Coupling Simulation of Groundwater Seepage and Land Subsidence
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摘要: 为了准确模拟由地下水开采导致渗流场和应力场发生变化而引起的地面沉降问题，根据Terzaghi有效应力原理，建立了地下水三维渗流与一维垂向固结的地下水渗流与地面沉降耦合数值模拟模型和以比奥固结理论为基础，并结合土体非线性流变理论，将土体本构关系推广到粘弹塑性，同时考虑土体力学参数及水力参数的动态变化关系的地下水渗流与地面沉降三维全耦合数值模拟模型.通过对比分析，结果表明：基于Terzaghi有效应力原理建立的地下水三维渗流与一维垂向固结地下水渗流与地面沉降耦合数值模拟模型模拟所得地面沉降与地下水位呈现出同步变化的趋势，并且当地下水位逐步回升至初始水位时，地面沉降也逐步回升到初始的零沉降状态.而以比奥固结为基础建立的地下水渗流与地面沉降三维全耦合数值模拟模型模拟所得的地面沉降变化趋势滞后于地下水位的变化趋势，并且当地下水位逐步回升至初始水位时，地面沉降虽也逐步得到回升，但回不到初始的零沉降状态，存在一个永久的残余沉降量.在土体参数变化方面，土体的孔隙度、渗透系数及泊松比均呈现先减小后增大的变化趋势，而弹性模量则呈现先增大后减小的变化趋势，与地面沉降的变化相对应.Abstract: In order to accurately simulate land subsidence caused by seepage field as a result of groundwater exploitation and stress field, two models are established in this study: one is groundwater seepage and land subsidence coupling numerical simulation model of the three-dimensional seepage of groundwater and one-dimensional vertical consolidation in light of Terzaghi effective stress principle; and the other is three-dimensional coupling model of groundwater seepage and land subsidence based on the Biot's consolidation theory combined with the nonlinear rheological theory of soil, extending the constitutive relation in Biot's consolidation theory to viscoelastic plasticity, taking into consideration of the dynamic change relationship of mechanical parameters and hydraulic parameters. The comparison and analysis show that the changing tendency of land subsidence calculated by groundwater seepage and land subsidence coupling numerical simulation model of the three-dimensional seepage of groundwater and one-dimensional vertical consolidation is the same as that of water level variation. When the water level falls back to the initial water level, total subsidence is 0. Land subsidence calculated by Biot's three-dimensional full coupling model falls behind of water level change. When the water level falls back to the initial water level, soil does not rebound to initial 0 subsidence state. There exists permanent remain of subsidence. In aspect of parameter change, porosity, hydraulic conductivity and Poisson's ratio have the tendency of decreasing first and then increasing. Modulus of elasticity has the tendency of decreasing first and then increasing. But these parameter values tend to be stable, corresponding to land subsidence variation.
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图 2 地下水三维渗流与一维垂向固结沉降耦合有限元计算机程序计算结果
Fig. 2. Schematic of groundwater three-dimensional seepage and one-dimensional vertically consolidated finite element computer program calculation results
图 3 比奥固结三维全耦合有限元计算机程序计算结果
Fig. 3. Schematic of Biot consolidation three-dimensional coupling finite element computer program calculation results
图 4 孔隙度及地下水位随应力期变化
Fig. 4. Variation between porosity, groundwater level and stress periods
图 5 垂向渗透系数及地下水位随应力期变化
Fig. 5. Variation between vertical hydraulic conductivity, groundwater level and stress periods
图 6 水平向渗透系数及地下水位随应力期变化
Fig. 6. Variation between horizontal hydraulic conductivity, groundwater level and stress periods
图 7 弹性模量及地下水位随应力期变化
Fig. 7. Variation between elastic modulus, groundwater level and stress periods
图 8 泊松比及地下水位随应力期变化
Fig. 8. Variation between Poisson's ratio, groundwater level and stress periods
表 1 地下水三维渗流与一维垂向固结沉降耦合模型地层参数
Table 1. Stratum parameters of the three-dimensional seepage of groundwater and one-dimensional vertical consolidation subsidence coupling model
参数分区 Kx(m·d-1) Ky(m·d-1) Kz(m·d-1) SS Sy(m -1) μske μskv 1 6×10-3 6×10-3 6×10-3 6×10-3 - 3.2×10-5 2.8×10-4 2 5×10-4 5×10-4 5×10-3 - 6×10-6 3.8×10-5 3.1×10-4 3 1.9 1.9 0.19 - 8×10-3 1.3×10-5 1.0×10-4 4 6×10-6 6×10-6 6×10-7 - 6×10-6 4.0×10-5 3.5×10-4 5 2.0 2.0 0.2 - 6×10-4 1.3×10-5 1.1×10-4 6 5×10-4 5×10-4 5×10-5 - 6×10-5 4.4×10-5 4.0×10-4 7 2.8 2.8 0.32 - 9×10-4 1.3×10-6 1.4×10-4 
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表 2 比奥固结地下水渗流与地面沉降三维全耦合模型地层参数
Table 2. Stratum parameters of the three-dimensional coupling model of groundwater seepage and land subsidence based on Biot consolidation
参数分区 K0x
(m·d-1)K0y
(m·d-1)K0z
(m·d-1)SS Sy
(m-1)r
(kN·m-3)φ
(°)C
(kPa)ν0 E0
(MPa)1 6×10-3 6×10-3 0.006 6×10-3 - 19.7 18 21 4.8×10-1 38 2 5×10-4 5×10-4 5×10-3 - 6×10-6 18.9 20 23 4.8×10-1 32 3 1.9 1.9 0.19 - 8×10-3 20.1 18 21 4.9×10-1 45 4 6×10-6 6×10-6 6×10-7 - 6×10-6 17.8 22 23 4.8×10-1 30 5 2.0 2.0 0.2 - 6×10-4 20.0 20 21 4.9×10-1 46 6 5×10-4 5×10-4 5×10-5 - 6×10-5 18.1 20 20 4.8×10-1 27 7 2.8 2.8 0.32 - 9×10-4 20.2 20 22 4.9×10-1 46
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