Three-dimensional dynamic response of multilayered poroelastic media

ABSTRACT

The dynamic response of a multilayered poroelastic medium under 3D time-harmonic loading is studied using an exact stiffness method. The poroelastic medium under consideration consists of N layers of different thicknesses and properties and an underlying poroelastic half-space. The exact stiffness matrices for each layer and the underlying half-space are derived explicitly using Biot’s poroelastodynamic theory and double-dimensional Fourier transforms. Selected numerical results are presented to demonstrate the influence of various parameters on dynamic response of multilayered poroelastic media under traction and fluid loading. The application of proposed solution scheme to soil–structure interaction problems is also presented.     

Evaluation of vertically and laterally loaded bucket foundation in clay using a three-dimensional displacement approach

ABSTRACT

An investigation is made to present analytical solutions provided by a three-dimensional displacement approach for analysis of bucket foundations subjected to vertical and lateral loads in cohesive soils. The nonlinear vertical and lateral stiffness coefficients along the skirt of the bucket foundation in nonhomogeneous soil are presented using three-dimensional solutions for vertical and lateral loads and taking into account the dependence of stiffness coefficients on the shear strain. The vertical, lateral, and rocking stiffness coefficients on the base of the skirt of a bucket foundation are obtained from the solutions of hollow rigid cylindrical punch acting on the surface of a soil. The ultimate vertical stress of a soil under the base of a bucket foundation subjected to vertical and moment loads is presented analytically by considering only compression and ignoring tension on the base. The vertical and lateral yields along the skirt and the compression and shear failures on the base are taken into account in analysis of ultimate load capacities. Envelopes of the combined ultimate horizontal and moment load capacities of a bucket foundation in clay are shown. Relationships between ultimate lateral and moment load capacities and the embedment ratio (skirt length to diameter) are presented.     

Natural frequency of offshore wind turbines on rigid and flexible monopiles in cohesionless soils with linear stiffness distribution

A simplified method is introduced to obtain the fundamental frequency of offshore wind turbines supported by monopile foundations. Soil-pile interaction is modeled based on Winkler approach and concept of beam on elastic foundation. The soil is considered to have linearly varying modulus of subgrade reaction along depth which is a typical assumption for cohesionless soils. Rayleigh method which is based on conservation of total energy of the system is utilized. Firstly the natural frequency of the system with rigid pile is derived and then an innovative procedure is introduced to take pile flexural stiffness into consideration. Comparison between results of the present method with those of a numerical FE model for a typical 2 MW wind turbine structure shows excellent agreement for rigid pile and flexible pile with small value of slenderness ratio. The agreement is also good for flexible pile with higher slenderness ratios. A parametric study is carried out to investigate the effect of important parameters of foundation including pile slenderness ratio, pile aspect ratio and pile mass on the system natural frequency.     

Effect of embedment on the vertical capacity of bucket foundation in loose saturated sand: Physical modeling

ABSTRACT

Bucket foundations have been widely used for a variety of offshore applications. The effects of skirt length on ultimate bearing capacity of bucket foundation have been studied and reported in published scientific papers. However, few studies have addressed the behavior of bucket foundations in loose saturated sand. In this paper, a series of experimental investigations were performed to determine the bearing capacity of bucket foundation under uniaxial loading. The experiments were conducted on small-scale foundations under vertical loading in loose saturated sand. It was found that increasing the skirt length would enhance the bearing capacity of bucket foundation. As reflected in the present study, bearing strength might be enhanced more than 5 times in loose saturated sand in comparison to surface footing with equivalent diameter. Based on the experimental investigation, a depth factor was proposed to approximate bearing capacity of bucket foundations in terms of those for surface footing and embedment ratio. Moreover, the corresponding settlement of foundation at the failure load was found to increase with skirt length.     

