Beam On Nonlinear Winkler Foundation Research Articles

Development of the fragility curve of structural collapse considering the joint effects of structural and soil uncertainties

The present study focuses on the simultaneous effects of the structural and soil uncertainties on the fragility curve of a four-story reinforced concrete moment frame on a soft bed. Structural uncertainties were considered in the parameters of the modified Ibarra-Medina-Krawinkler moment-rotation curve, and soil uncertainties were taken into account in modeling using the beam on nonlinear Winkler foundation (BNWF) method. In the uncertainty analysis, the correlation between the parameters of the moment-rotation curve in one component and between two structural components, as well as the correlation between soil properties, were considered. In this study, 189 random samples considering the mentioned uncertainties, along with the probability distribution and correlation between them, were all together prepared using the Latin hypercube sampling (LHS). The samples were subjected to incremental dynamic analyses (IDA) using 20 far-field records, and fragility curves of the collapse were extracted along with the collapse response functions using the response surface method for each sample. In the next step, 104 random samples were simulated, and their fragility curves were predicted using collapse response functions. Eventually, the contribution of the uncertainties to structural collapse responses was calculated using the screening method. The outcomes indicated a good agreement between the predicted fragility curves and those obtained from the IDAs. Moreover, beam and soil uncertainties had the most significant and negligible effects, respectively, on the collapse responses of the structure.

Modelling Study of Pile Group Foundation by Including Lateral Load in Clay Soil

 Indonesia’s geographical condition causes earthquakes to occur more frequently. This study aims to investigate pile group response under earthquake loading by performing pushover analysis. Since clay soil is dominant and widespread in Indonesia, the study focused on pile group embedded in single layer of clay. The undrained shear strength (Su) parameters of the clay are varied from 20 kPa, to 100 kPa with 20 kPa intervals. The pile and soil were modelled by Beam-on-Nonlinear-Winkler-Foundation (BNWF), and the soil was presented as a series of Winkler springs using the nonlinear p-y method. The analysis was conducted with a finite element method (FEM) software, OpenSees. The pile was modelled as a fiber section, where the transversal and longitudinal reinforcement can be considered. The research found that the soil’s Su affects the ductility and formation of plastic hinge. Greater Su resulted in higher ductility and occurrence of plastic hinge. Higher Su was also found to increase the internal force experienced in the pile, as well as lead to higher group efficiency factor. There was no shear failure detected in the results, but bending failure happened at the lead pile in Su 100 kPa. The overturning moment phenomenon occurred on the pile group in Su 20 kPa and 100 kPa. For Su = 20 kPa, this phenomenon is caused by the middle pile and rear pile, which did not have optimal performance. Bending failure at the lead pile led to the phenomenonin Su 100 kPa.

A New p–y Curve for Laterally Loaded Large-Diameter Monopiles in Soft Clays

In harsh offshore environmental conditions, the monopile foundations supporting offshore wind turbines must be designed for lateral loads such as winds, waves, and currents. The Beam on Nonlinear Winkler Foundation (BNWF) method has been widely used because of its clear concept and lower calculation cost. The selection of a reasonable p–y curve is critical to the calculation accuracy of this method. This paper clarified the defects of widely used API p–y curves for soft clays and then proposed a new p–y curve with better versatility and applicability. The suitability of the proposed p–y curve was validated by comparing it with the calculation results from the three-dimensional finite element method (3D FEM). Compared with the API p–y curve, the proposed p–y curve can better predict the lateral behavior of large-diameter piles in soft clays, such as the load–displacement curve of the pile head, lateral deflection profile, and bending moment profile. The research findings can provide guidance for the design of monopile foundations supporting offshore wind turbines in soft clays.

An extended BNWF model for root piles incorporating soil–root interactions under lateral loading

Root piles constitute a new type of pile in which a series of prefabricated reinforced concrete roots are inserted into the surrounding soil to improve the bearing capacity of the pile foundation. To investigate the nonlinear behaviour of root piles under lateral loading, an extended beam on nonlinear Winkler foundation (BNWF) model incorporating the soil–root interactions is proposed in this paper. The proposed model is aimed at simultaneously describing the additional bearing capacity provided by roots and the nonlinear soil–root interactions for laterally loaded root piles. Lateral loading tests are conducted on two full–scale root piles to verify the applicability and reliability of the proposed model. It is demonstrated that the proposed model can describe the lateral behaviour of root piles with a reasonable calculation accuracy. Further parametric analyses are conducted to investigate the lateral bearing behaviour of the root piles. It is found that the root pile increases the lateral bearing capacity of the piles owing to the roots. Increasing the number or length of roots and locating them in shallow soil layers can improve the lateral bearing capacity of the root piles. The obtained results are useful for the design and application of root piles.

