Soil-foundation System Research Articles

Seismic analysis of a soil-liquid tank system using the two-step method

Seismic analysis of soil-structure interaction (SSI) is a challenge due to the non-linearities of soil-foundation interaction (SFI). The reliability of the design and the analysis results will suffer if SSI is ignored. In this paper, a two-step method based on the superposition theorem is used to perform a seismic analysis of a soil-foundation-tank-liquid system (soil-liquid tank system). The SFI analysis was conducted in the first step using the CyclicTP program's finite-element method. Meanwhile, the liquid tank system was analyzed in the second step using the lumped-parameter method. Numerical simulations conducted in homogeneous strata of sand soil demonstrated that the responses of the liquid tank were 24–70% higher than the results of the fixed-base model. Compared to the sway-rocking model, these responses did not differ by 20%. This study also investigated cohesive soils of homogeneous clays and multiple strata. The paper recommends that future research investigate the experimentation, the geometric nonlinearity of the soil-foundation system, and the stress-strain analysis of the tank wall

Effect of Footing Shape on the Rocking Behavior of Shallow Foundations

Sources such as wind or severe seismic activity often exert extreme lateral loading onto the shallow foundations supporting high-rise structures such as bridge piers, buildings, shear walls, and wind turbine towers. Such loading conditions may cause the foundation to exhibit nonlinear responses such as uplift and bearing capacity mobilization of the supporting soil (i.e., rocking behavior). Previous numerical and experimental studies suggest that while such inelastic behaviors may engender residual deformations in the soil–foundation system, they offer potential benefits to the overall integrity of structures through dissipating energy and reducing inertia forces transmitted to the superstructure, thereby limiting seismic demand on structural elements. This study investigates the effect of footing shape on the rocking performance of shallow foundations in different subgrade densities and initial vertical factor of safety (FSv). To this end, a series of reduced-scale slow cyclic tests under 1 g condition were conducted using a single degree of freedom (SDOF) structure model. The performance of different footing shapes was studied in terms of moment capacity, recentering ratio, rocking stiffness, damping ratio, and settlement. For three foundations with different length-to-width ratios, the results indicate that increasing the safety factor and length-to-width ratio leads to thinner, S-shaped moment–rotation curves, mainly owing to the enhanced recentering capability and the P-δ effect. Moreover, across all foundation types, the repetition of a limited loading cycles with consistent rotation amplitude does not cause stiffness degradation or moment capacity reduction.

Building Vibration Measurement and Prediction during Train Operations

Urban societies face the challenge of working and living in environments filled with vibration caused by transportation systems. This paper conducted field measurements to obtain the characteristics of vibration transmission from soil to building foundations and within building floors. Subsequently, a prediction method was developed to anticipate building vibrations by considering the soil and structure interaction. The rigid foundation model was simplified into a foundation–soil system connected via spring damping, and the building model is based on axial wave transmission within the columns and attached floors. Building vibrations were in response to measured input vibration levels at the ground and were validated through field measurements. The influence of different building heights on soil and structure vibration propagation was studied. The results showed that the predicted vibrations match well with the measured vibrations. The proposed prediction model can reasonably predict the building vibration caused by train operations. The closed-form method is an efficient tool for predicting floor vibrations prior to construction.

Relevance of the Foundation Input Motion in the assessment of the seismic response of pile-supported bridge piers

The seismic response of pile-supported bridge piers is commonly studied avoiding the assessment of the Foundation Input Motion (FIM) (i.e., the motion at the foundation level, which is different compared to that in the free-field, due to the filtering effect exerted by the piles) and assuming fixed-base conditions. A better approach is represented by the substructure method which consists of 3 steps: 1) the assessment of the FIM; 2) the computation of the impedance functions of the soil-foundation system, 3) the analysis of the superstructure response resting on a compliant-base at which is applied the FIM. In many cases this method is not used in a rigorous way (as the assessment of the FIM is not commonly considered an easy task by the structural engineers) and the seismic motion at the base of the model is assumed to be the same as in the free-field. Thus, the effect of Soil-Structure Interaction (SSI) is neglected. Nevertheless, this effect might be beneficial, as piles can filter out some high-frequency components of the free-field motion, especially in the case of large-diameter piles and soft soil conditions (i.e., in those cases in which piles are generally necessary). On the other hand, special attention should be given to those foundations composed by very small pile groups, since the FIM will consist of both a horizontal and a rotational component (which would play a detrimental role). Moreover, it should be remembered that considering SSI would lengthening the fundamental period of the system compared to that under fixed-base hypothesis. This aspect would lead to both positive and negative effects based on the seismic motion properties. This contribution will attempt to show the relevance of a proper assessment of the FIM while studying the seismic response of pile-supported bridge piers. To this end a specific software has been developed to properly compute the FIM considering the filtering effect exerted by the piles.

