Variation Of Soil Stiffness Research Articles

Vertical and horizontal dynamic response of suction caisson foundations

Abstract In this article, the dynamic response of suction caisson foundations is studied using a three-dimensional finite element model with an absorbing boundary. The adopted formulation is based on the substructuring method. This formulation has been applied to analyze the effect of soil–structure interaction on the dynamic response of the suction foundation as a function of the kind of load. The suction caisson foundations are embedded in viscoelastic homogenous soils and subjected to external harmonic forces. For each frequency, the dynamic impedance connects the applied forces to the resulting displacement. The constitutive elements of the system are modeled using the finite element volumes and shell elements. The numerical results for the dynamic response of the suction foundations are presented in terms of vertical and horizontal displacements as well as vertical and horizontal dynamic impedances. The results indicated that the overall dynamic response is highly affected by the suction caisson diameter, the soil stiffness variation, and the suction caisson length.

A stochastic approach on modeling the long-term unevenness of pavements considering spatially varying soil properties/Ein stochastischer Ansatz zur Modellierung der langfristigen Entwicklung von Fahrbahnunebenheiten unter Berücksichtigung räumlich variierender Bodeneigenschaften

Even within nominally homogenous soil layers, spatial variations of soil properties occur. Current design methods simplify varying soil properties by applying constant values. In order to achieve a reliable geotechnical design, the local variance of soil properties needs to be considered with respect to the long-term development of road unevenness. Hence, a variation of soil stiffness leads to spatially varying settlements and increasing dynamic forces on passing vehicles as time increases. This process continues steadily resulting in a noticeable reduction of driving comfort until a repair of the pavement is required. In this paper, a numerical model is applied to determine the long-term unevenness of pavements considering the spatial variation of soil properties. Thereby, the asphalt pavement, the subbase, and the subgrade are modeled by a set of coupled spring elements representing the soil behaviour of the respective layer. A stochastic distribution of soil properties based on a random walk is assumed to account for the spatial variation of the subsoil stiffness. The long-term unevenness development due to passing vehicles is extensively evaluated with respect to resulting dynamic forces and the impact of a deviating soil stiffness in individual soil layers. Finally, conclusions with respect to driving comfort are drawn.

Simulation of cyclic laterally-loaded piles in undrained clays accounting for soil small-strain characteristics

The performance of pile foundations subjected to cyclic lateral loading is central to offshore geotechnical engineering. Although non-linearity and path-dependence of soil mechanical behavior at small strains are widely recognized, the influences of these local behavior on global response of pile foundations are less explored. This work presents numerical analyses of cyclically-loaded piles in undrained clays that explicitly account for soil small-strain characteristics. By using intergranular strain (IGS) elasticity method, a soil model proposed by the authors for undrained clays during cyclic loading is extended to include non-linear small-strain behavior. Via comparing against element tests, the constitutive relation is shown capable of representing the observed variation of soil stiffness and damping with strain magnitudes, as well as the dependence of such non-linearity on stress paths. Based on the above soil model, finite element simulations are performed to interpret the response of laterally loaded piles from geotechnical centrifuge tests. The impacts of soil small-strain behavior on pile force–displacement relations, hysteric loops, and the ability of a pile–soil system to dissipate energy are investigated. This work highlights that the sensitivity of these foundation responses to small-strain non-linearity of soils can vary considerably, depending on pile geometry features and head constraint conditions.

Three-Dimensional Modeling of Monopiles in Sand Subjected to Lateral Loading under Static and Cyclic Conditions

