Rocking vibrations of rigid foundations on multi-layered poroelastic media

Abstract

This paper presents rocking vibrations of a rigid foundation resting on a multi-layered poroelastic half-space. The foundation is assumed to be rigid and massless, and subjected to a time–harmonic moment. In addition, each layer of the multi-layered half-space is governed by Biot’s theory of poroelastodynamics. The contact surface between the foundation and the layered half-space is smooth, and either fully permeable or impermeable. This dynamic interaction problem is studied by employing a discretization technique and an exact stiffness matrix scheme. Comparisons with existing solutions on rocking vibrations of rigid foundations on elastic and poroelastic media are shown to verify the accuracy of the present scheme. Selected numerical results on rocking compliances of rigid foundations of various shapes and mudmat foundations are presented. In addition, a dynamic interaction problem involving closely spaced foundations under rocking vibrations is also presented to demonstrate the applicability of the present solution scheme.     

Dynamic response of a large-diameter pile with variable section in layered saturated soil considering construction disturbance effect

ABSTRACT

An analytical solution is developed in this paper to investigate the vertical time-harmonic response of a large-diameter variable-section pile, and it considers the radial inhomogeneity of the surrounding soil caused by construction disturbance. First, the saturated soil surrounding the pile is described by Biot’s poroelastic theory and a series of infinitesimally thin independent layers along the shaft of the pile, and the pile is represented by a variable-section Rayleigh–Love rod. Then, the dynamic equilibrium equations of the soil and pile are solved to obtain an analytical solution for the impedance function at the pile top using the complex stiffness transfer method and impedance function transfer method. Finally, the proposed solution is compared with previous solutions to verify its reliability, and a parameter study is conducted to provide insights into the sensitivity of the vertical dynamic impedance of the pile and velocity response in low-strain integrity testing on defective piles.     

Hydromechanical behavior of radially multilayered cylinders under time-varying loads

ABSTRACT

Geotechnical strata are often treated as horizontally homogeneous for hydromechanical analysis due to the vertical deposition of geological layers; however, such a treatment becomes no longer valid when vertical drilling or construction causes the localized disturbance of subsurface, which would result in radial heterogeneity of geomaterials. This paper presents a poroelastic solution for the saturated multilayered cylinder where multilayer is used to represent radial heterogeneity. After the application of Laplace transform, the governing equations in cylindrical coordinates are derived to obtain the stiffness matrix between stresses, displacements, and pore water pressure. The global matrix is assembled by the boundary conditions and the compatibility of interfaces between adjacent layers. Under time-dependent horizontal compression loads, a parametric study is performed for a cylinder comprised of two layers with distinct properties, and the results show that the load frequency and radial heterogeneity play a significant role in hydromechanical behavior of geomaterials: (1) the time-varying loading can induce a negative pore pressure, and the influence of cyclic loading with a high frequency is limited near the outer surface; (2) the radial heterogeneity due to permeability and compressibility affects the development of pore pressure.     

A simplified calculation method for axial cyclic degradation of offshore wind turbine foundations in clay

Abstract

Pile foundation is the most popular option for the foundation of offshore wind turbines. The degradation of stiffness and bearing capacity of pile foundation induced by cyclic loading will be harmful for structure safety. In this article, a modified undrained elastic–plastic model considering the cyclic degradation of clay soil is proposed, and a simplified calculation method (SCM) based on shear displacement method is presented to calculate the axial degradated capacity of a single pile foundation for offshore wind turbines resisting cyclic loadings. The conception of plastic zone thickness R_p is introduced to obtain the function between accumulated plastic strain and displacement of soil around pile side. The axial ultimate capacity of single piles under axial cyclic loading calculated by this simplified analysis have a good consistency with the results from the finite element analysis, which verifies the accuracy and reliability of this method. As an instance, the behavior of pile foundation of an offshore wind farm under cyclic load is studied using the proposed numerical method and SCM. This simplified method may provide valuable reference for engineering design.     

