Comparison of the Dynamic Response of a Saturated Soil Between Two Models

By comparing the dynamic responses of saturated soil to Biot's and Yamamoto's models, the properties of the two models have be pointed out. First of all, an analysis has been made for energy loss of each model from the basic equations. Then the damping of elastic waves in coarse sand and fine sand with loading frequency and soil's parameters have been calculated and the representation of viscous friction and Coulomb friction in the two models has been concluded. Finally, the variations of loading wave damping and stress phase angles with water depth and soil's parameters have been obtained as loading waves range in ocean waves.

Comparison of existing poroelastic models for wave damping in a porous seabed

Mechanism of wave-seabed interaction has been extensively studied by coastal geotechnical engineers in recent years. Numerous poro-elastic models have been proposed to investigate the mechanism of wave propagation on a seabed in the past. The existing poro-elastic models include drained model, consolidation model, Coulomb-damping model, and full dynamic model. However, to date, the difference between the existing models is unclear. In this paper, the fully dynamic poro-elastic model for the wave-seabed interaction will be derived first. Then, the existing models will be reduced from the proposed fully dynamic model. Based on the numerical comparisons, the applicable range of each model is also clarified for the engineering practice.

Optimal bounded control of first-passage failure of quasi-integrable Hamiltonian systems with wide-band random excitation

The optimal bounded control of quasi-integrable Hamiltonian systems with wide-band random excitation for minimizing their first-passage failure is investigated. First, a stochastic averaging method for multi-degrees-of-freedom (MDOF) strongly nonlinear quasi-integrable Hamiltonian systems with wide-band stationary random excitations using generalized harmonic functions is proposed. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximizinig reliability and maximizing mean first-passage time are formulated based on the averaged It$\ddot{\rm o}$ equations by applying the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraints. The relationship between the dynamical programming equations and the backward Kolmogorov equation for the conditional reliability function and the Pontryagin equation for the conditional mean first-passage time of optimally controlled system is discussed. Finally, the conditional reliability function, the conditional probability density and mean of first-passage time of an optimally controlled system are obtained by solving the backward Kolmogorov equation and Pontryagin equation. The application of the proposed procedure and effectiveness of control strategy are illustrated with an example.

Orientation-based Continuum Damage Models for Rocks

A general formulation of the Helmholtz free energy used in thermodynamics of damage process of rocks is derived within a multi-scale framework. Such a physically-based thermodynamic state potential has a hybrid, discrete/continuum, nature in the sense tha

Flood Routing Models in Confluent and Dividing Channels

By introducing a water depth connecting formula, the hydraulic equations in the dividing channel system were coupled and the relation of discharge distribution between the branches of the dividing channels can be yielded. In this manner, a numerical model for the confluent channels was established to study the variation of backwater effects with the parameters in the channel junction. The meeting of flood peaks in the mainstream and tributary can be analyzed with this model. The flood peak meeting is found to be a major factor for the extremely high water level in the mainstream during the 1998 Yangtze River flood. Subsequently the variations of discharge distribution and water level with channel parameters between each branch in this system were studied as well. As a result, flood evolution caused by Jingjiang River shortcut and sediment deposition in the entrance of dividing channels of the Yangtze River may be qualitatively elucidated. It is suggested to be an effective measure for flood mitigation to enhance regulation capability of reservoirs available upstream of the tributaries and harness branch entrance channels.

Modeling Nonlinear Peeling of Ductile Thin Films-Critical Assessment of Analytical Bending Models Using FE Simulations

Three analytical double-parameter criteria based on a bending model and a two-dimensional finite element analysis model are presented for the modeling of ductile thin film undergoing a nonlinear peeling process. The bending model is based on different governing parameters: (1) the interfacial fracture toughness and the separation strength, (2) the interfacial fracture toughness and the crack tip slope angle, and (3) the interfacial fracture toughness and the critical Mises effective strain of the delaminated thin film at the crack tip. Thin film nonlinear peeling under steady-state condition is solved with the different governing parameters. In addition, the peeling test problem is simulated by using the elastic-plastic finite element analysis model. A critical assessment of the three analytical bending models is made by comparison of the bending model solutions with the finite element analysis model solutions. Furthermore, through analyses and comparisons for solutions based on both the bending model and the finite element analysis model, some connections between the bending model and the finite element analysis model are developed. Moreover, in the present research, the effect of different selections for cohesive zone shape on the ductile film peeling solutions is discussed.

