Rectangular Foundations Research Articles

3D seismic bearing capacity of rectangular foundations near rock slopes using upper bound method

The analysis of foundation's bearing capacity is generally conducted under the assumption of plane strain. However, the damage of rectangular foundation usually presents obvious three-dimensional (3D) effect. This article considers this 3D effect, which, for the first time, provides a theoretical framework for assessing the bearing capacity of rectangular foundations placed on rock slopes under seismic condition. In order to apply the kinematic method of limit analysis, a new 3D kinematically admissible collapse mechanism is first constructed. Owing to the point-to-point discretized technique, this 3D mechanism can avoid complex surface integration and effectively reduce spatial coordinate iterative calculations while maintaining high accuracy. The pseudo-static method is adopted to simulate the effects of earthquakes. Generalized multi‑tangential technique is employed to derive the Mohr-Coulomb constants from Hoek-Brown criterion. The comparison between the present results and results of previous literatures proves the validity of the theoretical framework in this paper. Shape factor and reduction factor are introduced in the parametric study, showing that the 3D effect is more obvious when the rectangular foundation aspect ratio is reduced. As the rectangular foundation location moves away from the slope, its bearing capacity gradually converges towards that of the horizontal foundation. The critical collapse mechanism is also explored, demonstrating that the collapse extent expands with increasing internal friction angle of the rock.

The Possibility of Detrimental Effects on Soil–Structure Interaction in Seismic Design Due to a Shift in System Frequency

Soil–structure interaction (SSI) leads to a modification in the dynamic properties of structure, but due to the complexity of analysis, it is traditionally assumed in seismic designs that the structure is fixed-supported on the ground, which brings about potential risks to the seismic performances of structure. The study works on the possibility of SSI having detrimental effects by comparing the dynamic responses of the SSI system to a fixed-base structure, and presents charts for an evaluation of the system frequency of SSI for the purpose of engineering practice. In order to reveal the physical nature, the SSI model is reduced to its simplest form, consisting of a SDOF oscillator, a three-dimensional rectangular foundation, and a multi-layered half-space. The energy dissipation in the soil is achieved by foundation impedances and the substructure method. Previously, the foundation impedances are usually acquired by two-dimensional or axisymmetric three-dimensional models in uniform half-space to avoid the high cost of the more realistic, fully 3D models, while a high-precision indirect boundary element method is employed, combined with the non-singular Green’s functions of distributed loads to calculate the foundation impedances. Although SSI dampens the peak amplitude of structure response in the frequency domain, case studies on four buildings’ responses to 42 earthquakes in the time history show a possibility of 15–20% that SSI amplifies the dynamic responses of structures, such as the maximum and the mean values in the time history, depending on the properties of the structures and the site, as well as the frequency component of incident waves.

Numerical studies of the distribution capability of a continuous linear strain soil base model for largesized raft foundations

The paper examines the existing methodology for determining the main design parameters of the model in the form of a continuous linearly strained layer of finite distribution capability (the design thickness of the layer H0 and design stress-strain modulus E0) to simulate the adequate interaction between soil bases and large-size slab foundations. The aim of this work is to numerically study the stress-strain state of a uniformly loaded flexible rectangular foundation slab when the thickness of the soil base model layer is reduced in the form of a continuous linearly deformed layer of finite distribution capacity. Numerical studies of the effect of the thickness of the layer of the specified soil base model that interacts with a large-size flexible slab foundation of various rectangular shapes in plan were conducted in the SCAD package using the finite element method. The numerical study results have shown that when the ratio H0/Ha (the design thickness of the layer of the soil base model H0 to the actual compressible thickness of the soil base Ha) decreases, the maximum moment forces along the orthogonal axes of rectangular foundations decrease to 50% because of the decrease in the distribution capability of the soil base model and, accordingly, in the edge reactions R under the slab at equal average settlements of the slab saver. Numerical studies have shown interesting results on the distribution of moment forces in flexible rectangular slabs, where the maximum is outside the center of gravity of a uniformly loaded raft, which confirms the peculiarity of the interaction of flexible slabs with relatively narrow compressible layers under the sole. With an appropriate in-situ experimental justification, the use of the soil base model in the form as a continuous linearly strained layer of finite distribution capability with the design parameters (H0 and E0) rather than with the actual parameters (Ha and Ea) in calculations of large-size slab foundations can be of fundamental practical importance in their rational design, as the reinforcement can be reduced to 50%