Evaluation of the Seismic Response of Reinforced Concrete (RC) Buildings Considering Soil-Structure-Interaction Effects

The dynamic response of the structure is influenced by soil-structure interaction (SSI), and is distinct from the fixed-base one. When stiff structures are supported by soft to very soft soil, SSI has a substantial effect. This work intends to investigate the effects of SSI using various estimation techniques in order to quantify the foundation damping effect on the response of reinforced concrete (RC) buildings. Generalized and completely viscous damping formulas were utilized to estimate the damping of the soil-foundation system. The investigated structures are 4, 8, and 12-story RC buildings built on very soft soil in a high seismic zone. In comparison to the fixed base condition, the study demonstrated an increase in the natural period, damping of the system, and a decrease in base shear. The study's response parameters are compared to those obtained in accordance with ASCE7-16 code provisions.

Numerical modelling of traffic-induced dynamic loading on a two-story residential building

BackgroundThis paper presents a numerical modelling procedure of dynamic loading due to traffic on a two-story residential building. In developing countries cities and towns, poor quality narrow road sections with high traffic density are common. In such cases, ground vibration due to traffic could be higher and lightweight buildings located closer are exposed to traffic-induced dynamic loading. Design codes require a proper assessment of such vibrations. However, a clear and definite procedure of assessment is not usually provided. This research presents an assessment procedure of dynamic loading due to traffic on a soil foundation system of light weight buildings based on numerical modeling. Traffic induced ground vibration acceleration amplitudes, frequencies and durations were measured, and the dynamic loads were calculated from measured vibration accelerations and vibrating mass of the vehicle. A two-story residential building with flexible square shallow footings was modelled together with the foundation soil using PLAXIS-2D. The dynamic load was modelled as harmonic loading considering the highest amplitude of vibration measured.ResultsOn the calculation stage, static loading analysis, dynamic loading analysis and free vibration dynamic analysis were carried out. A maximum increase in extreme total displacement of the soil to 22.03 mm was observed after the dynamic loading from 18.96 mm extreme total displacement due to static loading. Extreme effective mean stress in the soil increased to 112.81 kPa from 110.5 kPa, due to the dynamic loading. In addition, a differential settlement of 3.14 mm between two adjacent footings was observed after the traffic induced ground vibration. Furthermore, the Mohr–Coulomb plastic points were observed to be concentrated to the side of the soil-foundation system which the dynamic load was acting on.ConclusionThe regular exposure to traffic-induced vibrations may cause frequent change in stress and deformation response of the foundation-soil system. In areas where lightweight buildings are exposed to regular traffic induced vibrations, proper assessment of the effect should be carried out and measures should be taken to mitigate the problem. Improving road surfaces and limiting vehicle speed are possible remedial measures to reduce ground vibrations due to traffic.

The effect of foundation–soil–foundation interaction on the response of continuous, multi-span railway bridges

This paper focuses on the effect of dynamic soil–structure interaction (SSI), including foundation–soil–foundation interaction (FSFI), on the dynamic response of multi-span railway bridges, which constitute an important part of high-speed rail networks around the world. We consider an infinitely long box girder bridge on piled foundations and use periodic structure theory to restrict the computational domain to a reference cell. The superstructure is modeled with finite elements, while a periodic finite element-boundary element (FE-BE) model is used to compute the dynamic stiffness of the piled foundation, taking into account FSFI. It is demonstrated that (1) the natural frequencies of the in-phase torsional and bending modes are significantly lowered due to the flexibility of the foundation–soil system; (2) the effect of FSFI on the bridge response is limited for typical span lengths and soil stiffness; and (3) the peak bridge deck acceleration is lower if SSI is taken into account, as is the resonant train speed.

