In this study, analytical solutions of vertical deformation of ground surface and horizontal displacement of strata are derived combining the Mindlin solution and the mirror method due to rectangular pipe jacking tunneling in composite strata, which considers the combined effect of five factors of additional excavation pressure, friction of rectangular pipe jacking and soils, segment-soil friction, grouting filling and strata loss, respectively. The theoretical calculation results were verified against the measured data in two project cases. Moreover, effect factors of rectangular jacking pipe cross-sectional dimensions, embedment of tunnel axial depth, elasticity modulus on the interlayer and the Poisson's ratio of the interlayer on strata deformation is investigated. The results imply that the theoretical calculation values obtained using this method are more closely correlated with the observed values compared to those computed using the single stratum model. The primary cause of terrene upheaval in front of the working surface is the increased excavation pressure on the working face and the horizontal displacement of the deep soils and the surface subsidence behind the excavation face is resulting from the soil loss as the main influencing factor. The varying cross-section size of pipe jacking is able to impact on the vertical deformation of the soil, but it has a limited impact on the lateral displacement of the strata. The affection of the buried depth of the tunnel axis on strata deformation is more notable in the rectangular pipe jacking construction. As the axial tunnel depth growth, the ground surface maximum subsidence value gradually decreases, while the crest value of horizontal distortion mildly increases. When the rise of the interlayered modulus of elasticity, the maximum earth surface subsidence enlarged gradually while the subsidence trough slight diminution. Moreover, the greatest horizontal displacement exhibits a relatively minor fluctuation, but there is a trend of upward movement in the position. The influence of Poisson's ratio of the interlayer on the strata deformation is comparatively weak.

中文翻译：

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复合层状地基矩形顶管施工引起地层变形的数学模型


本研究结合Mindlin解和镜像法，推导了复合地层矩形顶管施工地表竖向变形和地层水平位移的解析解，考虑了附加开挖压力5个因素的综合影响，分别为矩形顶管与土体的摩擦力、管片与土体的摩擦力、注浆充填和地层损失。理论计算结果与两个工程实例的实测数据进行了验证。并研究了矩形顶管截面尺寸、隧道轴向埋深、夹层弹性模量、夹层泊松比对地层变形的影响因素。结果表明，与使用单层模型计算的结果相比，使用该方法获得的理论计算值与观测值的相关性更加紧密。工作面前方地表隆起的主要原因是工作面开挖压力增大和深层土体水平位移，而开挖面后地表沉降则以土壤流失为主要影响因素。顶管断面尺寸的变化能够对土体的竖向变形产生影响，但对地层的横向位移影响有限。矩形顶管施工中隧道轴线埋深对地层变形的影响更为显着。随着隧道轴向埋深的增长，地表最大沉降值逐渐减小，而水平变形峰值则略有增大。 当层间弹性模量升高时，地表最大沉降逐渐增大，而沉降槽略有减小。而且最大水平位移波动较小，但位置有向上移动的趋势。夹层泊松比对地层变形的影响较弱。