雲林地區至今仍為台灣嚴重地層下陷區，其主沉陷區已涵蓋至高鐵路段影響其行車安全。為了有效治理因超抽地下水而引發之地層下陷，確切了解雲林地區之地層下陷機制為首要目標。先前研究已表明地層下陷的行為與特徵會隨著區域地質條件與地質架構的不同而有所差異。因此，透過可靠的地質模型可以準確預測地層下陷的規模與範圍，並有助於儘早地規劃防治之措施。考慮到地質材料分布在地層下陷行為之重要性，本研究參考雲林地層下陷區之水文地質剖面，以有限元素軟體COMSOL MULTIPHYSICS建置不同複雜度的地質模型，並以Biot耦合孔彈性理論為基礎，模擬飽和土體隨時間排水與壓密的過程。接著，在假想模型中使用相對敏感度(relative sensitivity)進行參數敏感度分析。最後，在現地模型中採用變形效應引起之時變參數系統，探討土體特性在排水與壓密的過程中之變化情形。在耦合模式下的模擬結果顯示，土體變形與水壓變化同時受水頭變化與應力-應變影響，當材料中水流傳遞速度顯著慢於應力傳遞時，力平衡與排水作用引起的沉陷量便可以區分。在地質模型中，累積沉陷量主要來自細顆粒材料的應變，而阻水層的排水與壓密速度受自身厚度與相鄰含水層特性所影響。地層下陷行為可分為即時沉陷與延遲沉陷，其中延遲沉陷由排水與壓密速度較為緩慢之阻水層控制。參數敏感度分析結果顯示，楊氏模數、帕松比與滲透性(permeability)對總沉陷量較為敏感，且滲透性的敏感度會隨時間變化。整體而言，阻水層參數比含水層參數更為敏感，並以土體壓縮性對總沉陷量的影響最為顯著。在現地模型中增加模型複雜度後，地層下陷在地表的分布更加局部化，土體之排水與壓密機制亦受影響，致使最終累積沉陷量與到達最終沉陷量時間的增加。另外，在現地模型採用時變參數系統後，孔隙率與滲透性在土體壓密過程中減小，楊氏模數則在土體壓密過程中增加，其變化情形在阻水層中尤為顯著。因此，現地模型中土體排水速率與壓縮性隨時間的變化，使得最終累積沉陷量與到達最終沉陷量時間的減少，而土體壓密情形受重力影響在不同深度變化。

Yunlin County is a serious land subsidence area in Taiwan, and the main subsidence area has covered the section of high-speed rail, threatening its operation safety. To effectively control land subsidence caused by groundwater overexploitation, it is necessary to understand the subsidence mechanism in Yunlin County. Previous studies indicated that local geological condition and geological structure affect the behavior and characteristics of land subsidence. Hence, a reliable hydrogeological model can help to accurately assess the subsidence quantity and extent area and the planning of mitigation strategy. Considering the importance of geological material distribution, this study constructs the geological models with different complexity in a finite element software, COMSOL MULTIPHYSICS, using the hydrogeological cross section in Yunlin County. Based on Biot’s poroelasticity theory, the interaction of water drainage and consolidation processes in fully saturated media is simulated. Parameter sensitivity analysis is performed in a synthetic model using the relative sensitivity. The time-varying parameters are adopted in an in-situ model to explore the variations of material properties during the deformation process. The simulation results in the coupled hydro-mechanical model show that soil deformation and pore pressure change are caused by both stress-strain and hydraulic head change. Subsidence quantity caused by force equilibrium and water drainage can be distinguished when the permeability of material is significantly lower. From the simulation results, significant subsidence mainly contributed by the compressive strain of aquitards. The drainage and consolidation rate of aquitards is affected by their thickness and the properties of the adjacent aquifers. Land subsidence behavior can be divided into timely subsidence and delay subsidence, of which delay subsidence is dominated by aquitards with slow drainage and consolidation rate. The results of parameter sensitivity analysis show that Young’s modulus, Poisson’s ratio, and permeability are sensitive to land subsidence, and the sensitivity of permeability varies with time. Overall, the parameters in aquitards are more sensitive to land subsidence than in aquifers, especially the soil compressibility. Adding complexity to the in-situ model makes the land subsidence more localized and affects drainage and consolidation behavior, leading to an increase in final subsidence quantity and the time to reach the final subsidence. After adopting the time-varying parameters in an in-situ model, the porosity and permeability decrease with soil consolidation process while Young's modulus increases. The variations of time-varying parameters are more significant in aquitards than in aquifers. Therefore, the drainage rate and compressibility of media change with time, resulting in a decrease in final subsidence and the time to reach the final subsidence.

[1] Baqersad, M., Haghighat, A. E., Rowshanzamir, M., & Bak, H. M. (2016). Comparison of coupled and uncoupled consolidation equations using finite element method in plane-strain condition. Civil Engineering Journal, 2(8), 375-388.
[2] Bear, J. (1972). Dynamics of fluids in porous media. Elsever: New York.