Seismic analysis of a soil-liquid tank system using MATLAB Simulink

In this paper, a model is proposed for analyzing the long-term responses of a liquid tank system to earthquake loads while taking soil interaction into account. Three degrees of freedom (DOFs) in the sway-rocking form and the monkey tail DOF are used to model the soil-foundation system, while the fluid in the tank is modeled as a 2-DOF lumped parameter using the substructure method. By using the MATLAB Simulink tool to numerically integrate the system of differential equations of motion, the response of the DOFs, shear force, and moment at the tank bottom can be tracked over time. The El Centro 1940 earthquake's acceleration excited a vertical cylindrical tank with a radius of 10 m and a water mass of 8 m; the results of the analysis show that the horizontal displacement of the convective mass increased by 16.36%, and the shear force and moment significantly increased in comparison to the case of the tank rigidly linked to the ground.

Virtual sensing of subsoil strain response in monopile-based offshore wind turbines via Gaussian process latent force models

Virtual sensing techniques have gained traction in applications to the structural health monitoring of monopile-based offshore wind turbines, as the strain response below the mudline, which is a primary indicator of fatigue damage accumulation, is impractical to measure directly with physical instrumentation. The Gaussian process latent force model (GPLFM) is a generalized Bayesian virtual sensing technique which combines a physics-driven model of the structure with a data-driven model of latent variables of the system to extrapolate unmeasured strain states. In the GPLFM, unknown sources of excitation are modeled as a Gaussian process (GP) and endowed with a structured covariance relationship with response states, using properties of the GP covariance kernel as well as correlation information supplied by the mechanical model. It is shown that posterior inference of the latent inputs and states is performed by Gaussian process regression of measured accelerations, computed efficiently using Kalman filtering and Rauch–Tung–Striebel smoothing in an augmented state-space model. While the GPLFM has been previously demonstrated in numerical studies to improve upon other virtual sensing techniques in terms of accuracy, robustness, and numerical stability, this work provides one of the first cases of in-situ validation of the GPLFM. The predicted strain response by the GPLFM is compared to subsoil strain data collected from an operating offshore wind turbine in the Westermeerwind Park in the Netherlands. A number of test cases are conducted, where the performance of the GPLFM is evaluated for its sensitivity to varying operational and environmental conditions, to the instrumentation scheme of the turbine, and to the fidelity of the mechanical model. In particular, this paper discusses the capacity of the GPLFM to achieve relatively robust strain predictions under high model uncertainty in the soil-foundation system of the offshore wind turbine by attributing sources of model error to the estimated stochastic input.

Closed-form solutions to investigate the nonlinear response of foundations supporting operating machines under blast loads

Machine foundations are subjected to significant dynamic impacts. These impacts could spread to the surrounding regions, affecting workers, sensitive equipment in the same institution, or nearby areas. This study analyzes the response of machine-supporting foundations to harmonic and explosive loads under operational conditions and provides closed-form solutions for predicting responses in terms of displacement, velocity, and acceleration time-histories to two common types of blast loads: a more accurate typical profile and simplified triangular profile. The soil-machine foundation system is regarded as a single-degree-of-freedom (SDOF) system that exhibits elastic–perfectly flexible resistance behavior. For the analysis of the SDOF system, two cases are considered: one assumes that the supporting soil keeps elastic during the explosion, and the peak displacement is less than the elastic one, while the other assumes that the blast occurs in an elastic state, and the peak displacement occurs in a plastic state. By using the closed-form analytical solutions, a detailed parametric analysis is carried out to evaluate the impacts of significant soil-foundation system characteristics such as mass, stiffness, and damping ratio on the response-time history of machine foundations. The findings are compared to those reported in the literature, and relevant conclusions are derived. Obtained results demonstrated that, despite its simplicity and usage of only positive phase to simulate blast loads, the simplified model’s response behavior differs significantly from the typical one. Furthermore, the derived solutions are utilized to design the foundations supporting vibrating machines for both harmonic and blast loads in a variety of conceivable scenarios depending on the blast magnitude.