考虑桩土作用独桩海洋平台横向振动特性研究

采用动Winkler弹性地基梁模型模拟桩土问动力相互作用，并考虑了流体与桩问相互作用，通过组合成层土中、水中桩单元的刚度阵，推得了独桩海洋平台连续系统横向振动的动刚度阵及在波浪力作用下平台甲板处的频率响应函数，进而求得了在确定性波浪力及随机波浪力作用下桩身任意点的位移响应。最后，通过算例研究和分析了在随机波浪力作用下成层土参数、甲板上重量及冲刷淘深等因素对平台振动响应的影响。     

Numerical analysis on random wave-induced porous seabed response

Research on the response of random wave on offshore structures has received great deal of attention of many researchers and engineers in the design of marine structures. Most previous investigations have been limited to the regular waves. In this paper, based on Longuet–Higgins random wave theory and finite element method, a numerical model for random wave-induced seabed response is established. The seabed is treated as poroelastic medium and characterized by Biot’s partly dynamic equations (u–p model). The JONSWAP spectrum is adopted in Longuet–Higgins model, which is based on the cumulative superposition of linear diffraction solution. Based on the numerical results, the effects of random wave on seabed response are investigated by comparing with the corresponding Stokes wave and cnoidal wave. Then, a parametric study is conducted to examine the effect of wave and soil characteristic on the seabed.     

Passive control of offshore jacket platforms

The wave-induced dynamic force is one of the most important excitations to be dealt with in the design of offshore structures. In order to perform a reliable design of an offshore structure, it is important to obtain an exact evaluation of its dynamic response but also to examine the ways of reducing the response. This paper presents the response of offshore jacket platforms installed with energy dissipation devices such as viscoelastic, viscous and friction dampers under wave loading. The offshore jacket platforms are modeled as multi-degrees-of-freedom system provided with dampers at each floor location. The wave forces are modeled as per Morison's equation. The governing equations of motion of the jacket platform with dampers are derived and their solution in the frequency domain is presented. The uni-directional random wave loading is expressed by the Pierson-Muskowitz spectrum. The response of the jacket platform with viscoelastic, viscous and friction dampers is compared with the corresponding response without dampers in order to investigate the effectiveness of the passive control systems. It is observed that the additional dampers add substantial damping to structure and thus favorably control the response of platform structure. Among the various energy dissipation devices used for study, the viscoelastic dampers perform better in comparison to the other dampers. This is due to the fact that the added viscoelastic dampers contribute to increased viscous damping as well as lateral stiffness which reduces the response of the offshore jacket platforms significantly.     

Triangular Configuration Tension Leg Platform behaviour under random sea wave loads

This study investigates the dynamic response of a Triangular Configuration Tension Leg Platform (TLP) under random sea wave loads. The random wave has been generated synthetically using the Monte-Carlo simulation with the Peirson–Moskowitz (P–M) spectrum. Diffraction effects and second-order wave forces have not been considered. The evaluation of hydrodynamic forces is carried out using the modified Morison equation with water particle kinematics evaluated using Airy's linear wave theory. Wave forces are taken to be acting in the surge degree-of-freedom. The effect of coupling of various structural degrees-of-freedom (surge, sway, heave, roll, pitch and yaw) on the dynamic response of the TLP under random wave loads is studied. Parametric studies for random waves with different H_s and T_z under the presence of current have also been carried out. For the orientation of the TLP, surge, heave and pitch degrees-of-freedom responses are influenced significantly. The surge power spectral density function (PSDF) indicates that the mean square response is affected by the amplification at the natural frequency of the surge degree-of-freedom and also at the peak frequency of the wave loading. The PSDF of the heave response shows higher peak values near the surge frequency and near the peak frequency of the wave loading. Surge response, therefore, influences heave response to the maximum. Variable submergence seems to be a major source of nonlinearity and significantly enhances the responses in surge, heave and pitch degrees-of-freedom. In the presence of current, the response behaviour of the TLP is altered significantly introducing a non-zero mean response in all degrees-of-freedom.     

