3-D fracture network dynamic simulation based on error analysis in rock mass of dam foundation

Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network model and measured data,a 3-D fracture network dynamic modeling method based on error analysis was proposed.Firstly,errors of four fracture volume density estimation methods(proposed by ODA,KULATILAKE,MAULDON,and SONG)and that of four fracture size estimation methods(proposed by EINSTEIN,SONG and TONON)were respectively compared,and the optimal methods were determined.Additionally,error index representing the deviation between fracture network model and measured data was established with integrated use of fractal dimension and relative absolute error(RAE).On this basis,the downhill simplex method was used to build the dynamic modeling method,which takes the minimum of error index as objective function and dynamically adjusts the fracture density and size parameters to correct the error index.Finally,the 3-D fracture network model could be obtained which meets the requirements.The proposed method was applied for 3-D fractures simulation in Miao Wei hydropower project in China for feasibility verification and the error index reduced from 2.618 to 0.337.

Nonlinear transverse vibrations of a slightly curved beam carrying a concentrated mass

In this study, a slightly curved Euler Bernoulli beam carrying a concentrated mass was handled. The beam was resting on an elastic foundation and simply supported at both ends. Effects of the concentrated mass on nonlin- ear vibrations were investigated. Sinusoidal and parabolic type functions were used as curvature functions. Equations of motion have cubic nonlinearities because of elongations during vibrations. Damping and harmonic excitation terms were added to the equations of motion. Method of mul- tiple scales, a perturbation technique, was used for solving integro-differential equation analytically. Natural frequen- cies were calculated exactly for different mass ratios, mass locations, curvature functions, and linear elastic foundation coefficients. Amplitude-phase modulation equations were found by considering primary resonance case. Effects of nonlinear terms on natural frequencies were calculated. Frequency-amplitude and frequency-response graphs were plotted. Finally effects of concentrated mass and chosen curvature function on nonlinear vibrations were investigated.

Effect of seismic wave propagation in massed medium on rate-dependent anisotropic damage growth in concrete gravity dams

Seismic modeling of massive structures requires special caution,as wave propagation effects significantly affect the responses.This becomes more crucial when the path-dependent behavior of the material is considered.The coexistence of these conditions renders numerical earthquake analysis of concrete dams challenging.Herein,a finite element model for a comprehensive nonlinear seismic simulation of concrete gravity dams,including realistic soil-structure interactions,is introduced.A semi-infinite medium is formulated based on the domain reduction method in conjunction with standard viscous boundaries.Accurate representation of radiation damping in a half-space medium and wave propagation effects in a massed foundation are verified using an analytical solution of vertically propagating shear waves in a viscoelastic half-space domain.A rigorous nonlinear finite element model requires a precise description of the material response.Hence,a microplane-based anisotropic damage-plastic model of concrete is formulated to reproduce irreversible deformations and tensorial degeneration of concrete in a coupled and rate-dependent manner.Finally,the Koyna concrete gravity dam is analyzed based on different assumptions of foundation,concrete response,and reservoir conditions.Comparison between responses obtained based on conventional assumptions with the results of the presented comprehensive model indicates the significance of considering radiation damping and employing a rigorous constitutive material model,which is pursued for the presented model.