Stability Evaluation Model of Large Rectangular Foundations on Soil under Combined Loading

Stability Evaluation Model of Large Rectangular Foundations on Soil under Combined Loading

A simplified three-parameter model for analyzing torsional vibration of rectangular foundations on layered soil

Dynamic soil-structure interaction (SSI) significantly impacts structural vibration. Over the past few decades, numerous simplified models were developed to analyze dynamic SSI on homogeneous soil. In this study, however, a lumped-parameter model is adopted to investigate the dynamic behavior of rectangular foundations overlying nonuniform soil. The simplified three-parameter model is utilized to analyze the torsional vibration of rectangular foundations on layered soil with linearly varying shear-wave velocities. Non-dimensional parameters (shear-wave velocity ratios, layer depth ratios, and mass ratios) are also investigated herein. The frequency-magnification curves of the foundation using three-parameter model are found to agree well with theoretical solutions. Consistent agreements are also observed at the resonant response and its corresponding frequency ratio. Additionally, the resultant resonant magnification factors against mass ratios clearly show the impacts of the whipping effect resulting from soil-foundation interactions. The proposed model excels in simulating layered soil and includes fewer parameters than existing lumped-parameter models. The proposed model also demonstrates the adaptivity and reliability to simulate the dynamic responses calculated from the published in-situ experimental data. The time-domain application based on the proposed model effectively estimates the structural displacement of the soil-foundation-superstructure system. This research could contribute to the SSI analysis regarding the torsional vibration of a foundation on nonuniform soil.

Prediction of Damping Ratio and Shear Modulus of Saturated Clay Soil under Rotating Machine

Developing countries' industrial growth necessitates innovative machine foundation design and resilient infrastructure. Meanwhile, soil properties play a significant role in the satisfactory design of machine foundations. The paper presents an experimental work to determine accurately the damping ratio and shear modulus by equations. The paper studies the effect of different parameters (embedded depth of foundation, shape of footing, and changing operating frequency of machine) on the damping ratio and shear modulus of saturated clay soil. Moreover, mathematical expressions are derived from statistical analysis to predict the damping ratio for rectangular and circular footing on saturated clay. The physical model results reveal that the damping ratio inside the soil will be increased with an increase in the depth of the point inside the soil for all cases. The damping ratio tends to decrease with an increase in operating frequency. The maximum damping ratio has occurred below a rectangular foundation with a 16.6 Hz operating frequency in saturated clay. The damping ratio is a function of many factors, such as embedment depth, degree of saturation, shape of foundation, and operation frequency of the machine.

Optimal borehole placement for the design of rectangular shallow foundation systems under undrained soil conditions: A stochastic framework

This contribution proposes a framework to identify optimal borehole configurations for the design of shallow foundation systems under undrained soil conditions. To this end, the minimization of a performance measure defined in terms of the bearing capacity standard deviations is considered. The random failure mechanism method is adopted for random bearing capacity evaluation, thereby enabling explicit treatment of soil spatial variability with tractable numerical efforts. A sampling-based optimization scheme is implemented to account for the non-smooth nature of the resulting objective function. The proposed framework provides non-trivial sensitivity information of the chosen performance measure as a byproduct of the solution process. Further, the method allows assessing the effect of increasing the number of soil soundings into bearing capacity standard deviations. Three cases involving different foundation layouts are studied to illustrate the capabilities of the approach. Numerical results suggest that the herein proposed framework can be potentially adopted as a supportive tool to determine optimal soil sounding strategies for the design of a practical class of civil engineering systems.