New p-y model for seismic loading prediction of pile foundations in non-liquefiable and liquefiable soils considering modulus reduction and damping curves

In this study, a new p-y model is proposed for the seismic loading prediction of pile foundations using the Beam on Nonlinear Winkler Foundation (BNWF) method. It matches the desired modulus reduction curve by identifying three parameters in a hyperbolic function and a linear function using a genetic algorithm (GA), and the desired damping curve by applying the Ishihara-Yoshida rule that controls the unloading–reloading curves iteratively through the three parameters. The rate effect is integrated into the proposed PySimple5 model for clay by exerting influence on the ultimate capacity and maximum material damping through a power function, while the pore pressure effect is reflected in the proposed Pyliq5 model for sand by relating the ultimate capacity to the mean effective stress. For a single pile in non-liquefiable soil, the predicted superstructure acceleration and pile bending moment by PySimple5 agree well with those from centrifuge tests for different soil shear strain levels, while the equivalent linear and PySimple1 models underestimate them for soil shear strain levels higher than 1%. For a pile in liquefiable soil, PyLiq5 shows a reasonable agreement with the centrifuge tests in terms of the superstructure acceleration and pile bending moment by considering the pore pressure effect.

Seismic Performance Analyses of Pile-supported Transmission Tower-line Systems Subjected to Depth-varying Spatial Ground Motions

ABSTRACT Past major earthquakes have witnessed extensive pile-supported transmission tower-line systems (PSTLs) failing, which highlights the great susceptibility of PSTLs to damage from earthquakes. However, a comprehensive literature review in seismic analysis of PSTLs reveals that two critical aspects, i.e. soil–structure interaction (SSI) and depth-varying spatial ground motions (DVSGMs), have been completely overlooked in numerous previous studies. To be specific, pile-supported transmission towers are generally assumed to be fixed to the ground surface and are excited using uniform ground motion inputs. Such analytical schemes may result in severe misestimates of seismic response predictions of PSTLs. Within this context, the main objective of the present study is to accurately assess the seismic performance of PSTLs by considering SSI and using DVSGMs as inputs. For this purpose, an existing prototype PSTL is firstly selected and the corresponding three-dimensional finite element model is created in ABAQUS software, in which SSI is simulated by the Beam on Nonlinear Winkler Foundation (BNWF) model. Then, the three-dimensional DVSGMs are stochastically synthesized based on the computed ground motion transfer functions (GMTFs) of local sites. Next, seismic performance of the PSTL with SSI, including dynamic responses, ultimate bearing capacity, and failure mechanism, is assessed using the generated DVSGMs as seismic inputs. Finally, a parametric study is conducted to comprehensively examine and discuss the influences of SSI, seismic excitation types, coherence loss, and local site conditions on seismic performance of the PSTL. Numerical results show that seismic performance of PSTLs can be affected significantly by the above mentioned influencing factors. This research is expected to offer a meaningful reference to seismic performance assessments of PSTLs.

Seismic assessment of irregular RC frames with tall ground story incorporating nonlinear soil–structure interaction

This paper is dedicated to evaluate the nonlinear Soil–Structure Interaction (SSI) impact on the earthquake-based response of vertically irregular reinforced concrete (RC) moment resisting frames. The main contribution of this paper is to evaluate the seismic performance of RC structures with 5 and 10 stories considering a number of key parameters including irregularity ratio, soil type and the vertical safety factor (FSv) of the foundation. In this regard, the beam on nonlinear Winkler foundation (BNWF) scheme is used for the modeling of shallow foundations resting on a semi-infinite sandy medium. Vertical irregularity is considered by using a tall ground story in the RC frames. The models are subjected to 15 earthquake ground motions for conducting nonlinear dynamic time-history analyses to capture the seismic demands of soil–structure systems. The results demonstrate that considering SSI influence reduces the seismic demands in the lower stories, which is more evident in the case of soft soils (site class E). Moreover, a rational relationship between the maximum inter-story drifts and the response of the foundations is observed. It is also concluded that for both regular and irregular structures, lower values of the FSv lead to a considerable decrease in the structural demands (story drifts) and an impressive growth in transient and residual foundation settlements.

