Abstract
Based on the repeated “tensile-compressive-tensile-compressive” stress characteristics of tunnel-base concrete structure, double scalar damage variables were defined using the concrete stochastic damage mechanics. The elastoplastic Helmholtz free energy was corrected by introducing the hardening parameter. A stochastic dynamic damage constitutive model with the nonlinear and strain-rate effect behavior of concrete was derived via dynamic expansion of damage energy based on the principle of energy dissipation. An “elastic prediction-plastic correction” numerical analysis algorithm was developed based on the solution of the probability density evolution equation. Secondary development of the algorithm was achieved using the Universal Distinct Element Code (UDEC) for numerical calculation of the proposed constitutive model. A comparison was made between the calculation result and the result of laboratory rapid uniaxial compression test to verify the model. Dynamic response and damage features of the tunnel-base structure in three working conditions, i.e., filled layer without seam, filled layer with seam and ground water, and filled layer with seam but without water, were analyzed based on engineering practice. According to the analysis, structural vibration response was intensified in the presence of a seam. With and without groundwater, the vertical dynamic stress attenuation at both sides of the seam was 41.07% and 47.13%, respectively; vertical vibration acceleration was attenuated by 91.17% and 91.73%, respectively; and the acceleration amplitude at the upper structure of the seam increased by 724.67% and 765.02%, respectively. Groundwater in the seam would aggravate damage accumulation. It could be seen from the analysis that the current design parameters satisfied the antifatigue requirements within the design reference period at a train speed of 300 km/h when there was no seam in the tunnel-base concrete structure with IV-class surrounding rocks. When there was a seam in the tunnel-base concrete structure, however, antifatigue life was 56 years in the presence of groundwater and 62 years without groundwater, which suggested that current design parameters failed to satisfy the antifatigue requirements within the design reference period.
Highlights
High-speed railways have been constructed at a furious pace in China, which makes trips more convenient and has even fundamentally changed the conventional lifestyle
As a two-dimensional universal distinct element code, Universal Distinct Element Code (UDEC) is a tool providing geotechnical engineers with accurate and effective analysis using explicit problem-solving ability. e explicit problem-solving scheme has been widely used since it provides unstable physical processes with stable solutions and simulates the failure process of the object [13]
When the generalized probability density evolution equation is an explicit expression, an analytical solution exists in the given initial condition
Summary
High-speed railways have been constructed at a furious pace in China, which makes trips more convenient and has even fundamentally changed the conventional lifestyle. A stochastic dynamic damage constitutive model for high-speed railway tunnel-base concrete was derived from the improved elastoplastic Helmholtz free energy and energy-dissipation principle using the stochastic damage theory according to the energy variable theory and the laws of thermodynamics. Since concrete damage is an irreversible thermodynamic process and there was strain with energy dissipation during concrete failure process, the Helmholtz free energy was the state function of effective strain tensor ε and damage variable:. Where μD is the mean function of damage D; subscript j (j 1, 2) of εe is the elastic strain in the direction of max or min principal stress; F is the one-dimensional function of stochastic field (x); θ is the equivalent coefficient of energy transformation, and the subscript i (i 1, 2) of θ is the equivalent transformation coefficient of tensile and compressive energy, respectively; V2D is the variance of damage D; and η is the absolute value of the relative distance between independent variables of the probability density function in the one-dimensional stochastic field. Where ß0initial± is the threshold of the initial energy damage rate that physically signifies that there will be damage when the damage energy release rate is higher than this threshold. ß0initial+ is the linear limit strength of concrete under tension, which is the uniaxial tensile strength; ß0initial-is the linear limit strength of concrete under compression, ß0initial- (1 − α) f0, f0 (0.3 – 0.5) fc, where fc is the uniaxial compressive strength; and α is the function of the ratio Δ between biaxial compressive yield strength fby- and uniaxial compressive yield strength fy-. e calculation formula for α is α Δ− 1,
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