Analytical Solutions of Water Inflow for Foundation Pit in Confined Water Stratum

This paper is aimed at the problem of inaccurate calculation of the water inflow of a foundation pit with a suspended water-proof curtain in a confined water stratum. According to the groundwater hydraulics principle, the theoretical model of the seepage field of the foundation pit is established, and the analytical formula of the water inflow for the circular, strip, and rectangular foundation pits is deduced. The seepage path influence coefficient α related to the water-proof curtain insertion ratio, the thickness of the confined aquifer, and the radius of the foundation pit is proposed and obtained by the positive and negative analysis of numerical simulation. The coefficient is used to correct the equivalent seepage length in the pit and directly affect the calculation result of water inflow. Finally, based on the calculation results of the analytical solution of water inflow, the relationship between the scale of the foundation pit and the water control effect is discussed. The research results show that the theoretical analysis results in this paper are in good agreement with the numerical results and the measured data in the field: when the size of the foundation pit is too large, it is not suitable to use the suspended water-proof curtain as the water control measure.

Performance assessment of borehole arrangements for the design of rectangular shallow foundation systems

This study proposes a framework to evaluate the performance of borehole arrangements for the design of rectangular shallow foundation systems under spatially variable soil conditions. Performance measures are introduced to quantify, for a fixed foundation layout and given soil sounding locations, the variability level of the foundation system bearing capacities in terms of their mean values and standard deviations. To estimate these measures, the recently proposed random failure mechanism method (RFMM) has been adopted and extended to consider any arrangement of rectangular foundations and boreholes. Hence, three-dimensional bearing capacity estimation under spatially variable soil can be efficiently performed. Several numerical examples are presented to illustrate the applicability of the proposed framework, including diverse foundation arrangements and different soil correlation structures. Overall, the proposed framework represents a potentially useful tool to support the design of geotechnical site investigation programs, especially in situations where very limited prior knowledge about the soil properties is available.

Undrained capacity of two rigidly connected rectangular foundations under general V-H-M loading

Analytical and numerical solutions of the undrained load-carrying capacity of shallow foundations are mainly available for single foundations. This paper investigates the undrained limit states of two-spaced rectangular foundations with rigid connections. Three-dimensional finite-element analyses are carried out to systematically examine the coupled interaction of foundation spacing and degree of soil strength heterogeneity on the load-carrying capacity of the foundation systems under general loading. Results are presented in the form of ultimate limit states under pure vertical (V), horizontal (H), and moment (M) loads, and the failure envelopes under combined V-H, V-M, H-M and V-H-M loading. Soil failure mechanisms obtained from the finite-element analyses are shown for the representative loading paths of the two-foundation systems. Based on the failure mechanisms, the methods are established for calculating the undrained load-carrying capacity of the two-foundation systems to assist the foundation design in practice.

The Effect of Foundation Shape on Subgrade Reaction Coefficient

This paper numerically examines the effect of foundation shape on the subgrade reaction coefficient. The distribution of the subgrade reaction coefficient on the foundation area and the values of this coefficient in different regions are studied. A method is also introduced to determine the subgrade reaction coefficient of unusually shaped foundations sometimes encountered in practice. It has been shown that it is possible to divide the foundation area into several regions, and the subgrade reaction coefficient of each part is a multiplier of the central point reaction coefficient. The reaction coefficient of a trapezoidal foundation is equal to the reaction coefficient of a rectangular foundation with a similar area, and the length of the rectangle is the same as the height of the trapezoid. Also, the settlements of two foundations are equal. An L-shaped foundation’s reaction coefficient is a product of multiplying the reaction coefficient of a rectangular foundation to a ratio of the rectangular area by an L-shaped area if the settlements of the two foundations are equal. Besides, the reaction coefficient of a ring-shaped foundation is a product of multiplying the reaction coefficient of a circular foundation with the same outside diameter by the ratio of the circular area to the ring area if the settlements of both foundations are the same.