Lumped parameter model for vertical vibrations of surface circular foundations on nonhomogeneous soil

PurposeA newly developed frequency-independent lumped parameter model (LPM) is the purpose of the present paper. This new model’s direct outcome ensures high efficiency and a straightforward calculation of foundations’ vertical vibrations. A rigid circular foundation shape resting on a nonhomogeneous half-space subjected to a vertical time-harmonic excitation is considered.Design/methodology/approachA simple model representing the soil–foundation system consists of a single degree of freedom (SDOF) system incorporating a lumped mass linked to a frequency-independent spring and dashpot. Besides that, an additional fictitious mass is incorporated into the SDOF system. Several numerical methods and mathematical techniques are used to identify each SDOF’s parameter: (1) the vertical component of the static and dynamic foundation impedance function is calculated. This dynamic interaction problem is solved by using a formulation combining the boundary element method and the thin layer method, which allows the simulation of any complex nonhomogeneous half-space configuration. After, one determines the static stiffness’s expression of the circular foundation resting on a nonhomogeneous half-space. (2) The system’s parameters (dashpot coefficient and fictitious mass) are calculated at the resonance frequency; and (3) using a curve fitting technique, the general formulas of the frequency-independent dashpot coefficients and additional fictitious mass are established.FindingsComparisons with other results from a rigorous formulation were made to verify the developed model’s accuracy; these are exceptional cases of the more general problems that can be addressed (problems like shallow or embedded foundations of arbitrary shape, other vibration modes, etc.).Originality/valueIn this new LPM, the impedance functions will no longer be needed. The engineer only needs a limited number of input parameters (geometrical and mechanical characteristics of the foundation and the soil). Moreover, a simple calculator is required (i.e. we do not need any sophisticated software).

Ensuring safe operation of monolithic structures in undermined areas

In order to ensure safe operation of buildings in undermined areas, it is necessary to take into account the influence of loads extrinsic to typical structures. The solution of the generalized boundary value problem on the evaluation of the stress-strain state (SSS) of the building–foundation–soil system with due regard for the complete geometry and physically nonlinear behavior of all the elements is inexpedient since it is complicated by the large dimensionality of the problem. This paper discusses an approach allowing the state of monolithic reinforced concrete building structures located in an undermined area to be estimated by solving boundary value problems on different scales, from modeling the whole system in an elastic formulation to modeling joints between load-bearing members (columns and floors) in a nonlinear formulation for concrete and reinforcement. In these problems, strain energy is taken as the parameter characterizing the deformation process at critical deformation stages and connecting the boundary value problems. The obtained loading diagrams for a unit and the evaluation of the SSS of the whole structure enable one to find the values of maximum permissible horizontal soil deformations in the vicinity of the foundation, at which the bearing members reach the SSS preceding the loss of bearing capacity.

Effective stress analysis of residual wave-induced liquefaction around caisson-foundations: Bearing capacity degradation and an AI-based framework for predicting settlement

Excessive wave-induced pore pressure buildup around offshore foundations results in liquefaction, settlement and bearing capacity degradation, which may threaten the safety of Offshore Wind Turbines (OWTs). Despite the extensive research efforts on wave-induced seabed residual response in the recent years, there is still a lack of knowledge on mechanisms of wave-induced liquefaction and settlement around caisson foundations. Employing a code-based framework implemented in OpenSees, the cyclic response of wave-seabed-foundation (WSF) system is evaluated. Biot’s consolidation theory, linear wave theory and CycLiqCPSP constitutive soil model are integrated to evaluate the response of soil-foundation system accounting for the hydrodynamic pressure of wave imposed on the seabed surface considering the fully-coupled wave-seabed-foundation interaction (WSFI). Soil model parameters are calibrated against cyclic simple shear (CSS) tests and the numerical model is validated by a well-documented centrifuge experimental model. Various seabed characteristics, and a range of the geometrical properties of foundation with different OWT weights are put into practice for evaluating the geotechnical aspects of wave-induced liquefaction. Stress paths are provided to demonstrate quite different level of reduction in effective stresses and likelihood of liquefaction occurrence upon cyclic shear stresses application for different locations in the vicinity of the foundation area. The present study will also improve understanding of the interplay among the state variables on the wave-induced foundation settlement and bearing capacity degradation allow to feed the output data into development of simplified procedure for assessing the bearing capacity. Finally, results from over 250 analyses with different model configurations are used to provide an estimate of wave-induced caisson settlement with reasonable accuracy on the basis of artificial intelligence (AI) method known as Group Method of Data Handling (GMDH).