First-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems

An n degree-of-freedom Hamiltonian system with r (1¡r¡n) independent 0rst integrals which are in involution is calledpartially integrable Hamiltonian system. A partially integrable Hamiltonian system subject to light dampings andweak stochastic excitations is called quasi-partially integrable Hamiltonian system. In the present paper, the procedures for studying the 0rst-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems are proposed. First, the stochastic averaging methodfor quasi-partially integrable Hamiltonian systems is brie4y reviewed. Then, basedon the averagedIt ˆo equations, a backwardKolmogorov equation governing the conditional reliability function, a set of generalized Pontryagin equations governing the conditional moments of 0rst-passage time and their boundary and initial conditions are established. After that, the dynamical programming equations and their associated boundary and 0nal time conditions for the control problems of maximization of reliability andof maximization of mean 0rst-passage time are formulated. The relationship between the backwardKolmogorov equation andthe dynamical programming equation for reliability maximization, andthat between the Pontryagin equation andthe dynamical programming equation for maximization of mean 0rst-passage time are discussed. Finally, an example is worked out to illustrate the proposed procedures and the e9ectiveness of feedback control in reducing 0rst-passage failure.

Designing Of Partial Similarity Models And Evaluation Method In Polymer Flooding Experiment

Based on the scaling criteria of polymer flooding reservoir obtained in our previous work in which the gravity and capillary forces, compressibility, non-Newtonian behavior, absorption, dispersion, and diffusion are considered, eight partial similarity models are designed. A new numerical approach of sensitivity analysis is suggested to quantify the dominance degree of relaxed dimensionless parameters for partial similarity model. The sensitivity factor quantifying the dominance degree of relaxed dimensionless parameter is defined. By solving the dimensionless governing equations including all dimensionless parameters, the sensitivity factor of each relaxed dimensionless parameter is calculated for each partial similarity model; thus, the dominance degree of the relaxed one is quantitatively determined. Based on the sensitivity analysis, the effect coefficient of partial similarity model is defined as the summation of product of sensitivity factor of relaxed dimensionless parameter and its relative relaxation quantity. The effect coefficient is used as a criterion to evaluate each partial similarity model. Then the partial similarity model with the smallest effect coefficient can be singled out to approximate to the prototype. Results show that the precision of partial similarity model is not only determined by the number of satisfied dimensionless parameters but also the relative relaxation quantity of the relaxed ones.

Transitions Between Different Contact Models

The transitions between the different contact models which include the Hertz, Bradley, Johnson-Kendall-Roberts (JKR), Derjaguin-Muller-Toporov (DMT) and Maugis-Dugdale (MD) models are revealed by analyzing their contact pressure profiles and surface interactions. Inside the contact area, surface interaction/adhesion induces tensile contact pressure around the contact edge. Outside the contact area, whether or not to consider the surface interaction has a significant influence on the contact system equilibrium. The difference in contact pressure due to the surface interaction inside the contact area and the equilibrium influenced by the surface interaction outside the contact area are physically responsible for the different results of the different models. A systematic study on the transitions between different models is shown by analyzing the contact pressure profiles and the surface interactions both inside and outside the contact area. The definitions of contact radius and the flatness of contact surfaces are also discussed. (C) Koninklijke Brill NV, Leiden, 2008.

