Coupled model for one-dimensional nonlinear consolidation and contaminant transport in a compacted clay liner considering mechanical-chemical loading
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摘要: 针对力学-化学荷载下压实黏土垫层中一维固结与污染物运移耦合过程，考虑了土体压缩性和渗透性的非线性变化，建立了相应的耦合模型，并利用有限差分法对该模型进行了求解。通过与有限元软件COMSOL Multiphysics计算结果和已有解析解计算结果展开对比分析，对所建耦合模型正确性进行了验证。基于所建模型，比较研究了两种假定情况下力学荷载pu和渗滤液中污染物浓度Cb对耦合过程的影响。结果表明：当忽略非线性压缩和渗透特性时，力学荷载pu的增大会使污染物运移速率降低；但当考虑非线性压缩和渗透特性时，pu的增大会使污染物运移速率增大，这主要是由于污染物运移过程会受对流和扩散作用的综合影响。污染物浓度Cb的增大会使沉降量增大，超孔隙水压力值减小，也会使得污染物运移速率降低；相比于忽略非线性的情况，考虑非线性情况下Cb对沉降量、超孔隙水压力和污染物运移速率的影响会减弱。Abstract: For the coupled process of one-dimensional consolidation and contaminant transport in a compacted clay liner under mechanical-chemical loading, the corresponding coupled model is established by considering the nonlinear changes of compressibility and permeability of soils, and the finite difference method is adopted for solving the model. The correctness of the proposed coupled model is validated by comparing its results with the calculation ones of the finite element software COMSOL Multiphysics and the existing analytical solution. Based on the proposed model, the effects of mechanical loading pu and contaminant concentration Cb in leachate on the coupled process under two assumptions are compared and investigated. The results show that when the nonlinear compressibility and permeability characteristics are neglected, the increase of pu reduces the transport rate of contaminants. However, when the nonlinear compressibility and permeability characteristics are considered, the increase of pu leads to the increase of transport rate, which is mainly due to the comprehensive effects of advection and diffusion on the transport process. The increase of Cb increases the settlement, reduces the excess pore water pressure and decreases the transport rate of contaminants. Compared with the case of ignoring nonlinearity, the effects of Cb on the settlement, excess pore water pressure and transport rate of contaminants are reduced when the nonlinearity is considered.
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图 2 本文所建耦合模型与COMSOL Multiphysics的对比情况
Figure 2. Comparison between proposed coupled model and COMSOL Multiphysics
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图 3 本文所建耦合模型与Li等[31]近似解析解的对比情况
Figure 3. Comparison between proposed coupled model and Li et al' s approximate analytical solutions
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图 5 不同力学荷载pu下污染物浓度的分布
Figure 5. Distribution of contaminant concentration under different pu
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图 6 不同渗滤液中污染物浓度Cb下沉降量的变化
Figure 6. Variation of settlement with time under different Cb
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图 7 不同渗滤液中污染物浓度Cb下超孔隙水压力的分布
Figure 7. Distribution of excess pore water pressure under different Cb
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图 8 不同渗滤液中污染物浓度Cb下污染物浓度的分布
Figure 8. Distribution of contaminant concentration under different Cb
表 1 耦合模型的计算参数
Table 1 Parameters for proposed coupled model
参数 取值 厚度L/m 1.0 初始孔隙率n0 0.5 液相密度ρf/(kg·m-3) 1000 固相密度ρs/(kg·m-3) 2600 渗透指数Ck 0.198 压缩指数Cc 0.13 初始有效应力σ′0/kPa 60 渗透系数kv0/(m·s-1) 1.0×10-10 力学荷载pu/kPa 100 渗滤液水头hb/m 0.3 比值ζ 0.005 化学渗透效率系数ω 0.005 温度T/K 293.15 污染物浓度Cb/(kmol·m-3) 4 线性吸附系数Kd/(m3·kg-1) 0.8142×10-3 经验系数β 1.82 自由扩散系数D0/(m2·s-1) 5.0×10-10 注：表中参数的取值源于参考文献[3, 16~19, 24, 30]。 
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表 2 t=10 a时不同力学荷载pu下的沉降量
Table 2 Settlements under different pu when t=10 a
力学荷载
pu/kPa忽略非线性/
cm考虑非线性/
cm沉降差/
cm50 3.57 2.28 1.29 100 5.92 3.19 2.73 150 8.27 3.88 4.39
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