Dynamic analysis of a vertical plate exposed to breaking wave impact

From the experimental studies in recent years, it has become known that when a wave breaks directly on a vertical faced coastal structure, high magnitude impact pressures are produced. The theoretical and experimental studies show that the dynamic response of such structures under wave impact loading is closely dependent on the magnitude and duration of the load history. The dynamic analysis and design of a coastal structure can be succeeded provided the design load history for the wave impact is available. Since these types of data are very scarce, it is much more convenient to follow a method which is based on static analysis for the dynamic design procedure. Therefore, to facilitate the dynamic design of a vertical plate that is exposed to breaking wave impact, a multiplication factor called “dynamic magnification factor” is herein presented which is defined as the ratio of the maximum value of the dynamic response to that found by static analysis. The computational results of the present study show that the dynamic magnification factor is a useful ratio to transfer the results of static analysis to the dynamic design of a coastal plate for the maximum impact pressure conditions of p_max/γH₀≤18.     

Experimental simple shear study of composite soil with cemented soil core

Abstract

Cement soil mixing piles are an effective treatment method for marine soft clay. To investigate the static and dynamic characteristics of the composite soil with cemented soil core, a series of experiments are carried out by using the cyclic simple shear test. The result shows that, the static shear strain showed strain hardening, cemented soil core can improve static shear strength of composite soil, vertical stress can enlarge reinforcement of cemented soil core. The tendency of strain development of composite soil with different area replacement ratios under cyclic loading is the same as that of pure clay, existing critical cyclic stress ratios corresponding to different area replacement ratios. In addition, improving area replacement ratio can increase cyclic strength. At same time, adding of cemented soil core does not change shape of hysteresis curve compared with it for clay either. Moreover, cemented soil core can also obstruct stiffness softening. Through regression analysis of the experimental data, relationship between cyclic number and soil softening index is proved to be linear. The results can give a reference for the dynamic characters of the marine soft clay foundation with cement soil mixing piles.     

Review of flexible risers and articulated storage systems

The anchorage system for mid-ocean loading or production consists of an articulated tower for mooring the tanker. Flexible risers are also essential components of the anchorage system. The present paper provides a state-of-the-art review on articulated storage systems and flexible risers, giving theoretical background for the development of computer software for the static analysis of flexible risers.In the state-of-the-art review for flexible risers, various analysis techniques for elastic lines and flexible risers under self-weight, current and wave forces are presented. The dynamic response of the flexible riser, including vortex-induced oscillations, is also outlined.The literature concerning the articulated tower and tanker is relatively scarce. Available works related only to dynamic responses of articulated towers. The combined response of tower and tanker is only studied by Chakrabarti and Cotter [(1978), Analysis of a tower-tanker system. In Proceedings of the 10th Offshore Technology Conference, OTC 3202, pp. 1301–1310] in a limited sense. The review of these works is summarised relevant to this paper.In the end, the static analysis of the flexible riser under its self-weight and current is presented using a finite difference approach. The problem essentially involves geometrical non-linearity, which is tackled with the help of an iterative solution based on modified Newton-Raphson technique. The theoretical formulation presented is being used to develop the computer software for the static analysis of the flexible risers.     

Marine geotechnology—state of the art

Abstract

The state of the art in marine geotechnology can best be defined with reference to what is known about soils on land. Differences between these two states of knowledge are the significant problems for the marine environment. Among the major problems addressed in this paper are (a) Sampling of soils, which involves much more serious disturbance than is considered acceptable on land. Disturbance results from several uniquely marine factors including total stress release and drilling mud overpressure, (b) Underconsolidation, or excess in situ pore pressure, caused by rapid rates of sedimentation, gas, leaks from an artesian pressure source, or cyclic loading. (c) Gas in sediments, which can cause an increase in the in situ pore pressure, hinders subsurface investigation, and is a major cause of sample disturbance. (d) The difficulty and necessity of in situ measurements. (e) The predominance of dynamic loading effects which can cause significant changes in soil behavior. A major difference between geotechnical engineering on land and in marine areas is the use of effective stress methods. Significant improvement in geotechnical engineering offshore can be achieved through the increased use of effective stress methods. Illustrations of these improvements are presented in this paper with particular reference to the problems of submarine slope stability.     