Here, the results of a three-dimensional finite element study of the complex interaction of horizontal and moment loads (HM) on offshore monopiles as failure envelope, are reported. A new design criterion is described which is based on critical length, ultimate limit states, load characteristics and Eigen-frequency to ensure stable behavior of laterally loaded monopiles. Numerical analyses were performed to examine nonlinear interaction of a soil-pile system for 10,000 load cycles. The resulting framework can predict angular rotation due to cyclic loading. According to the loading level and duration of a load, elastic strains accumulate in the vicinity of a pile. Fairly intermediate two-way cyclic loading induced the largest rotations irrespective of the analysis performed (i.e., drained versus partially drained). Based on the regression coefficients of the non-dimensional frameworks used, accumulating rocking deformations of a pile at seabed level appear to be dependent on cyclic load ratio, drainage condition, and duration of loading. For safe design, sensitivity of the natural frequency of offshore wind turbine (OWT) at a monopile critical length as well as shorter lengths were also examined. The analytical model proposed here for determining the natural frequency of an OWT considers that soil-structure interaction (SSI) can be represented by monopile head springs characterized by lateral stiffness, KL, rotational stiffness, KR, cross-coupling stiffness, KLR, and parabolic soil stiffness variation with depth.

Concept design of jacket foundations for offshore wind turbines in 10 steps

Simplified design procedures for offshore wind turbine (OWT) support structures are necessary in the concept and tender design stages for assessing the financial viability. Building upon the previous research on simplified monopile design, this paper presents a similar method to design jacket supported OWTs founded on piles or suction caissons. The method is based on the minimum and necessary data, namely the site characteristics (wind speed at reference height, wind turbulence intensity, water depth, wave height and wave period), turbine characteristics (rated power, rated wind speed, rotor diameter, cut-in and cut-out speed, mass of the rotor-nacelle-assembly) and ground profile (soil stiffness variation with depth and soil strength). A flowchart of the design process is also presented for visualisation of the rather complex multi-disciplinary analysis. Insights are given for 3 and 4 legged jackets. The calculation procedures that are required can be easily carried out either through a series of spreadsheets or simple hand calculations. An example problem emulating the design of a jacket on piles is taken from literature to demonstrate the proposed calculation procedure. The data used for the calculations are obtained from publicly available sources and the example shows that the simplified method arrives at a similar foundation to the one reported.

Seismic harmonic response of inhomogeneous soil: scaling analysis

The study of the seismic response of inhomogeneous soil deposits, underlying rigid bedrock, has traditionally been framed as a one-dimensional wave propagation problem in a linear viscoelastic medium. When it comes to modelling soil inhomogeneity, the current trend to model the continuous variation of soil stiffness with depth employs a ‘generalised parabolic function’. Exact solutions have already been obtained, but these come in terms of Bessel functions, which muddle the interpretation of results and obstruct assessment of the parameters’ influence. This also hinders the definition of an ‘equivalent homogeneous’ soil deposit (a relevant concept utilised in many seismic codes). It is shown herein that the so-called inhomogeneity factor plays a secondary role in determining the response in many cases; thus straightforward guidelines are suggested for simplifying the problem, leading to elementary scaling relations. The scalings provide simple yet meaningful relations that reveal and explain the fundamental traits of the dynamic behaviour of these systems.

Vertical dynamic impedance of suction caissons

Nowadays, suction caissons are being increasingly deployed as foundations to support offshore wind turbines (OWTs). Due to the overturning moment induced by waves and wind, vertical forces are the dominating ones acting on these foundations. In this study the dynamic stiffness and damping coefficients of suction caissons embedded in a viscoelastic soil layer over bedrock, subjected to vertical dynamic load were investigated. Numerical analyses of representative 3D finite element models were performed, while the numerical modelling was validated against existing analytical solutions for end bearing piles. The vertical dynamic response of suction caissons was evaluated by considering the effects of the foundation’s geometry, i.e. the slenderness ratio, and the stiffness of the soil layer on the vertical dynamic impedance of suction caissons. Results showed that the overall dynamic response is profoundly affected by the skirt length and by the variation of soil stiffness with depth.Mathematical expressions of the dynamic stiffness and damping coefficients were derived pertaining to foundations with various slenderness ratios and embedded in different soil profiles. The proposed expressions can be implemented in structural models used for the dynamic analysis of the support structure of a wind turbine, taking thus into consideration the effects of soil-structure-interaction.

