the soil (density, shear modulus and the Poisson’s ratio) using just a simple calculator. Impedance functions will no longer be needed in this new simplified method. The methodology used for the development of the new simplified model can be applied for the resolution of other problems in dynamics of soil and foundation (superficial and embedded foundations of arbitrary shape, other modes of vibration and foundations resting on non-homogeneous soil).

Radiation damping for rigid foundations. Approximate expressions

The dynamic response of machine foundations was one of the first problems studied in soil dynamics with results going back to the 1930s. A number of approximations and graphical results were proposed in the 60s. In this paper we present a series of approximate expressions for the natural frequencies and effective damping of rigid masses on the surface of an elastic half space subjected to both vertical and coupled horizontal-rocking harmonic excitations. The formulas are obtained using the approximate expressions for the dynamic stiffness of circular foundations suggested by Veletsos et al [1, 2] for two different values of Poisson’s ratio of the soil. For the vertical case the expressions are only a function of the mass ratio (ratio of the mass of the foundation to an effective mass of soil) and of Poisson’s ratio. For the horizontal-rocking case they depend also on the ratio of the height of the foundation to its equivalent radius (a slenderness ratio).

An approach for calculating the vertical ultimate bearing capacity of a shallow circular foundation

In this work, a new method for the vertical bearing capacity of a shallow circular foundation was proposed with the amended formula by combining the limit equilibrium method and the principle of conservation of energy. Then the vertical ultimate bearing capacity of eight different circular foundations was acquired with the above mentioned method, an empirical formula method, and the static load test to obtain comparative results. The results showed that the relative error for the proposed method was deemed as the most accurate, close to the result of Vesic method, while much less than the relative error for both Meyerhof method and Hansen method. In addition, the impact factors for vertical ultimate bearing capacity including density, cohesion, friction angle of soil, radius, and burial depth of shallow circular foundation were also discussed, indicating that the shear strength parameters and density of soil, and especially the friction angle were the main influencing factors of the bearing capacity.

Contact pressure distribution under circular shallow foundation subjected to vertical and rocking vibration modes

In this paper, a rigid circular foundation with diameter of 150 mm is subjected to two modes of vibration each mode applies with two frequencies. The foundation was placed at three different depths within dry sand with two relative densities in a test model with dimensions of (800 × 800 × 1000) mm. A total of 18 models have been tested to study the effect of initial conditions on contact pressure distribution and vertical settlement. It was concluded that a circular footing subjected to rocking vibration mode tends to have escalated stress distribution in the direction of the rocking vibration to reach a peak at the center followed by a gentle drop. Edge points stresses for circular foundation showed an increase from one side to another (the increase in the direction of the rocking mode) by 150-100%, while most test models subjected to vertical vibration mode had a depression under the center of the foundation making peak stress levels just around the center of footing. The study revealed that increase of foundation depth results to increase the total settlement for all test models subjected to both vibration modes.

Prediction of ultimate bearing capacity of circular foundation on sand layer of limited thickness using artificial neural network

ABSTRACT The present study focuses on the development of an Artificial Neural Network (ANN) model equation to estimate the average ultimate load of shallow circular foundation on a sand layer of limited thickness underlain by a rigid rough base subjected to an eccentrically inclined load. The model is developed using the 260 number of data points obtained from extensive laboratory model tests. The input parameters considered are depth of embedment (Df /B) of the foundation, thickness of the sand layer to diameter of foundation ratio (H/B), eccentricity ratio (e/B), and load inclination to friction angle ratio (α/ϕ) to estimate the reduction factor RF as output. The RF is the ratio of the ultimate eccentrically inclined load on a sand layer of limited thickness to the ultimate eccentrically inclined load on a sand layer, which is extending to a great depth. Importance of input parameters, which reflect the output, is studied using Pearson’s correlation and Spearman’s rank correlation. The sensitivity analyses are carried out using Variable Perturbation methods and Weight methods. It has been professing that H/B ratio is the most important input parameter.