Scour effects on bearing capacity of composite bucket foundation for offshore wind turbines

Abstract

Composite bucket foundation (CBF) is a wide-shallow foundation for offshore wind turbines, which can be transported and installed with the turbine as one unit at a one-step operation. Compared with deep pile foundations, its structural stability is more sensitive to the scouring by waves and currents. In this paper, a three-dimensional finite element model with CBF and surrounding soil is established to estimate the failure mode at different given soil scour conditions. The loading on CBF for offshore wind turbines is characterized by relatively small vertical loading V, larger horizontal loading H, and bending moment M, and the effect of erosion on bearing capacity of CBF is determined by using the fixed displacement ratio method. In addition, the failure envelopes of the CBF applied in H–M and V–H–M loading modes are obtained. Results indicate that the bearing capacity of CBF under horizontal loading and bending moment will be significantly reduced by the decrease in the embedded depth of CBF due to the scouring depth and extent, as well as the H–M, and V–H–M failure envelopes. The structural stability safety factor of CBF under different scouring conditions can be obtained through the three-dimensional envelope surface with respect to scouring depth and extent.     

循环荷载作用下合成纤维系缆粘弹塑性应力应变关系

在循环载荷作用下,合成纤维系缆的应力应变关系表现出明显的非线性特性,直接影响系泊缆绳的动力响应。如何针对其在循环载荷作用下的应力应变关系进行准确的定量描述是有关绷紧式系泊系统设计的关键问题。国内外研究者之前的研究不能反映缆绳的载荷历史、蠕变特性以及刚度变化过程,因此提出一个粘弹性粘塑性模型来描述合成纤维系缆的应力应变关系。本模型能够反映合成纤维缆绳的时间变化特性以及在整个加载—卸载过程中的刚度变化。此外,提出了明确的参数确定方法及步骤,基于简单的蠕变实验可以确定模型的各个参数。将两种载荷条件下聚酯缆绳的实验结果与模型结果进行对比,二者吻合较好,证明了模型的有效性和可靠性。本研究对于绷紧式系泊系统的研发和工程应用具有重要意义。     

Evaluation of undrained failure envelopes of caisson foundations under combined loading

In this paper, results of a three-dimensional finite element study addressing the effect of embedment ratio (L/D) of caisson foundations on the undrained bearing capacity under uniaxial and combined loadings are discussed. The undrained response of caisson foundations under uniaxial vertical (V), horizontal (H) and moment (M) loading are investigated. A series of equations are proposed to predict the ultimate vertical, moment and maximum horizontal bearing capacity factors. The undrained response of caisson foundations under combined V-H and V-M load space is studied and presented using failure envelopes generated with side-swipe method. The kinematic mechanism accompanying failure under uniaxial loading is addressed and presented for different embedment ratios. Predictions of the uniaxial bearing capacities are compared with other models and it is confirmed that the proposed equations appropriately describe the capacity of caisson foundations under uniaxial vertical, horizontal and moment loading in homogenous undrained soils. The results of this paper can be used as a basis for standard design codes of off-shore skirted shallow foundations which will be the first of its kind.     

Lateral dynamic response of a partially embedded pile subjected to combined loads in saturated soil

In this article, an analytical solution is proposed to investigate the lateral dynamic response of a pile which is partially embedded in saturated soil layer and subjected to combined lateral and vertical loads. The saturated soil is described by Biot’s poroelastic theory and the resistance of soil is derived by potential function method. The governing equation of the pile is solved by coupling soil resistance and continuity conditions between the pile and the soil. The dynamic impedances of the pile are then obtained through transfer matrix method. To verify the validity of the proposed procedure, the present solution is compared with available solution for an idealized case. Finally, a parametric study is performed to investigate the effects of various parameters on the stiffness and damping properties of the pile-soil system. It is found that permeability of the soil and vertical load has significant effects on the dynamic response of the pile.     