Investigation of the impact of complex loading on the shallow foundations and the formation of a reactive layer in the soil base

The effect of a complex load on the shallow foundations, features of pressure transfer to the base soil, formation of a reactive layer in the soil base, features of determining the dimensions of the sole of square and rectangular foundations, as well as the character of the reinforcement of the foundations and the dependence of the reinforcement of the foundation sole on the stress formed under it were studied . Particular attention is paid to the action of various combinations of complex loads on the foundation, which can lead to separation of the foundation sole and, as a result, to its overturning.
 The studies were carried out on the shallow foundations, columnar, made of monolithic reinforced concrete, on which metal columns rest and are fastened with the help of anchor (foundation) bolts. Buildings with a metal frame on such foundations are most often intended for warehouses, production or trade centers, agricultural facilities, service stations and many others.
 The effect of additional loads on the foundations during the verification of the accepted sizes of the soles of the foundations is shown. Such additional loads can be: the weight of the foundations, the weight of the soil on the ledges of the foundations, the weight of the backfill under the floor, the weight of the floor structure, the useful load on the floor, the weight of the foundation beam, the weight of the hanging walls, etc.
 Under the action of a complex off-center load at different moments of time, as a result of the action of various combinations of loads, under the sole of the foundations there are alternating stresses: average, maximum and minimum, which can lead to separation of the foundation sole. These stresses depend on the accepted dimensions of the foundation sole, and also affect their reinforcement. But the question arises: do the same stresses under the sole of the foundations affect the dimensions of the foundations and the determination of their reinforcement? The paper shows that to check the dimensions of the sole of the foundations, it is necessary to take into account the "standard" stresses under the sole of the foundations, and to determine their reinforcement - completely different stresses. Many scientists and designers are unaware of this fact. Therefore, incorrect consideration of the stresses under the sole of the foundations precisely to determine their reinforcement can lead to incorrect results, which will affect the reliability and cost of the foundations of the above buildings.
 The work presents methods of constructing foundations of shallow laying under the action of an off-center load with the aim of absorbing it.

The Effect of Ecentric Load on The Carrying Capacity Rectangular Foundation on Clay


 
 
 
 TThe foundation is part of the structure that directly functions to transmit the load from the weight of the structure above it to the ground. In this study, a rectangular foundation is used which is placed on clay soil with 3 variations in dimensions and 7 variations in eccentricity loading. This data will be used in finding the ultimate bearing capacity value. The purpose of this study was to determine the effect of eccentricity loads on the bearing capacity of rectangular foundations on clay soil types. The method used is the Meyerhof method (1963). The results obtained are the magnitude of the value of the bearing capacity of the foundation in each variation of its dimensions which is influenced by the eccentricity of the load. The conclusion of this study is that the bearing capacity of the foundation can be viewed from the coordinates of the axis of the foundation which is affected by the eccentricity of the load. The greater the eccentricity of the load received by the y-axis, the greater the value of the ultimate bearing capacity of the foundation. Meanwhile, the greater the eccentricity load received by the x-axis, the smaller the ultimate bearing capacity value.
 
 
 

