高速铁路隧道基底混凝土结构的随机损伤模型

Stochastic Damage Model for Concrete Structure of High-Speed Railway Tunnel Substrate

基于热力学原理与能量耗散原理,针对高速铁路隧道基底混凝土结构"拉—压—拉—压"反复受力特点,定义双标量损伤变量,引入硬化函数,建立混凝土受拉、受压条件下基于修正弹塑性亥姆霍兹自由能的随机损伤本构模型。在有效应力空间,根据塑性力学正交法则推导损伤变量的演化法则;在概率密度演化方程求解的基础上,建立"弹性预测—塑性修正—损伤修正"数值分析算法,并进行程序二次开发,实现对随机损伤本构模型的求解。通过与混凝土单轴拉伸、单轴压缩室内试验结果对比,验证所建立随机损伤本构模型的准确性和适用性。该模型既可在均值意义上反映混凝土受拉、受压的应力—应变关系,也可以在概率意义上模拟其离散范围,较为全面地反映了混凝土受力行为的非线性与随机性;可用于计算分析隧道基底混凝土结构的损伤演化规律及损伤疲劳寿命。

Based on the principles of thermodynamics and energy dissipation,and focused on the＂tension to compression＂repeated stress characteristics of high-speed railway tunnel substrate concrete structure,a double scalar damage variable was defined.By introducing a hardening function and revising the elastoplastic Helmholtz free energy,a stochastic damage constitutive model for concrete structure of highspeed railway tunnel substrate was established.In the effective stress space,the damage evolution law of damage variable was derived according to the orthogonal rule of plastic mechanics.Combined with the probability density evolution equation theory,the three-step numerical framework,i.e., ＂elastic predictor-plastic corrector-damage corrector＂was provided,and a secondary development program was developed to achieve the numerical calculation of the proposed constitutive model.Uniaxial tension and uniaxial compression numerical tests of concrete were conducted,the results were compared with laboratory tests,through which,the accuracy and applicability of the proposed model were verified.Moreover,the proposed model can also reflect stress-strain relationship of concrete in the mean sense,and simulate its discrete range in the probabilistic sense.By applying it,the nonlinear and stochastic characteristics of concrete mechanical behavior can be comprehensively reflected and can also be used to calculate the damage evolution law and damage fatigue life of tunnel substrate concrete structure.