Peeling Experiments Of Ductile Thin Films Along Ceramic Substrates - Critical Assessment Of Analytical Models

Two types of peeling experiments are performed in the present research. One is for the Al film/Al2O3 substrate system with an adhesive layer between the film and the substrate. The other one is for the Cu film/Al2O3 substrate system without adhesive layer between the film and the substrate, and the Cu films are electroplated onto the Al2O3 substrates. For the case with adhesive layer, two kinds of adhesives are selected, which are all the mixtures of epoxy and polyimide with mass ratios 1:1.5 and 1:1, respectively. The relationships between energy release rate, the film thickness and the adhesive layer thickness are measured during the steady-state peeling process. The effects of the adhesive layer on the energy release rate are analyzed. Using the experimental results, several analytical criteria for the steady-state peeling based on the bending model and on the two-dimensional finite element analysis model are critically assessed. Through assessment of analytical models, we find that the cohesive zone criterion based on the beam bend model is suitable for a weak interface strength case and it describes a macroscale fracture process zone case, while the two-dimensional finite element model is effective to both the strong interface and weak interface, and it describes a small-scale fracture process zone case. (C) 2007 Elsevier Ltd. All rights reserved.

Statistical analysis of synthetic earthquake catalogs generated by models with various levels of fault zone disorder

The stress release model, a stochastic version of the elastic rebound theory, is applied to the large events from four synthetic earthquake catalogs generated by models with various levels of disorder in distribution of fault zone strength (Ben-Zion, 1996) They include models with uniform properties (U), a Parkfield-type asperity (A), fractal brittle properties (F), and multi-size-scale heterogeneities (M). The results show that the degree of regularity or predictability in the assumed fault properties, based on both the Akaike information criterion and simulations, follows the order U, F, A, and M, which is in good agreement with that obtained by pattern recognition techniques applied to the full set of synthetic data. Data simulated from the best fitting stress release models reproduce, both visually and in distributional terms, the main features of the original catalogs. The differences in character and the quality of prediction between the four cases are shown to be dependent on two main aspects: the parameter controlling the sensitivity to departures from the mean stress level and the frequency-magnitude distribution, which differs substantially between the four cases. In particular, it is shown that the predictability of the data is strongly affected by the form of frequency-magnitude distribution, being greatly reduced if a pure Gutenburg-Richter form is assumed to hold out to high magnitudes.

Long-range automaton models of earthquakes: Power-law accelerations, correlation evolution, and mode-switching

We introduce a conceptual model for the in-plane physics of an earthquake fault. The model employs cellular automaton techniques to simulate tectonic loading, earthquake rupture, and strain redistribution. The impact of a hypothetical crustal elastodynamic Green's function is approximated by a long-range strain redistribution law with a r(-p) dependance. We investigate the influence of the effective elastodynamic interaction range upon the dynamical behaviour of the model by conducting experiments with different values of the exponent (p). The results indicate that this model has two distinct, stable modes of behaviour. The first mode produces a characteristic earthquake distribution with moderate to large events preceeded by an interval of time in which the rate of energy release accelerates. A correlation function analysis reveals that accelerating sequences are associated with a systematic, global evolution of strain energy correlations within the system. The second stable mode produces Gutenberg-Richter statistics, with near-linear energy release and no significant global correlation evolution. A model with effectively short-range interactions preferentially displays Gutenberg-Richter behaviour. However, models with long-range interactions appear to switch between the characteristic and GR modes. As the range of elastodynamic interactions is increased, characteristic behaviour begins to dominate GR behaviour. These models demonstrate that evolution of strain energy correlations may occur within systems with a fixed elastodynamic interaction range. Supposing that similar mode-switching dynamical behaviour occurs within earthquake faults then intermediate-term forecasting of large earthquakes may be feasible for some earthquakes but not for others, in alignment with certain empirical seismological observations. Further numerical investigation of dynamical models of this type may lead to advances in earthquake forecasting research and theoretical seismology.

First-passage failure of quasi-integrable Hamiltonian systems

The first-passage failure of quasi-integrable Hamiltonian si-stems (multidegree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations) is investigated. The motion equations of such a system are first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving these equations with suitable initial and boundary conditions. Two examples are given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the procedure.