A numerical study of influential parameters on rocking response of shallow foundations of single degree of freedom (SDOF) structures

In recent years, designing structures with rocking foundations has been introduced as an effective method to decrease seismic energy transmission to the superstructure and reduce the structure’s ductility demand. In this approach nonlinear behavior of the soil-foundation system dissipates the earthquake energy. Despite the promising results of this technique, it is not considered as a practical method yet. The main reason could be the uncertainties about the rocking foundation deformations during an actual earthquake. The present study uses the finite element method to evaluate the response of a single degree of freedom (SDOF) type structure under lateral monotonic and seismic loading. The influence of the static safety factors against soil bearing capacity failure, ground motion characteristics, and the foundation embedment depth on system behavior is investigated. Results demonstrate that due to these parameters, the response of a system with rocking foundation may change drastically during seismic events.

Stochastic Dynamic Response and Long-Term Settlement Performance of Superstructure–Underground Tunnel–Soil Systems Subjected to Subway-Traffic Excitation

The vibration impact force from the long-term operation of a subway affects the comfort of the residents living above the superstructure and the long-term settlement deformation of the tunnel foundation. A method for evaluating the dynamic responses of superstructure–tunnel systems is important, especially because of the randomness of vibration impact force. The coupling effect of the randomness of train-vibration excitation and the nonlinearity of the geotechnical properties that are subjected to dynamic action leads to challenges in the evaluation of the performance of superstructure–underground tunnel–soil systems under train vibration. In this study, a stochastic dynamic model of subway vibration-load excitation was established; then, the time histories of samples with rich probability characteristics in the same set system were generated. According to the nonlinear dynamic finite element analysis, several nonlinear dynamic responses of the deterministic superstructure–tunnel soil-foundation system were obtained. Finally, the probabilistic performance evolution of the superstructure–tunnel soil-foundation system was obtained by integrating the first-passage and probability density evolution theories, and the long-term deformation performance of the tunnel foundation was evaluated using time-varying reliability. This study presents a novel probabilistic method and a more objective performance index for the dynamic performance assessment of superstructure–underground tunnel–soil systems that are subjected to subway-traffic excitation.

Vertical vibration of rigid strip footings on poroelastic soil layer of finite thickness

This paper presents a numerical solution that describes the response to forced vertical vibrations of rigid strip footings founded on the surface of a poroelastic soil layer of finite thickness. To mathematically describe this mixed boundary value problem, we relax the boundary conditions and cast it as a pair of dual integral equations, which are transformed to a system of linear equations by means of Jacobi orthogonal polynomials. The system is solved numerically to provide the frequency-dependent footing compliance, and the associated nearby soil displacement. Results obtained with the model at hand underline the important contribution of standing waves to the response of the soil-foundation system, and draw the limits of existing solutions that consider the foundation soil as infinite half-space, where standing waves cannot form.

A multiaxial inertial macroelement for deep foundations

A hyperplastic macroelement is proposed as an efficient means for simulating nonlinear and multi-directional soil-piles interaction in the nonlinear analysis of structures. The macroelement relates the generalised forces exchanged between the superstructure and the foundation to the corresponding displacements and rotations of the foundation raft. The inertial effects developing under dynamic loading can be reproduced by coupling the macroelement with the participating masses of the soil-foundation system, obtainable with a modal identification of the pile group. Failure conditions of the foundation are described by a hyper-ovoidal ultimate limit state surface in the force space, which is calibrated through standardised procedures. The plastic behaviour, controlled by a series of yield surfaces with kinematic hardening, produces the desired directional coupling and allows to model the cyclic response and the irreversible deformation of the foundation. The macroelement is implemented in the analysis framework OpenSees for a prompt use in earthquake engineering applications. Its predictions under monotonic loads are validated against experimental data and advanced, fully coupled numerical modelling, while its dynamic response is tested on a reference case study.