Dynamic lateral response of suction caissons

Deeper water installations of offshore wind turbines may be supported by jacket structures. This study investigates the dynamic response of suction caissons for jackets by analysing 3D finite element models in the frequency domain. The numerical modelling was firstly validated by analytical solutions for pile foundations. Groups of crucial dimensionless parameters related to the soil profile and the foundation geometry are identified and their effects on the response of suction caissons are studied. Static stiffness coefficients are presented in a form of mathematical formulas obtained by fitting the numerical results, pertaining foundations with different slenderness ratios and embedded in different soil profiles.Sensitivity of the dynamic impedances of suction caissons on the skirt length was showed in this study. Moreover, the results for the suction caissons indicated that the overall dynamic response is profoundly affected by the relative thickness of the soil layer and by the variation of soil stiffness with depth.

Design of monopiles for offshore wind turbines in 10 steps

A simplified design procedure for foundations of offshore wind turbines is often useful as it can provide the types and sizes of foundation required to carry out financial viability analysis of a project and can also be used for tender design. This paper presents a simplified way of carrying out the design of monopiles based on necessary data (i.e. the least amount of data), namely site characteristics (wind speed at reference height, wind turbulence intensity, water depth, wave height and wave period), turbine characteristics (rated power, rated wind speed, rotor diameter, cut-in and cut-out speed, mass of the rotor-nacelle-assembly) and ground profile (soil stiffness variation with depth and soil stiffness at one diameter depth). Other data that may be required for final detailed design are also discussed. A flowchart of the design process is also presented for visualisation of the rather complex multi-disciplinary analysis. Where possible, validation of the proposed method is carried out based on field data and references/guidance are also drawn from codes of practice and certification bodies. The calculation procedures that are required can be easily carried out either through a series of spreadsheets or simple hand calculations. An example problem emulating the design of foundations for London Array wind farm is taken to demonstrate the proposed calculation procedure. The data used for the calculations are obtained from publicly available sources and the example shows that the simplified method arrives at a similar foundation to the one actually used in the project.

Closed form solution of Eigen frequency of monopile supported offshore wind turbines in deeper waters incorporating stiffness of substructure and SSI

Offshore wind turbines (OWTs) are dynamically loaded structures and therefore the estimation of the natural frequency is an important design calculation to avoid resonance and resonance related effects (such as fatigue). Monopiles are currently the most used foundation type and are also being considered in deeper waters (>30m) where a stiff transition piece will join the monopile and the tapered tall tower. While rather computationally expensive, high fidelity finite element analysis can be carried to find the Eigen solutions of the whole system considering soil–structure interaction; a quick hand calculation method is often convenient during the design optimisation stage or conceptual design stage. This paper proposes a simplified methodology to obtain the first natural frequency of the whole system using only limited data on the WTG (Wind Turbine Generator), tower dimensions, monopile dimensions and the ground. The most uncertain component is the ground and is characterised by two parameters: type of ground profile (i.e. soil stiffness variation with depth) and the soil stiffness at one monopile depth below mudline. In this framework, the fixed base natural frequency of the wind turbine is first calculated and is then multiplied by two non-dimensional factors to account for the foundation flexibility (i.e. the effect of soil–structure interaction). The theoretical background behind the model is the Euler–Bernoulli and Timoshenko beam theories where the foundation is idealised by three coupled springs (lateral, rocking and cross-coupling). 10 wind turbines founded in different ground conditions from 10 different wind farms in Europe (e.g. Walney, Gunfleet sand, Burbo Bank, Belwind, Barrow, Kentish flat, Blyth, Lely, Thanet Sand, Irene Vorrink) have been analysed and the results compared with the measured natural frequencies. The results show good accuracy (errors below 3.5%). A step by step sample calculation is also shown for practical use of the proposed methodology.

A simplified Nonlinear Sway-Rocking model for evaluation of seismic response of structures on shallow foundations

This paper presents a simplified Nonlinear Sway-Rocking model as a preliminary design tool for seismic soil-structure interaction analysis. The proposed model is intended to capture the nonlinear load-displacement response of shallow foundations during strong earthquake events where foundation bearing capacity is fully mobilised. Emphasis is given to heavily-loaded structures resting on a saturated clay half-space. The variation of soil stiffness and strength with depth, referred to as soil non-homogeneity, is considered in the model. Although independent springs are utilised for each of the swaying and rocking motions, coupling between these motions is taken into account by expressing the load-displacement relations as functions of the factor of safety against vertical bearing capacity failure (FSv) and the moment-to-shear ratio (M/H). The simplified model has been calibrated and validated against results from a series of static push-over and dynamic analyses performed using a more rigorous finite-difference numerical model. Despite some limitations of the current implementation, the concept of this model gives engineers more degrees of freedom in defining their own model components, providing a good balance between simplicity, flexibility and accuracy.