Seismic analysis of extended piles in sand considering effect of scouring and effect of water as added mass

Scouring is one of the major causes of the failure of bridges and offshore wind turbines. Piles under extreme scouring and earthquake loads are vulnerable to failure and need to be investigated thoroughly. In this study, the seismic responses of an extended concrete pile with no scour and four scouring depths conditions are investigated under an input motion based on a Kobe earthquake record. The effect of water during an earthquake has a significant impact on the structure as hydrodynamic pressure; however, it is generally ignored in the seismic analysis of piles. The present study uses the concept of added mass to consider the effects of water. The combined soilstructure-interaction and shear beam model is used to simulate pile and soil using the beam-on-nonlinear-Winkler foundation (BNWF) method. Soil is divided into multiple layers with increasing shear modulus and the mass of each soil layer is lumped into two nodes of the layer. Modal analysis and nonlinear time history analysis are performed on different models. Results of the modal analysis show the decrease in fundamental frequencies of the pile with increasing scouring depths. The time history analysis results are reported in the form of Arias and Housner intensities, envelopes of acceleration, velocity, displacement of pile top, and envelopes of shear force and bending moment of the pile. Results show significant changes with scouring depth and the effect of water.

Probabilistic estimation of inelastic displacement demands in soil–structure interaction systems on cohesive soils

AbstractInelastic displacement ratios (IDRs) of nonlinear soil–structure interaction (SSI) systems located at sites with cohesive soils are investigated in this study. To capture the effects of inelastic cyclic behavior of the supporting soil, the Beam on Nonlinear Winkler Foundation (BNWF) model is used. The superstructure is modeled using an inelastic single‐degree‐of‐freedom (SDOF) system model. Nonlinear SSI systems representing various combinations of unconfined compressive strengths and shear wave velocities are considered in the analysis. A set of strong ground motions recorded at sites with soft to stiff soils is used for considering the record‐to‐record variability of IDRs. It is observed that IDRs for nonlinear SSI systems are sensitive to the strength and the stiffness properties of both the soil and the structure. For the case of SSI systems on the top of cohesive soils, the compressive strength of the soil has a significant impact on the IDRs, which cannot be captured by considering only the shear wave velocity of the soil. Based on the results of nonlinear time‐history analysis, a new equation is proposed for estimating the mean and the dispersion of IDRs of SSI systems depending on the characteristic properties of the supporting soil, dimensions of the foundation, and properties of the superstructure. A probabilistic framework is presented for the performance‐based seismic design of SSI systems located at sites with cohesive soils.

Sensitivity of fatigue assessment for offshore jacket platform to different pile–soil–structure interaction models

ABSTRACT One of the main factors that affect the response of fixed offshore jacket platforms under wave loading is Pile–Soil–Structure Interaction (PSSI); thereby, it must be expected that different PSSI models may impact the fatigue damage assessments in harsh environments. In this study, the sensitivity analyses of fatigue damage results of an offshore jacket platform to different PSSI models have been performed by modelling piles up to the actual penetration depth with computationally demanding Beam on Nonlinear Winkler Foundation (BNWF) as the Reference Model (RM). Also, two different models were applied by analysing RM under Center-of-Damage (CD) wave (M2 and M4) as well as conducting the linear analysis (M1 and M3) to develop stiffness matrix and independent springs models. It was concluded that the independent springs model obtained by linear analysis provides acceptable fatigue damage compared to other alternative linear models in the case of large CD wave and shallow weak soil layers.

