This study presents a non-linear spring model for modelling the backfill grout consolidation behind shield tunnel lining. Two important parameters, i.e. the time-dependent grout pressure decay induced by consolidation and the grout-cake thickness, were derived through a non-linear spring model and continuity equation. The proposed non-linear spring model for backfill grout consolidation was validated based on vertical pressure and strain relationships determined from an oedometer test. The derived equations were applied to the Groene Hart Tunnel (GHT) project. The results show that the calculated grout pressures agree well with the measured values. The calculated grout-cake thicknesses are in good agreement with the measured values. Two key factors influencing the grout consolidation are discussed: grout diffusion into the soil, and the initial distribution of the grout injection pressure. It is found that grout diffusion into the soil can dissipate the grout pressure quicker than grout consolidation. The distribution of the initial grout injection pressure dominates the final distributions of the grout pressure/grout cake around the tunnel lining.

这项研究提出了一个非线性弹簧模型，用于对盾构隧道衬砌后面的回填浆固结进行建模。通过非线性弹簧模型和连续性方程推导了两个重要参数，即固结引起的随时间变化的灌浆压力衰减和灌浆饼的厚度。基于里程表测试确定的垂直压力和应变关系，对提出的用于回填砂浆固结的非线性弹簧模型进行了验证。导出的方程式已应用于Groene Hart隧道（GHT）项目。结果表明，计算出的灌浆压力与实测值吻合良好。计算出的灌浆饼厚度与测量值非常吻合。讨论了影响灌浆固结的两个关键因素：灌浆扩散到土壤中，和灌浆注入压力的初始分布。发现灌浆向土壤中的扩散比灌浆固结能更快地消散灌浆压力。初始灌浆压力的分布支配着隧道衬砌周围灌浆压力/灌浆饼的最终分布。