A Methodology for Extracting the Physical Parameters of Soil-Foundation-Pier Systems from Dynamic Tests

The paper presents a methodology for the identification of the physical parameters of a model describing the transverse dynamics of soil-foundation-pier systems founded on piles, starting from results of dynamic experimental tests. In detail, the procedure exploits the identified state-space models of the systems obtained from results of dynamic tests through consolidated identification techniques available in the literature. The procedure permits to compute the physical parameters of the real system (e.g. masses, pier stiffness matrix, and soil-foundation impedance) by directly comparing the components of the analytical and identified stiffness, mass and damping matrices; the latter extracted from the identified state-space models. The proposed approach allows the direct definition of the numerical model that best fits the experimental data, and permits the identification of the soil-foundation compliance. Firstly, the dynamics of the analytical model, which includes the frequency-dependent behaviour of the soil-foundation system through the introduction of a lumped parameter model, is formulated adopting the continuous-time first-order state-space form. Then, an identification strategy of the physical parameters of a soil-foundation-pier system is proposed, starting from the discrete-time state-space model identified from dynamic tests. The procedure allows the identification of the soil-foundation system compliance through experimental tests.

A probabilistic study on impedances and kinematic response factors of square pile groups in homogeneous soils

The complexity of the Soil-Structure Interaction (SSI) problem is mainly due to difficulties related to the modelling of the soil-foundation behaviour, which is not only frequency-dependent, but is also largely influenced by uncertainties related to soil properties and stratigraphic conditions. According to a sub-structuring scheme for the analysis of SSI problems, a deterministic approach is usually adopted for the analysis of the soil-foundation system assuming properties and geotechnical models based on the expert judgment, despite the fact that uncertainties related to the intrinsic variability of soil parameters are widely recognised and confirmed by experimental campaigns and laboratory tests.This paper presents a probabilistic study on the dynamic behaviour of square pile group foundations in homogeneous soils, focusing on the effects of the uncertainties related to (i) the frequency-dependent impedance functions and (ii) the kinematic response factors. Above quantities are required to define compliant restraints for the modelling of the soil-foundation system in performing inertial soil-structure interaction analysis, and for the definition of the foundation input motion starting from the free-field motion. Square pile groups are considered, and uncertainties are described through probabilistic distributions of parameters governing the soil-foundation dynamic response. The probabilistic analyses are performed through a numerical model developed by the Authors and some results are presented to show and discuss the variability of the results. In addition, a sensitivity analysis is performed to assess the influence of each variable uncertainty on the system response. Overall, response quantities are found to be very sensitive to shear wave velocity, although soil density and pile elastic modulus may often play a significant role.

Linear equivalent seismic response of a surface foundation excited by an SH harmonic wave

The main objective of this study is to analyse the effect of the non-linear behaviour of the soil on the seismic response of a foundation by taking into account the soil-structure interaction. The foundation is square-shaped, and rigid, resting on the surface of a homogeneous semi-infinite soil, and solicited only by the incident harmonic wave SH. However, for higher deformations (during strong earthquakes), the behaviour of the soil will be characterised by a nonlinear behaviour law. The phenomenon of soil nonlinearity due to the seismic excitation imposed on the soil is reflected in the curve of reduction of the normalised shear modulus G/G max and the curve of increase of the normalised hysteretic damping coefficient ξ/ξ max as a function of the unit shear deformation γ/γr. This behaviour is obtained by the equivalent linear method with the Masing model implemented in the one-dimensional (1D) computational code Caldynasoil. In this study, first, determine the nonlinear behaviour of a soil profile stressed by different levels of seismic accelerations applied at the bedrock level. The Caldynasoil computational code was used to find the variations of the nonlinear dynamic properties of the soil profile for different levels of seismic loading. Secondly, integrating the nonlinear dimensionless properties of the soil in a three-dimensional computational code Fonvib_Wave based on the boundary elements method combined with the theory of thin layers (BEM-TLM) in the frequency domain allows calculating the nonlinear displacements of a surface foundation. The obtained results represent the influence of the nonlinear behaviour of the soil on the vibration modes of a rigid foundation subjected to a shear wave SH as a function of the dimensionless frequency a0, and the angles of incidence θV and θH. The conclusions that may predict from this research have shown the importance of the influence of the nonlinear behaviour of the soil and the angles of incidence of the SH wave on the response of the soil-foundation system compared to the linear case.