Parametric Study on Seismic Behaviors of a Buried Pipeline Subjected to Underground Spatially Correlated Earthquake Motions

ABSTRACT For underground structures with large spans, such as buried pipelines, the seismic motions may vary not only at distinct horizontal locations due to the wave passage, incoherence and local site effects; but also at different vertical soil depths owing to the site amplification effect. This paper numerically investigates the influences of underground spatially correlated earthquake motions (USCEMs) on the seismic behaviors of large-span buried pipelines. To accomplish this task, the widely used buried gas steel pipeline of API X65 is chosen as a case study and the corresponding three-dimensional finite element (3D FE) model is created using the ABAQUS software, which accounts for the soil-pipe interaction (SPI) by the beam on nonlinear Winkler foundation (BNWF) model. The three-dimensional USCEMs for the nonlinear time-history analyses of the buried pipeline are stochastically synthesized based on the computed underground transfer functions of local sites. A total of 11 analysis cases associated with different spatial variability parameters of USCEMs (i.e. seismic excitation type, incoherence loss, local site condition and seismic motions at different soil depths) are considered. Based on increment dynamic analysis (IDA), a parametric study is carried out to comprehensively examine and discuss the influences of different spatial variability parameters on the seismic responses and critical operable capacity of the exemplar buried pipeline by comparing the analysis results of different cases. Numerical results demonstrate that these influencing factors can impact the seismic behaviors of the exemplar buried pipeline in different degrees and cannot be neglected in the seismic analysis. This research can serve as a vital reference for the seismic performance assessment and design of large-span buried pipelines.

Estimation of the critical buckling load of pile foundations during soil liquefaction

Buckling instability of slender piles may occur based on the effect of excessive axial loads acting on a pile with diminishing effective stress and shear strength owing to surrounding soil liquefaction. However, several guidelines for pile design often provide insufficient consideration of buckling failure, and it is significant to study the buckling failure of piles in liquefiable sites for the design and inspection of piles. In this paper, an efficient method of determining the critical buckling load of piles considering the material and geometric nonlinearities of piles based on the excess pore pressure distribution is proposed based on the beam-on nonlinear Winkler foundation (BNWF) model. Then, the method is verified and validated using results from centrifuge tests. Next, plots of the main effects and analysis of variance (ANOVA) were used for the sensitivity analysis of pile failure modes under axial loading. The initial imperfections and flexural rigidity of the pile have significant effects on the pile failure modes, and the pile is susceptible to buckling failure with low initial imperfections and flexural rigidity. Furthermore, the effects of the flexural rigidity of the pile, unsupported length ratio, initial imperfections, and degree of soil layer liquefaction on the critical buckling load of the pile in liquefiable soil are examined. The axial load-carrying capacity of the pile decreases with increasing initial imperfection amplitude, decreasing flexural rigidity of the pile, decreasing unsupported length ratio and severer degree of soil layer liquefaction. Finally, an estimating formula for predicting the critical buckling load of piles in liquefiable soil and an application example are presented.

Settlement of shallow strip footing on granular soil under eccentric static and cyclic loads

The traditional way of analyzing the behavior of shallow foundations is based on applying the load to the center of the footing, but this is not always the case in practice. The settlement of a strip footing resting on dense sand under eccentrically applied static and cyclic loads is studied in this paper to find out the foundation’s behavior in realistic conditions. During cyclic loading, the shear modulus of the soil is changed, due to which the stiffness of the soil and footing response are greatly affected. Under the influence of cyclic loading, in coarse-grained soil, the strain accumulates depending on the intensity of the cyclic loading. In low-intensity cyclic load conditions, the accumulated strain reaches a constant value after a finite number of load cycles. In this study, the analysis of settlement is carried out with the help of a numerical technique, based on Beam on Nonlinear Winkler Foundation (BNWF). The parameters, namely, static load, the intensity of the cyclic load (qd(max)), the depth of embedment of footing (Df) and the eccentricity ratio (e/B) are varied to observe the effect of the cyclic reversal of the load on the foundation’s response. Using the simulation results of 144 model conditions, an empirical equation is proposed to estimate the total settlement of the footing using Multivariate Adaptive Regression Splines (MARS). The analysis of the numerical results and a parameter-sensitivity study suggest that the settlement under combined eccentric static and cyclic loads is mainly controlled by the existing static load.