[3] Bear, J., & Corapcioglu, M. Y. (1981). Mathematical model for regional land subsidence due to pumping: 1. Integrated aquifer subsidence equations based on vertical displacement only. Water Resources Research, 17(4), 937-946.
[4] Biot, M. A. (1941). General theory of three‐dimensional consolidation. Journal of Applied Physics, 12, 155.
[5] Biot, M. A. (1962). Mechanics of deformation and acoustic propagation in porous media. Journal of Applied Physics, 33, 1482-1498.
[6] Biot, M. A., & Willis, D. G. (1957). The elastic coefficient of the theory of consolidation. Journal of Applied Mechanics, 24, 594-601.
[7] Biot, M. A. (1955). Theory of elasticity and consolidation for a porous anisotropic solid. Journal of Applied Physics, 26, 182-185.
[8] Bonì, R., Meisina, C., Teatini, P., Zucca, F., Zoccarato, C., Franceschini, A., ... & Herrera, G. (2020). 3D groundwater flow and deformation modelling of Madrid aquifer. Journal of Hydrology, 585, 124773.
[9] Bozzano, F., Esposito, C., Franchi, S., Mazzanti, P., Perissin, D., Rocca, A., & Romano, E. (2015). Understanding the subsidence process of a quaternary plain by combining geological and hydrogeological modelling with satellite InSAR data: The Acque Albule Plain case study. Remote Sensing of Environment, 168, 219-238.
[10] Chen, X. X., Luo, Z. J., & Zhou, S. L. (2014). Influences of soil hydraulic and mechanical parameters on land subsidence and ground fissures caused by groundwater exploitation. Journal of Hydrodynamics, 26(1), 155-164.
[11] Cheng, A. H. D. (2016). Poroelasticity. Switzerland: Springer International Publishing.
[12] COMSOL Multiphysics (1998). Introduction to COMSOL Multiphysics extregistered. COMSOL Multiphysics: Burlington, MA.
[13] Cryer, C. W. (1963). A comparison of the three-dimensional consolidation theories of Biot and Terzaghi. The Quarterly Journal of Mechanics and Applied Mathematics, 16(4), 401-412.
[14] Deng, J. H., Lee, J. W., Lo, W. C., & Wang, C. M. (2018). An assessment of the loading efficiency on the process of consolidation in unsaturated soils. Journal of Taiwan Agricultural Engineering, 64(4), 1-22.
[15] Fernández-Merodo, J. A., Ezquerro, P., Manzanal, D., Béjar-Pizarro, M., Mateos, R. M., Guardiola-Albert, C., ... & Herrera, G. (2021). Modeling historical subsidence due to groundwater withdrawal in the Alto Guadalentín aquifer-system (Spain). Engineering Geology, 283, 105998.
[16] Fitts, C. R. (2013). Groundwater science. 2nd ed. Oxford: New York, Academic Press.
[17] Freeze, R. A., & Cherry, J. A. (1979). Groundwater. Prentice-hall.
[18] Gambolati, G. (1974). Second-order theory of flow in three-dimensional deforming media. Water Resources Research, 10(6), 1217-1228.
[19] Holzbecher, E. (2017). Analytical solution for the steady poroelastic state under influence of gravity. COMSOL 2017 Conference.
[20] Jiang, G. Y. (2021). Theoretical analysis of ground displacements induced by deep fluid injection based on fully-coupled poroelastic simulation. Geodesy and Geodynamics, 12(3), 197-210.
[21] Kézdi, Á., & Rétháti, L. (1974). Handbook of soil mechanics. Amsterdam: Elsevier.
[22] Kihm, J. H., Kim, J. M., Song, S. H., & Lee, G. S. (2007). Three-dimensional numerical simulation of fully coupled groundwater flow and land deformation due to groundwater pumping in an unsaturated fluvial aquifer system. Journal of Hydrology, 335(1-2), 1-14.
[23] Kim, J. M., & Parizek, R. R. (1997). Numerical simulation of the Noordbergum effect resulting from groundwater pumping in a layered aquifer system. Journal of Hydrology, 202(1-4), 231-243.
[24] Li, J., Wang, W., Cheng, D., Li, Y., Wu, P., & Huang, X. (2021). Hydrogeological structure modelling based on an integrated approach using multi-source data. Journal of Hydrology, 600, 126435.
[25] Li, M. G., Chen, J. J., Xia, X. H., Zhang, Y. Q., & Wang, D. F. (2020). Statistical and hydro-mechanical coupling analyses on groundwater drawdown and soil deformation caused by dewatering in a multi-aquifer-aquitard system. Journal of Hydrology, 589, 125365.
[26] Lin, C. W., Hwung, H. H., Hsiao, S. C., Yeh, C. L., & Hsu, J. T. (2016). Land subsidence caused by groundwater exploitation in Yunlin, Taiwan. Proceedings of the 12th International Conference on Hydroscience & Engineering.