A model for obliquely incident wave interacting with a multi-layered object

This paper presents an analytical solution for scattering of oblique incident, small amplitude, monochromatic wave trains by a stationary rigid multi-layered objects with rectangular cross-section. The object is infinite long and consists of multilayers, which can be either solid or permeable. This paper extends the previous work by Hu and Liu [1] from normal incident wave condition with a special object configuration to oblique incident waves with multi-layered object. The present model is validated with several existing solutions for normal/oblique waves interacting with a single object; excellent agreement is observed. New numerical results are presented to investigate the effects of incidence angle on reflection, transmission and energy loss coefficients for a combined floating and bottom-mounted permeable breakwater. A new floating board-cage breakwater is developed from the present model and its solutions are discussed in detail. A computer program, AWAS-P, has been updated so that it is applicable for both oblique and normal incident waves, while the object is multi-layered.     

Dynamic Response of Fluid-Single Leg Gravity Platform-Soil Interaction System

- An approximate method is presented to investigate the earthquake response of the fluid-single leg (shortened for S. L.) gravity platform-soil interaction system. By assuming a suitable form of the velocity potential of the radiation waves and by using the motion equation and the boundary conditions, the unknown coefficients can be obtained. Thereafter the function of frequency for the interaction system may also be obtained. In this paper, the difference of the system dynamic response between rigid foundation is analyzed and the influences of the various foundation geometric dimension and the various water-depth on the hydrodynamic loading and dynamic response of the system is illustrated.     

Experimental Study on Stability of Breakwaters with Penetrating Box Foundations

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Effect of strain-dependent dynamic properties of backfill and foundation soil on the external stability of geosynthetic reinforced waterfront retaining structure subjected to harmonic motion

A simplified method to determine the minimum length of reinforcement required for the external stability of waterfront reinforced soil structures under seismic conditions is presented. In the present analysis, strain-dependent dynamic properties (shear modulus and damping ratio) are used. The results obtained from the present method are well compared with the results of pseudo-static method of analysis. For the set of input parameters, the estimated minimum length of reinforcement required against sliding failure is nearly 27–29% higher for an input normalized frequency of 1.06 and is nearly 22–25% lower for another input normalized frequency of 1.94 when compared with the results of pseudo-static approach. This can be attributed to the mode change behaviour of the waterfront structure. In addition, the effect of foundation type on the external stability of waterfront reinforced soil structures has also been presented and it is found that the foundation type has a significant effect on the same. For the given set of input parameters, the length of minimum reinforcement required for a slope and vertical wall having a flexible foundation are about 26–28% and 32–38% larger than that of a slope and vertical wall with rigid foundation, respectively.     

Numerical Analysis of Hydrodynamic Pressure Induced by Fluid-Solid Impact

—As a further development of the authors'work(Huang and Qian,1993),in this paper a newnumerical method based on the time domain boundary element technique is proposed for solving fluid-sol-id coupling problems,in which a rigid body impacts normally on the calm surface of a half-space fluid.Afundamental solution to the half-space potential flow problem is first derived with the method of images.Then,an equivalent boundary integral equation in the Laplace transform domain is established by meansof Green's second identity.Through the inverse Laplace transform and discretization in both time andboundary of the fluid region,the numerical calculation for the problem under consideration has been car-ried out.Several examples demonstrate that the present method is more efficient than existing ones,fromwhich it is also seen that the shape of the impacting body has a considerable effect on the total impactforce.     

Analysis of Dynamic Stability of Ocean Gravity Structure Foundations

Based on unified equivalent harmonic loading on seabed foundation and energy approach suggested by the authors, the development of dynamic pore water pressure and stability of soil foundation for the vibration of ocean gravity structures excited by random wave loading are analysed. It may be seen that the present method for the study of dynamic problems of ocean gravity structure soil foundations is more reasonable and convenient.     

Vibrations of a simply supported plate carrying an elastically mounted concentrated mass

A large number of papers and technical reports are available on the technically important problem of structural elements executing transverse vibrations and carrying concentrated masses. In general it is assumed that the attachment is perfectly rigid. On the other hand, a rather limited amount of published work is available when the mass is elastically connected to the structure. The system then exhibits a more complex behavior than in the case of rigid attachment. The present study deals with the solution of the title problem using the well-known normal mode, sinusoidal eigenfunction expansions.     