Evaluation of cyclic and monotonic loading behavior of bucket foundations used for offshore wind turbines

Suction caissons are considered as an alternative foundation solution for offshore wind turbines. In the present study, three-dimensional finite element (FE) analyses are performed to assess the behavior of a bucket foundation and soil supporting the bucket under cyclic and monotonic loading conditions. A parametric study is also performed for a wide range of bucket geometries and two different soil densities. The results indicate that bucket geometry and soil properties significantly affect the foundation response due to cyclic loading conditions. The bucket with the smallest geometry installed in medium dense soil exhibits the lowest stiffness in initial loading and then with the progress of cyclic loads experiences lower stiffness compared to the caissons with larger geometries. The sensitivity of the foundation response to the soil density is higher than its geometry. The bucket under the lowest vertical load experiences the lowest stiffness in both virgin loading and during the progress of cyclic loads. The highest soil displacement is observed near the lid at the interior of the bucket. Stresses caused by cyclic loading belong to certain ranges. Additionally, increases in the skirt length result in increases in the stress ranges and shift the range to the right side. With respect to the monotonic loading conditions, normalized diagrams are proposed that can be used for the preliminary design of suction bucket foundations.     

Wave propagation in a transversely isotropic porous ocean bottom

Abstract

The equations of wave motion are considered in this article for three-layered medium which consists of liquid and porous layers with finite depth and solid half-space such as ocean bed. By virtue of scalar potential functions for each layer, complicated differential equations of layers are reduced to ordinary differential equations. An analytical method is applied to determine the Green’s functions of media based on an arbitrary shaped time-harmonic excitation at the interface of liquid and porous layers. A Mathcad code is provided to compute the complex integrals. Displacement and stress fields of three layers are discussed. Comparing with special cases, existing answers represent the validity of the proposed method. Numerical results are carried out for circular patch, ring and point loads, and the effects of various parameters on the behavior of the system are plotted. Finally, the achieved results were under discussion.     

Undrained bearing capacity of spudcan under combined loading

The bearing capacities of spudcan foundation under pure vertical (V),horizontal (H),moment (M) loading and the combined loading are studied based on a series of three-dimensional finite element analysis.The effects of embedment ratio and soil non-homogeneity on the bearing capacity are investigated in detail.The capacities of spudcan under different pure loading are expressed in non-dimensional bearing capacity factors,which are compared with published results.Ultimate limit states under combined loading are presented by failure envelopes,which are expressed in terms of dimensionless and normalized form in three-dimensional load space.The comparison between the presented failure envelopes and available published numerical results reveals that the size and shape of failure envelopes are dependent on the embedment ratio and the non-homogeneity of the soil.     

Dynamic characteristics of marine soft clay under variable phase difference and initial static shear stress

Abstract

Under seismic loading, the soil layer is subjected to multidirectional cyclic shear stress with different amplitudes and frequencies because of the coupling of multiple shear waves and the soil element within a slope or behind a retaining wall is subjected to initial static shear stress before subjected to cyclic loading. Due to the complexity of seismic loading propagation, a phase difference exists between the initial static shear stress and cyclic shear stress. To investigate the influence of the phase difference and initial static shear stress on cyclic shear strain, cyclic modulus, and cyclic strength, a series of laboratory tests are performed on Wenzhou marine soft clay by multi-directional simple shear system, which can simulate the actual state better by controlling the horizontal cyclic stress in the x and y directions simultaneously. As the phase difference varies from 0° to 90°, the dynamic shear modulus increases and cyclic strain accumulation decreases with an increasing number of cycles. The shear strain increases with the initial shear stress.