Development of Simulation Based p-Multipliers for Laterally Loaded Pile Groups in Granular Soil Using 3D Nonlinear Finite Element Model

The behavior of laterally loaded pile groups is usually accessed by beam-on-nonlinear-Winkler-foundation (BNWF) approach employing various forms of empirically derived p-y curves and p-multipliers. Averaged p-multiplier for a particular pile group is termed as the group effect parameter. In practice, the p-y curve presented by the American Petroleum Institute (API) is most often utilized for piles in granular soils, although its shortcomings are recognized. In this study, we performed 3D finite element analysis to develop p-multipliers and group effect parameters for 3 × 3 to 5 × 5 vertically squared pile groups. The effect of the ratio of spacing to pile diameter (S/D), number of group piles, varying friction angle (φ), and pile fixity conditions on p-multipliers and group effect parameters are evaluated and quantified. Based on the simulation outcomes, a new functional form to calculate p-multipliers is proposed for pile groups. Extensive comparisons with the experimental measurements reveal that the calculated p-multipliers and group effect parameters are within the recorded range. Comparisons with two design guidelines which do not account for the pile fixity condition demonstrate that they overestimate the p-multipliers for fixed-head condition.

A p–y Model for Large Diameter Monopiles in Sands Subjected to Lateral Loading under Static and Long-Term Cyclic Conditions

The design of large diameter monopiles subjected to cyclic lateral loading is of interest in many applications, such as, for example, in the offshore wind energy industry. Engineering design methods to estimate the deflection of these structures are required for this purpose. In the present work, a p–y model for large diameter monopiles subjected to lateral loading is proposed. The model considers a pile in cohesionless soil subjected to static and long-term cyclic loading. Its formulation features the consideration of nonlinear relations for the ultimate soil resistance pu and the initial subgrade modulus Epy0 among the soil depth and a cyclic factor that accounts for the effect of the soil density and loading amplitude. A relation is also proposed to account for a base shear force at the tip of the monopile. The proposed relations were employed and solved under the beam on nonlinear Winkler foundation (BNWF) approach and were adjusted to simulate a number of three-dimensional (3D) finite-element (FE) models accurately, accounting for variations on pile geometry, soil properties, and loading conditions. In the end, the performance of the proposed relations was evaluated through the comparison with a field test and a centrifuge test.

SEISMIC UNIFORM DAMAGE-TARGETED DESIGN OF RC FRAME STRUCTURES

The seismic failure mode of uniform damage refers to that the structure has a uniform damage and story drift along the height and develops a global energy dissipation mechanism, and it is an ideal and expected failure mode. A uniform damage-based seismic optimization design approach for RC frame structures considering the soil-structure interaction is proposed. By taking the uniformity of maximum inter-story drift ratio (IDR) as the design objective, the seismic optimization design approach was developed. Moreover, the optimization procedure accounted for the IDR distribution and component rotation demands. The component’s sectional reinforcements were selected as the design variables, and the material cost and the reinforcement ratio were considered as the design constraints. Based on the Beam on Nonlinear Winkler Foundation (BNWF) model, the numerical model of the RC frame structure considering soil-structure interaction was established. Two RC frame structures with 5 and 12 stories were employed as the prototype structures. The effects of convergence parameters on the convergence speed and stability were investigated. The transfer of story reinforcements in the optimization was studied. The change of component rotation and IDR distribution after the optimization was analyzed. The analytical results indicate that the developed approach can achieve a uniform IDR distribution and a smaller maximum IDR, thus improving the seismic performance.

The Effect of Nonlinear Soil–Structure Interaction on the Ductility and Strength Demands of Vertically Irregular Structures

Soil–structure interaction (SSI) is key to the elastic and inelastic seismic responses of buildings. In this research, the ductility and strength demands of vertically irregular MDOF buildings, considering nonlinear SSI effects, are parametrically investigated. The superstructure is modeled as a nonlinear multi-story shear building, and the beam on nonlinear Winkler foundation (BNWF) concept is employed to simulate the response of shallow foundations. Specifically, combined stiffness–strength irregularities are introduced by reducing lateral properties at a specific story of the regular (reference) models. Soil–structure systems with 5, 10, and 15 stories are analyzed under three sets of earthquake records corresponding to different soil classes. A wide range of key parameters including number of stories, fundamental period, level of inelasticity, aspect ratio, and site class are scrutinized through nonlinear time history analyses. The results reveal that SSI can reduce the strength and ductility demands of the vertically irregular structures, especially those with short periods. This beneficial effect becomes even more significant for systems with low ductility ratios. It is also concluded that the median ductility demand increases in the modified story owing to the softness/weakness of the first story. Furthermore, this increase due to the code strength regularity limit reached up to 78% and 36% in fixed-base and flexible-base conditions, respectively. Finally, simplified equations are proposed to estimate the maximum ductility demands of regular and irregular structures with flexible-base conditions.

