基于分数阶模型的隧道周围土体非线性流变固结分析

Nonlinear rheological consolidation analysis of soil around tunnel based on fractional order model

考虑隧道周围饱和软土压缩性和渗透性非线性变化,建立二维非线性固结控制方程,引入分数阶Merchant模型考虑土体流变特性影响,采用Douglas-Jone格式的交替隐式差分法对方程进行求解.通过与现有解析解进行对比,验证了本研究解的正确性.利用得到的差分解进行参数分析,研究隧道周围饱和软土的非线性流变固结特性.结果表明,隧道渗漏模式、初始渗透系数和渗透指数对土体固结速率影响较大,透水通道越多、初始渗透系数越大、渗透指数越小,土体固结速率越快,而压缩指数对固结速率的影响较小;渗透各向异性系数对固结速率有较大影响,在进行固结性状分析时,应当充分考虑土体不同方向渗透系数的差异;当考虑土体流变特性时,土体固结速率显著减小,但当初始渗透系数增大到一定程度时,土体流变特性对土层固结速率的影响可以忽略.

The two-dimensional nonlinear consolidation control equation was established,considering the nonlinear changes of compressibility and permeability of the saturated soft soil around the tunnel.The fractional-order Merchant model was introduced to consider the influence of soil rheological properties,and the alternating implicit difference method in Douglas-Jone format was used to solve the equation.The correctness of the solutions was verified by the comparison with the existing analytical solutions.The nonlinear rheological consolidation characteristics of the saturated soft soil around the tunnel were investigated by using the obtained difference decomposition for parametric analysis.Results show that the tunnel leakage pattern,initial permeability coefficient,and permeability index have a large influence on the consolidation rate of the soil,and the more the permeable channels,the larger the initial permeability coefficient,and the smaller the permeability index,the faster the consolidation rate of the soil,while the compression index has a smaller influence on the consolidation rate.The coefficient of permeability anisotropy has a significant effect on the rate of consolidation,and the difference in permeability coefficients in different directions of the soil should be fully considered in the analysis of consolidation properties.When considering the rheological properties of the soil,the consolidation rate of the soil slows down significantly,but when the initial permeability coefficient increases to a certain degree,the effect of the rheological properties of the soil on the consolidation rate of the soil layer can be ignored.