Acoustic radiation from a pulsating spherical cap set on a spherical baffle near a hard/soft flat surface

Radiation of sound from a spherical piston, set in the side of a rigid sphere, undergoing harmonic radial surface vibrations in an acoustic halfspace is analyzed in an exact fashion using the classical method of separation of variables. The method of images in combination with the translational addition theorems for spherical wave functions is employed to take the presence of the flat boundary into account. The analytical results are illustrated with numerical examples in which the piston is pulsating near the rigid/compliant boundary of a water-filled halfspace. Subsequently, the basic acoustic field quantities such as the acoustic radiation impedance load and the radiation intensity distribution are evaluated for representative values of the parameters characterizing the system. Numerical results reveal the important effects of excitation frequency, source position, and cap angle on the acoustic radiation impedance load and the radiation intensity distribution. The presented work can lead to a better understanding of dynamic response of near-surface underwater transducers.     

The significance of earthquake-induced dynamic forces in coastal structures design

The dynamic forces of sea water and backfill soil acting on coastal embankments and the hydrodynamic forces on offshore breakwaters have been analyzed using a finite-difference scheme. A non-horizontal sea bottom is considered in the analysis. Both rigid and flexible embankments are included in the study. For a coastal embankment, the hydrodynamic pressure of sea water acting on the embankment face significantly increases as the slope of the sea bottom increases. On the other side of the embankment, the pore pressure and the interaction force between the soil and fluid will augment significantly when the backfill soil is compressed during earthquakes. When the sea-embankment-backfill soil interaction is included, the dynamic forces acting on a flexible embankment are much larger than those on a rigid one. The comparison of evaluating the sliding of a cassion in a case study of SPM by a conventional analysis and the present seismic analysis was made. The earthquake-induced dynamic pressures on both sides of the embankment (or breakwater) could be much larger than the force generated by the storm surge. The hydrodynamic (or seismic) analysis incorporating the effect of an earthquake should be included in the coastal embankment or offshore breakwater design, especially for the area with active earthquakes.     

沉箱式防波堤静力与动力稳定性设计体型分析

将沉箱式防波堤滑移和倾覆稳定性设计方法分为三类：静力设计方法、不允许沉箱出现滑移和摇摆角的动力设计方法、控制沉箱滑移量和摇摆角的动力设计方法。建立了满足给定抗滑和抗倾安全系数条件下，按静力设计方法确定沉箱尺度的控制方程，研究了波浪条件和安全系数取值对沉箱长宽比的影响。通过动力数值计算分析了沉箱长宽比对沉箱滑移量和摇摆角的影响，并与传统静力设计理论进行了比较，讨论了控制沉箱滑移量和摇摆角的动力设计方法的可行性。     

OTEC cold-water pipe research

Shelf-mounted Ocean Thermal Energy Conversion (OTEC) plants require installation of cold-water pipes (CWP) on slopes of40degto depths of 1000 m. In addition, tower platforms containing OTEC power systems may be located on lesser sloped terrain near shore and exposed to special environmental loading problems affecting foundation design. Shelf-mounted installations require careful attention to site selection and geotechnical considerations for foundation integrity on sloped surfaces. This paper primarily discusses research associated with cold-water pipe and foundation installations on steep slopes, although research continues on tower platforms located on the shelf. At least five nations are in various stages of development of OTEC systems for island applications. Each of their systems is either shelf mounted or land based and requires that a large diameter cold-water pipe be installed on a steep slope to provide cold water from 1000-m depths. In addition to the installation and deployment of the large cold-water pipe, the most significant problem is the design and installation of suitable foundations that will last for several decades. To date there is very little experience in the offshore industry for large installations on steep slopes. A major scale-model research project is underway on the slopes of the island of Hawaii. A section of pipe 2.4 m in diameter and 24 m long was installed using combination concrete foundations and joints. The pipe and foundations are fully instrumented to measure environmental loading forces due principally to currents and waves. Environmental measurements will also be taken in the test area. The measurement data will be used to validate available analytical models for subsequent use in aiding industry in providing more cost-effective designs for OTEC pipes and foundations.     