Effect of Foundation Shape on Settlement by Numerical Method

Five prototypes arranged in three different soil conditions is presented to find out the load-settlement relationship of soil and foundation. For creating three types of condition two types of managed soils are stiff clay and soft clay. The five prototypes used here represent the condition of shallow foundation. Prototypes area being same for cases has the shape of Triangular, Square, Rectangular, Pentagonal and Hexagonal. The load-settlement behavior has been found out plan-wise using Plaxis 3D software. Geotechnical engineering software which uses finite element method and Mohr-Coulomb failure criterion following mathematical differential equational problems. Plaxis 3D software uses the properties of soil cohesion, angle of internal friction, Elasticity modulus and unit weight, elasticity modulus of the foundation to settle a relation for the interaction between soil and foundation. Load-settlement behavior for the five prototypes as tried to be found out by Plaxis 3D has represented the immediate settlement of soil on which the prototypes have been rested. The graphs also help to understand the difference in the bearing capacity and settlement for the five prototypes, each of which acted as foundations. Pressure bulb is an effect of vertical pressure which differs from shape to shape of foundation. It directly affects the intensity of pressure and the intensity of pressure affects the settlement. The bearing capacity also affects the settlement. A triangular foundation has the best bearing capacity as its settlement is the lowest. But as a triangular shaped foundation is not practically used and not ideal it is not used for structural work. This study shows that square or rectangular foundation is best for a structure due to higher bearing capacity and lesser settlement compared to the same of pentagonal and hexagonal shaped foundation. But if comparison is done between square and rectangular shaped foundation, square is the best.

Torsion in symmetric buildings due to soil‐structure interaction: A discussion on code values of accidental eccentricity factor in seismic design

AbstractSoil‐structure interaction (SSI) is often neglected in seismic design because of its inherent complexity. Therefore, SSI‐related research is crucial for ensuring that more significant issues reach engineering practice. This study focused on torsional motion to investigate the accidental eccentricity caused by SSI effect by comparing the proportional relationship between the torsional motion of an SSI system and the translational motion of a fixed‐base oscillator. The SSI model was created using a three‐dimensional rectangular foundation embedded in a layered half‐space with an oscillator mounted on the top. We employed an indirect boundary element method (IBEM) combined with non‐singular Green's functions of distributed loads to calculate the system responses of the SSI. Parametric analysis‐based results in the frequency domain revealed that the accidental eccentricity factor owing to SSI was typically in the range of 0.03–0.15. Additionally, a case study of four buildings subjected to 42 earthquakes revealed that the accidental eccentricity factor exceeded 0.05 in several cases, and 0.2 in some cases. Furthermore, it depended on the excitation spectral shape and dynamic characteristics of the SSI system. Therefore, the coded accidental eccentricity factor value of 0.05 is insufficient for ensuring the safety of buildings from the torsional effect of SSI, and a value of 0.1 is more reasonable.

Dynamic Behavior of Machine Foundations on layered sandy soil under Seismic Loadings

In this paper, a dynamic investigation is done for strip, rectangular and square machine foundation at the top surface of two-layer dry sand with various states (i.e., loose on medium sand and dense on medium sand). The dynamic investigation is performed numerically using finite element programming, PLAXIS 3D. The soil is expected as a versatile totally plastic material that complies with the Mohr-Coulomb yield criterion. A harmonic load is applied at the base with an amplitude of 6 kPa at a frequency of (2 and 6) Hz, and seismic is applied with acceleration – time input of earthquake hit Halabjah city north of Iraq. A parametric study is done to evaluate the influence of changing L/B ratio (Length=12,6,3 m and width=3 m), type of sand, and frequency of the machine for soil with two layers (dense and medium sand) and (loose and medium sand). It was noticed that the displacement decreases when the foundation is strip, and has the highest values when the foundation is square. At the same time, the maximum vertical stress of the foundation (L/B = 4 and L/B = 1) appears to be (1262) kPa and (1255) kPa, respectively, due to increasing the foundation mass as a result of increasing its dimensions. Then again, the displacement increases by 20% for vertical displacement when decreasing the relative density. In addition, it has been noticed that there is a decrease in displacement when the frequency value changes from (2 to 6) Hz.