Critical buckling load of pile in liquefied soil

Buckling instability has been recently identified as a possible mechanism of pile failure in liquefiable deposits and this failure mechanism is not explicitly mentioned in most design codes. To carry out routine design and checking, it is necessary to reliably estimate the critical buckling load of pile for a given liquefiable site. However, the existing calculation methods for the critical buckling load of pile in liquefied soils do not consider the influence of geometric imperfections and nonlinear behavior of the pile. In this paper, an efficient approach using the Beam on Nonlinear Winkler Foundation (BNWF) model is proposed to calculate the critical buckling load of pile in liquefied soils considering geometric imperfections and nonlinear behavior of the pile. The method is verified and validated using the finite element method and results from centrifuge tests. Furthermore, parametric analysis has been carried out to understand the influence of buckling load for different soil relative density, initial geometric imperfections of pile, flexural rigidity of pile, and pier height. It is found that the critical buckling load of pile in liquefied soils increases with the increase of soil relative density and flexural rigidity of pile, and decreases with the increase of initial geometric imperfections of pile and pier height. Finally, a simplified estimation method based on Euler buckling theory is provided for predicting critical buckling load of pile in liquefied soils and an example is taken to show the application.

Roles of pile-group and cap-rotation effects on seismic failure mechanisms of partially-embedded bridge foundations: Quasi-static tests

Pile foundations, especially partially embedded in soils, are vulnerable parts of bridges under seismic loadings. In this study, to investigate seismic failure mechanisms of partially-embedded reinforced concrete (RC) pile-group foundations, a series of quasi-static cyclic loading tests were conducted on 1 × 1, 2 × 2 and 2 × 3 pile-foundation specimens in sand. Observed hysteretic behavior and pile damage were recorded, along with pile curvature distributions. Then, numerical models based on the Beam-on-Nonlinear-Winkler-Foundation (BNWF) approach were developed and validated by test data. The failure process of each specimen was reached, characterized by the sequence and locations of plastic hinges on piles. Combining the test and numerical results, seismic failure mechanisms of all partially-embedded pile specimens with different layouts are revealed: side piles yield before center piles, each pile forms two plastic hinges, and pile heads yield before underground portions. Special attentions are paid to the roles of cap rotation and pile-group effect (PGE) on the failure mechanisms. The results reveal that the existence of PGE leads to lower lateral loads and greater displacements at different limit states such as the first yielding and ultimate states etc., while the impact of cap rotation only increases corresponding lateral displacements at these limit states.

Axial and lateral resistance coupling in the analysis of large-diameter drilled shafts

Pier foundations subjected to lateral loads are commonly designed using beam on nonlinear Winkler foundation (BNWF) models. This form of soil-structure interaction (SSI) modeling typically involves load transfer between structural members (e.g., drilled shafts) and surrounding soil via nonlinear soil resistance springs, which are distributed along the centerline of beam-column elements. Physically, soil resistance develops at the shaft-soil interface, and special considerations may be warranted regarding coupling between axial and lateral resistance when modeling large-diameter drilled shafts. Presented in this paper are side (t-z) and lateral (p-y) soil-resistance relationships for Florida limestone, obtained from centrifuge tests, and moment-rotation springs associated with coupling of axial and lateral resistances of laterally loaded drilled shafts. Using the coupled approach, BNWF models are developed that: 1) Capture physically measured lateral load responses of shafts founded in a range of soil/rock types; and, 2) Are suitable for large-diameter shafts at variable embedment lengths. This study highlights the need for such analyses in cases when relatively stiff soil/rock materials exist at shallow depths and/or when shafts undergo significant rotations. Use of coupled analysis is found to reduce computed maximum values of shaft bending moment and deflection up to 12% and 19%, respectively, compared to uncoupled analysis.