Highlighting the Change of the Dynamic Response to Discrete Variation of Soil Stiffness in the Process of Dynamic Compaction with Roller Compactors Based on Linear Rheological Modeling

The paper presents the dynamic response in motion and stress transmitted to the soil to rotating inertial dynamic excitations, for each layer of soil with specific stiffness. Upon repeated passages on the same layer of soil, there will be taken into account the new rigidities that change the dynamic response called "successive transition" within the linear - elastic limit, up to the ultimate the achievement of the last end state of deformability.Parametric variation curves are specific to certain regularities families expressing multiple correlations, useful for assessing the degree of compaction by vibration of natural soils, by highlighting the movement of resonance points after each pass on the same layer of soil.

Ground heave induced by installing stone columns in clay soils

Measurements of ground heave induced by installing stone columns in soft clay are presented in this paper. These measurements are likely to provide guidance to practitioners concerned about the possible impact of column construction on adjacent structures and services. Heaved volume, variation in heave with radius and the radial extent of heave were found to follow experience of driven piles. Simplified finite-element analyses have also been performed which indicate that the thin stiff crust typical of soft clay profiles appears to have little influence on heave, whereas soil stiffness variation with depth and column length may be influential.

Tunnelling effects on lateral behavior of pile rafts in layered soil

The Mindlin’s solution or Winkler model is often adopted to estimate the response of piles subject to ground movements induced by tunnelling in the literature. Those methods are reasonable for piles in homogeneous soil, while soil systems are usually layered in practice. This paper presents a simplified analysis method that can be used to estimate lateral responses of pile rafts subject to ground movements induced by tunnelling in layered soil. The problem is solved in two stages: firstly, using the Loganathan–Poulos solution to calculate lateral free soil movements induced by tunnelling; secondly, composing the calculated free soil movements to the pile, the governing equilibrium equations of piles are solved by the finite difference method combined with the displacement and stress solutions for asymmetric loads in layered elastic system. Also, the lateral interactions between structural members, pile–pile, pile–soil, pile–raft and soil–raft, are modeled based on the solutions for asymmetric loads in layered elastic system in the method presented herein. The proposed method is verified using published results, centrifuge tests results and displacement-controlled finite element method results. The study shows that the proposed method can reasonably estimate the lateral responses of pile rafts induced by tunnelling. Additionally, the influence of soil stiffness variation is discussed. The study shows the maximum deflections and bending moments appear near the spring line of the tunnel. And the lateral behaviors of the piles are more significantly influenced by the stiffness of the underlying soil which the tunnel located in than the stiffness of the overlying soil.

Numerical modeling of centrifuge cyclic lateral pile load experiments

To gain insight into the inelastic behavior of piles, the response of a vertical pile embedded in dry sand and subjected to cyclic lateral loading was studied experimentally in centrifuge tests conducted in Laboratoire Central des Ponts et Chaussees. Three types of cyclic loading were applied, two asymmetric and one symmetric with respect to the unloaded pile. An approximately square-root variation of soil stiffness with depth was obtained from indirect in-flight density measurements, laboratory tests on reconstituted samples, and well-established empirical correlations. The tests were simulated using a cyclic nonlinear Winkler spring model, which describes the full range of inelastic phenomena, including separation and re-attachment of the pile from and to the soil. The model consists of three mathematical expressions capable of reproducing a wide variety of monotonic and cyclic experimental p-y curves. The physical meaning of key model parameters is graphically explained and related to soil behavior. Comparisons with the centrifuge test results demonstrate the general validity of the model and its ability to capture several features of pile-soil interaction, including: soil plastification at an early stage of loading, “pinching” behavior due to the formation of a relaxation zone around the upper part of the pile, and stiffness and strength changes due to cyclic loading. A comparison of the p-y curves derived from the test results and the proposed model, as well as those from the classical curves of Reese et al. (1974) for sand, is also presented.