Effect of Soil Nonlinearity on Analysis of Raft Foundation

Abstract Soil supporting foundations behave in a nonlinear manner at loading close to its bearing capacity. This behavior affects soil pressure distribution and the corresponding stresses in the raft foundation, which differs significantly from considering the soil as elastic linear material. The present research uses the finite element method to study the effect of soil nonlinearity on the behavior of raft foundations subjected to concentrated loads. The analysis is based on the Winkler type of foundation. The analysis considered different values of the average soil pressure to its bearing capacity. The supporting soil was modeled as elastic perfectly plastic material. The effects of soil nonlinearity on the intensity and distribution of soil pressure, punching shear force, and bending moments in the raft are investigated. The effects of the foundation stiffness evaluation factor L·λ on the behavior of rectangular raft foundations were studied. This parameter combines the effects of the modulus of subgrade reaction, raft thickness, modulus of elasticity of concrete, and column spacing, as these parameters are interrelated. The results indicated that considering the subgrade soil as a linear elastic material underestimates punching shear and bending moments compared to modeling the soil as an elastoplastic material.

Impedance functions of rigid rectangular foundations bonded on layered transversely isotropic elastic/poroelastic half-space

This paper explores a complete set of impedance functions including vertical, torsional, horizontal, rocking, and coupling impedances for a surface rigid rectangular foundation bonded on a multilayered transversely isotropic half-space composed of alternatively elastic and poroelastic layers with the use of boundary element method. The slow convergence issue of Green's functions in numerical evaluation is remedied by a simple asymptotic approach presented in this paper. To evaluate the impedances accurately and efficiently, new finite elements namely exponentially-gradient elements are employed to consider the singular behavior of tractions that happens at the edges and corners of the foundation. The validity and accuracy of the solutions are verified by comparing the results with some simpler existing cases. The impedance functions are presented for different aspect ratios of the foundation to be applicable for a variety of structures. The effects of anisotropy, inhomogeneity, layer thickness, underground water level, and soil damping are assessed.

Analysis of barrette foundations subjected to mechanical and thermal loads

In recent years, there has been increasing interest in the use of rectangular barrette foundations for the structural support and energy supply of tall buildings when circular piles become inefficient or uneconomical. In such applications, so-called energy barrettes are equipped with pipe heat exchangers to harvest shallow geothermal energy and thus undergo both mechanical and thermal loads while they structurally support the building. The mechanics of energy barrettes is currently poorly characterized, and analyses and designs of such foundations typically require time-consuming numerical simulations. This paper has a twofold objective: (1) provide a fundamental understanding of the mechanics of energy barrettes subjected to mechanical and thermal loads and (2) describe an analytical approach that can expediently model the vertical deformation of such foundations. This study indicates that the mechanics of rectangular barrettes under both semi-floating and end-bearing conditions is similar to that of circular piles with an equivalent diameter. From this perspective, an analysis approach is proposed to expediently address the vertical deformation of rectangular barrettes by modeling them as equivalent circular piles.

Estimation of Critical Safety Thickness of the Base against Confined Water Inrush for a Rectangular Foundation Pit

Affected by confined aquifer, basal inrush accidents caused by excavation are common in foundation pits, and accurate estimation of the safety thickness of the base is a big concern of engineers. In this paper, a three‐dimensional failure mechanism of base inrush was constructed for a rectangular foundation pit. In this mechanism, the strength of the soil mass was assumed to be nonhomogeneous along the depth, and the soil‐mass failure satisfied the linear and nonlinear Mohr–Coulomb strength criteria. Then, based on the limit equilibrium theory, the prediction method for the safety thickness of the base against confined water inrush was deduced, and a comparison with existing research works was conducted. Furthermore, the influence laws of soil strength parameters, pit design parameters, and confined water pressure on the critical safety thickness were analyzed. The results show that the critical safety thickness of the base is positively correlated with nonlinear coefficient and confined water pressure but negatively correlated with cohesion, internal friction angle, nonhomogeneity coefficient, and unit weight. The soil strength is a key factor affecting the base safety thickness, which should be paid enough attention to in engineering design and construction. The research findings in this paper can provide a theoretical reference for the prevention and control of basal inrush accidents in confined water strata.