Mathematical and Numerical Modeling in Maritime Geomechanics

A theoretical and numerical framework to model the foundation of marine offshore structures is presented. The theoretical model is composed by a system of partial differential equations describing coupling between seabed solid skeleton and pore fluids (water, air, oil,…) combined with a system of ordinary differential equations describing the specific constitutive relation of the seabed soil skeleton. Once the theoretical model is described, the finite element numerical procedure to achieve an approximate solution of the governing equations is outlined. In order to validate the proposed theoretical and numerical framework the seaward tilt mechanism induced by the action of breaking waves over a vertical breakwater is numerically reproduced. The results numerically attained are in agreement with the main conclusions drawn from the literature associated with this failure mechanism

Boundary element approach to the dynamic stiffness functions of circular foundations

A boundary element approach for time harmonic axisymmetric problems using the complete space point load fundamental solution is presented. The fundamental solution is integrated numerically along the azimuthal co-ordinate of each axisymmetric element. To increase the accuracy of the numerical integration a simple co-ordinate transformation is proposed. The approach is applied to the computation of the dynamic stiffness functions of rigid circular foundations on layered viscoelastic soils. Three different sites are considered: a uniform half-space, a soil layer on a half-space, and a soil consisting of four horizontal layers and a compliant half-space. The numerical results obtained by the proposed approach for surface circular foundations are very close to corresponding published results obtained by different procedures.

Study of bond stress-slip relationship and radial dilation in prestressed concrete

This paper presents two test procedures for evaluating the bond stress–slip and the slip–radial dilation relationships when the prestressing force is transmitted by releasing the steel (wire or strand) in precast prestressed elements. The bond stress–slip relationship is obtained with short length specimens, to guarantee uniform bond stress, for three depths of the wire indentation (shallow, medium and deep). An analytical model for bond stress–slip relationship is proposed and compared with the experimental results. The model is also compared with the experimental results of other researchers. Since numerical models for studying bond-splitting problems in prestressed concrete require experimental data about dilatancy angle (radial dilation), a test procedure is proposed to evaluate these parameters. The obtained values of the radial dilation are compared with the prior estimated by numerical modelling and good agreement is reached

Numerical and experimental study of overtopping and failure of rockfill dams

This paper aims to present and validate a numerical technique for the simulation of the overtopping and onset of failure in rockfill dams due to mass sliding. This goal is achieved by coupling a fluid dynamic model for the simulation of the free surface and through-flow problems, with a numerical technique for the calculation of the rockfill response and deformation. Both the flow within the dam body and in its surroundings are taken into account. An extensive validation of the resulting computational method is performed by solving several failure problems on physical models of rockfill dams for which experimental results have been obtained by the authors.

The use of non-reflecting boundary conditions in soil dynamics

In this paper some aspects of the use of non-reflecting boundaries in dynamic problems, analyzed in time domain, are considered. Current trends for treating the above mentioned problems are summarized with a particular emphasis on the use of numerical techniques, such as Boundary Element Method (BEM) or mixed and hybrid formulations, Finite Element Method (FEM) plus BEM. As an alternative to these methods, an easy time domain boundary condition, obtained from the well known consistent transmitting boundary developed by Waas for frequency domain analysis, can be applied to represent the reactions of the unbounded soil on the interest zone. The behaviour of this proposed boundary condition is studied when waves of different frequency to the one used for its obtention are acting on the physical edge of the model. As an application example,an analysis is made of the soil-structure interaction of a rigid strip foundation on a horizontal non-linear elastic layer on bed rock. The results obtained suggest the need of time domain solutions for this type of problem

Seismic earth thrust against massive building walls

The problem of earth thrust for a massive building in a seismic environment is analysed. Intertial and kinematic soil-structure interactions are considered by modelling the soil and the structure together. The problem is solved in the frequency domain by using the computer code FLUSH. Results show that the horizontal component of the seismic earth thrust is much greater than that obtained when applying the Mononobe-Okabe theory. This study establishes a set of conclusicns and recommendations for both design and practical purposes, and proposes future lines of investigation.

Analytical bearing capacity of strip footing in weightless materials with power-law failure criteria

Sokolovskii’s method of characteristics is extended to provide analytical solutions for the ultimate load at the moment of plastic failure under plane-strain conditions of shallow strip foundations on weightless rigid-plastic media with a noncohesive power-law failure envelope. The formulation is made parametrically in terms of the instantaneous friction angle, and the key idea to obtain the bearing capacity is that information can be transmitted from the free surface (where external loads are known) to the contact plane of the foundation. The methodology can consider foundations adjacent to a slope, external surcharges at the free surface, and inclined loads (both on the slope and on the foundation). Sensitivity analyses illustrate the influence on bearing capacity of changes in the different geometrical parameters involved. An application example is presented and design plots are provided, and model predictions are compared with results of bearing capacity tests under low gravity.