A simple numerical model for analysis of propped embedded retaining walls

A simple, efficient and practical numerical model is described for analysis of cantilevered and strutted flexible retaining walls. The model accommodates a variety of features that affect the performance of retaining walls in the field such as application and removal of struts, application of surcharge, changes in the water table, changes in the soll properties and simulation of staged excavations. Unlike conventional finite element and finite difference models that require a considerable effort and knowledge to prepare the input data, the proposed model requires only a few lines of data to define the problem and control the analysis. The computational results include bending moment, shear force and deflection of the wall, strut loads and lateral stresses in the soil at any stage of the analysis. The model can be used effectively to perform a broad suite of parametric studies at the design stage and also as a reliable tool for predicting performance. To demonstrate the latter, the model is applied to analyze several problems involving different wall types in stiff and soft soils. Despite the implicit idealizations in the formulation of the model, such as a linear variation of soil stiffness with depth, the model is shown to provide results that are acceptable for design purposes and of the same quality as those obtained from conventional finite element models.

Spatial variation of soil stiffness: Spectral density approach

Measured data from an entire area using a dynamic compaction control device with vibrating rollers are reported and deviations of the measured values are interpreted. Entire area measurement is helpful in reducing geotechnical risk. Even in nominally homogeneous layers the soil stiffness varies from point to point. Using this device, it is possible to detect soft as well as hard spots. Spectral densities of the wave length of soil stiffness are calculated to investigate the spatial variation of soil stiffness. It was found that the amplitude of the waves of soil stiffness is proportional to the wave length. This phenomenon is called a 1/f spectrum or flickering noise: the stiffness variation is composed of long waves with high amplitudes and small waves with small amplitudes. A dominant wave length due to patterns could not be found. The 1/f spectrum has often been observed in natural processes. The phenomenon is illustrated in terms of soil mechanics using a simple generating process.

Nonlinear response of dams founded on alluvial deposits in narrow canyons

This paper presents a simplified model for the response of earth dams founded on alluvial deposits at the base of canyons. The goal of the model is to capture the effect of the most important factors influencing the response and to provide a realistic and efficient tool for preliminary safety evaluations. The developed theoretical closed-form solution combines the effects on the response of: (a) the foundation layer, (b) the canyon narrowness, (c) the variation of soil stiffness within the dam versus depth, and (d) soil nonlinearity. The latter is incorporated in a simple piece-wise linear scheme, in which the soil shear moduli and damping ratios within the dam and the layer are continuously updated at small time intervals during the analysis. The presence of a soft foundation layer is found to have a dramatic effect on the natural periods of the dam. A series of parametric studies is undertaken to investigate the effect on the response of the fundamental geometric and material characteristics of the dam-layer-canyon system subjected to transient and harmonic motion. The results show that a foundation layer with an average S -wave velocity similar or less than that of the dam under moderate or strong base excitation may experience significant shear strains. Such strains are capable of inducing high excess pore water pressures and perhaps liquefaction within contractive saturated cohesionless soils in the foundation. The cost of the simplified analysis is about three orders of magnitude less than that of an elastoplastic FE analysis.

Buckling loads of fully embedded vertical piles

Determination of critical buckling loads of columns in a medium which offers resistance to lateral deflections depend on:(a) Length of the pile, L.(b) Flexural stiffness of the pile, EI.(c) Stiffness of the soil, K, and(d) Boundary conditions of the pile, both at the top and the tip.In this paper, solutions for buckling loads have been obtained in closed form by energy methods for fully embedded vertical piles for boundary conditions, pinned top-pinned tip, fixed top-fixed tip, and a linear variation of soil stiffness. The effects of pile length, soil stiffness, and boundary conditions on buckling loads and mode of buckling have been studied for pile lengths up to 24 m with EI of 477 tm2, K0 [A] from 0 to 2000 t/m2 and Nh [B] from 0 to 2000 t/m3.