外文翻译--由隧道排水引起的地面反应曲线(编辑修改稿)

外文翻译--由隧道排水引起的地面反应曲线(编辑修改稿)内容摘要：

cement of the tunnel increases. Lastly, the ground reaction curve shows the increasing trends of radial displacement as the internal pressure of the tunnel decreases. Tunnelling below the ground water table induces additional seepage stresses (Shin et al., 2020), and the seepage forces are likely to have a strong influence on the ground reaction curve. Previous studies on the ground reaction curve by Stille (1989), Wang (1994), CarranzaTorres( 2020), Sharan (2020), and Oreste (2020) did not consider seepage forces. The effects of seepage forces on the tunnel face or the support system were studied by Muir Wood (1975), Curtis (1976), Atkinson (1983), Schweiger (1991), Fernandez and Alveradez (1994), Fernandez (1994), Lee and Nam (2020), Bobet (2020), Shin et al. (2020). A simplified analytical solution of the ground reaction curve was suggested by Lee et al. (2020)。 however, mathematical solutions of ground reaction curves influenced by seepage forces have not been suggested. In this study, based on these previous studies, the theoretical solutions of the ground reaction curve considering seepage forces due to groundwater flow under steadystate flow were derived. THEORETICAL SOLUTION OF GROUND REACTION CURVE WITH CONSIDERATION OF SEEPAGE FORCES Theoretical solution for stress It is assumed that a soilmass behaves as an isotropic, homogeneous and permeable medium. Also, an elastoplastic model based on a linear MohrCoulomb yield criterion is adopted in this study, as indicated in Figure 1. σ1′ = kσ3′ + (k −1)a (1) Here σ1′ indicates the major principal,σ3′ is the minor principal stress, k=tan2(45 + ∅2),a= ctan∅, where k and a are the MohrCoulomb constants, c is the cohesion, and ∅ is the friction angle. Figure 2 shows a circular opening of radius r0 with k0 soilmass subject to a hydrostatic in situ stress,σ0′ . The opening inner surface is subject to the outward radial pressure to the tunnel surface,pi(k0 means the ratio of effective vertical stress and horizontal stress). Considering all the stresses on an infinitesimal element abcd of unit thickness during excavation of a circular tunnel in Figure 3, when ∂θ is small, the equilibrium of radial forces with respect to r and can be expressed as follows: If the tunnel is excavated under the groundwater table, then it acts as a drain. The body force is the seepage stress, as illustrated in Figure 3. In this state, ir and iθ are the hydraulic gradients in the r and θ directions,respectively, and γw is the unit weight of the groundwater. Therefore, (2) and (3) can be rewritten as follows: If the stress distribution is symmetrical with respect to the axis O in Figure 3, then the stress ponents do not vary with angular orientation, θ , and therefore, they are functions of the radial distance r only. Accordingly, (6) reduces to the single equation of equilibrium as follows: For the plastic region, (1) can be modified as follows: Where kr=tan2(45 + ∅r2 ),ar = crtan∅r, where ke and ar are the MohrCoulomb constants, c r is the cohesion, and ∅ ris the friction angle in the plastic region. Substituting (9) into (8) and solving it with the boundary conditions σr′ = pi at r=r0 Then, the radial and circumferentia。