An investigation into the lateral loading response of shallow bucket foundations for offshore wind turbines through centrifuge modeling in sand

A shallow suction bucket is a new foundation type for offshore wind turbines. Due to its large size and bulky shape, the bucket and the soil within the bucket do not necessarily deform as a whole. Moreover, limited research has been conducted on the hydrodynamic wave influence on the shallow bucket bearing response. These factors pose great challenges to the shallow bucket foundation design. This paper presents a set of centrifuge tests of a shallow bucket model subjected to monotonic and dynamic lateral loads to study the lateral bearing response of shallow bucket foundations in the field under combined loads induced by wind, waves, etc. In addition to the routine measurements (e.g., load-displacement), the soil pressures on the bucket and the distribution and evolution of the excess pore pressures in the surrounding soils are also obtained. The deformation pattern of the bucket (e.g., rotation center) is revealed through displacement measurements. Finally, the proposed easy-to-use analytical equations using the limit equilibrium to assess the bearing capacity of bucket foundations, taking into account the influence of the soil strength degradation caused by hydrodynamic wave loadings, are found to yield good results upon comparison with the centrifuge data, providing useful guidelines for the design of shallow bucket foundations.     

Lateral Bearing Capacity of Multi-Bucket Foundation in Soft Ground

The bucket foundation is a new type of foundation for offshore application to intermediate-depth waters. It has advantages over conventional ones. However, there is no consensus in the analysis and design of this type of foundation. In this paper, the lateral bearing capacity and the failure mechanism of multi-bucket foundations are studied with different connection stiffness and bucket spacing by use of a three-dimensional finite element method. Based on the numerical analysis results, a limit analysis method of plasticity for evaluating the lateral bearing capacity of large-spacing multi-bucket foundation with rigid connection in soft ground is proposed. This method provides a simple procedure that gives results comparable to those from the finite element analyses.     

Modified moving particle method for modeling wave interaction with multi layered porous structures

Modified Moving Particle method in Porous media (MMPP) is introduced in this study for simulating a flow interaction with porous structures. By making use of the sub-particle scale (SPS) turbulence model, a unified set of equations are introduced for the entire computational domain and a proper boundary treatment is suggested at the interfaces between fluid and the porous media. Similar to the Incompressible Smoothed Particle Hydrodynamic (ISPH) method, a robust two-step semi-implicit scheme is utilized to satisfy the incompressibility criterion. By means of the introduced model, different flow regimes through multi-layered porous structures with arbitrary shapes can be simulated and there is no need to implement calibration factors.The developed MMPP model is then validated via simulating the experiments of Liu et al. (1999) i.e. linear and turbulent flows through porous dams and the experiments of Sakakiyama and Liu (2001) i.e. wave overtopping on a caisson breakwater protected by multi layered porous materials. Good agreements between numerical and laboratory data present the ability of the introduced model in simulating various flow regimes through multi-layered porous structures. It is concluded that the turbulent flow is an important issue particularly at the interface between the free fluid and porous media and consequently, the accuracy of the previous Lagrangian models that were based on neglecting the turbulence effect can be improved significantly by means of the present model. In addition, to satisfy the continuity criteria in the SPH models, it is necessary to modify density of particles in accordance with their porosity.     

Vibrating-Rocking Motion of Caisson Breakwater Under Breaking Wave Impact

The possible motions of a caisson breakwater under dynamic load excitation include vibrating, vibrating-sliding and vibrating-rocking motions. The models of vibrating motion and vibrating-sliding motion have been proposed in an early paper. In this paper, a model of vibrating-rocking motion of caisson breakwaters under breaking wave impact is presented, which can be used to simulate the histories of vibrating-rocking motion of caisson breakwaters. The effect of rocking motion on the displacement, rotation, sliding force and overturning moment of breakwaters is investigated. In case the overturning moment exceeds the stability moment of a caisson, the caisson may only rock. The caisson overturns only in case the rocking angle exceeds the critical angle. It is shown that the sliding force and overturning moment of breakwaters can be reduced effectively due to the rocking motion. It is proposed that some rocking motion should be allowed in breakwater design.     

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.