[27] Liu, C. H., Pan, Y. W., Liao, J. J., Huang, C. T., & Ouyang, S. (2004). Characterization of land subsidence in the Choshui River alluvial fan, Taiwan. Environmental Geology, 45(8), 1154-1166.
[28] Lizárraga, J. J., & Buscarnera, G. (2020). A geospatial model for the analysis of time-dependent land subsidence induced by reservoir depletion. International Journal of Rock Mechanics and Mining Sciences, 129, 104272.
[29] Lo, W. C., Chang, J. C., Borja, R. I., Deng, J. H., & Lee, J. W. (2021). Mathematical modeling of consolidation in unsaturated poroelastic soils under fluid flux boundary conditions. Journal of Hydrology, 595, 125671.
[30] Lo, W. C., Sposito, G., & Chu, H. (2014). Poroelastic theory of consolidation in unsaturated soils. Vadose Zone Journal, 13(5), 1-12.
[31] Lu, C. H., Ni, C. F., Chang, C. P., Chen, Y. A., & Yen, J. Y. (2016). Geostatistical data fusion of multiple type observations to improve land subsidence monitoring resolution in the Choushui river fluvial plain, Taiwan. Terrestrial, Atmospheric & Oceanic Sciences, 27(4), 505-520.
[32] Moslehi, M., Rajagopal, R., & de Barros, F. P. (2015). Optimal allocation of computational resources in hydrogeological models under uncertainty. Advances in Water Resources, 83, 299-309.
[33] Musso, G., Volonté, G., Gemelli, F., Corradi, A., Nguyen, S. K., Lancellotta, R., ... & Mantica, S. (2021). Evaluating the subsidence above gas reservoirs with an elasto-viscoplastic constitutive law. Laboratory evidences and case histories. Geomechanics for Energy and the Environment, 28, 100246.
[34] Phani, K. K., & Sanyal, D. (2005). Critical reevaluation of the prediction of effective Poisson's ratio for porous materials. Journal of materials science, 40(21), 5685-5690.
[35] Tabatabaian, M. (2014). COMSOL for Engineers. Mercury Learning & Information: Dulles, VA, USA.
[36] Terzaghi, K. (1925). Principles of soil mechanics, IV—Settlement and consolidation of clay. Engineering News-Record, 95(3), 874-878.
[37] Tsai, T. L. (2015). A coupled one‐dimensional viscoelastic–plastic model for aquitard consolidation caused by hydraulic head variations in aquifers. Hydrological Processes, 29(22), 4779-4793.
[38] Tzampoglou, P., & Loupasakis, C. (2018). Evaluating geological and geotechnical data for the study of land subsidence phenomena at the perimeter of the Amyntaio coalmine, Greece. International Journal of Mining Science and Technology, 28(4), 601-612.
[39] Wang, S. J., & Hsu, K. C. (2009). Dynamics of deformation and water flow in heterogeneous porous media and its impact on soil properties. Hydrological Processes: An International Journal, 23(25), 3569-3582.
[40] Wolff, R. G. (1970). Relationship between horizontal strain near a well and reverse water level fluctuation. Water Resources Research, 6(6), 1721-1728.
[41] Xiao, X., Gutiérrez, F., & Guerrero, J. (2020). The impact of groundwater drawdown and vacuum pressure on sinkhole development. Physical laboratory models. Engineering Geology, 279, 105894.
[42] Zhao, Y., Wang, C., Yang, J., & Bi, J. (2021). Coupling model of groundwater and land subsidence and simulation of emergency water supply in Ningbo urban Area, China. Journal of Hydrology, 594, 125956.
[43] 江崇榮、林燕初、陳建良 (2011)。濁水溪沖積扇地下水位與地表高程互動之模式與應用。地質，第30卷，第二期，32-35頁。
[44] 單信瑜、羅文俊、陳明城 (1999)。台灣西部沿海砂質土壤土體變形對地層下陷之影響。國立交通大學土木工程研究所。
[45] 經濟部中央地質調查 (1999)。濁水溪沖積扇水文地質調查研究總報告。經濟部中央地質調查所，共130頁。
[46] 經濟部水利署 (2014)。103年度多元化監測及整合技術應用於台北、彰化及雲林地區地層下陷監測。經濟部中央地質調查所，共269頁。
[47] 董家鈞 (2020)。知之為知之，不知為不知，是知也：淺談地質模型不確定性。大地技師，第20卷，72-83頁。
[48] 賴慈華、劉平妹、袁彼得、江崇榮 (1996)。濁水溪南岸平原之晚第四紀地下地質。濁水溪沖積扇地下水及水文地質研討會論文集，第79-100頁。
[49] 賴慈華、賴典章 (2002)。麥寮、西螺、台西、北港[臺灣地質圖幅及說明書1/50,000]。新北市：經濟部中央地質調查所。
[50] 羅文俊 (1997)。地層下陷地區淺層土壤土體變形行為研究。國立交通大學土木工程學系研究所碩士論文，新竹市。