由於台灣的降雨型態導致水資源在乾濕季分布不均，近年來降雨量減少及颱風來台數量遽減，抽取地下水則成為了一個快速且方便的來源。早期對於地下水取用並無明確規範，造成地下水過度取用進而產生嚴重地層下陷問題。除去過度抽取地下水外，地表的震動及地表建築物的荷重也會對地層產生下陷的情形，這種隨時間變化的外部載重，對土壤造成的影響，已經是在工程應用上需要正視的問題，像是最近高鐵在雲林地區每年有3至5公分的地層下陷量，如果能用一種數學框架來描述震動的模式，並計算出土壤壓密的結果，對以後解決工程問題可能有所幫助。
為探討未飽和土壤在不同形式震動之沉陷問題，本文利用Lo et al., (2014)所發表之一維未飽和土壤孔彈性壓密理論進行研究，並使用兩個非正弦波(方波、三角波)模擬震動，並配合兩種土壤(黏土、砂土)，三種振動頻率( 、 、 )，三種初始飽和度( 、 及 )在雙邊排水的條件下探討兩種震動載重造成土壤的超額孔隙水壓和沉陷量的影響，並把結果以飽和度及頻率的觀點進行比較。研究結果顯示，雖然初始飽和度會因為不同震動載重下及土壤下有不同的趨勢，但不管是在方波或三角波震動下，都可以發現相同的結果，頻率越大造成的超額孔隙水壓力也會越大，頻率越小造成較小的孔隙水壓力。同時根據總應力的概念，沉陷量所得出來的結果會與超額孔隙水壓力的結果相反，及為頻率越大造成較小的沉陷量，頻率越小造成較大的沉陷量。最後在探討兩個震動載重造成的影響時，從結果可以得知，方波造成的超額孔隙水壓力均會大於三角波，而沉陷量則是三角波大於方波。

Due to the uneven distribution of water resources during the wet and dry seasons in Taiwan, the amount of typhoon and rainfall has been declining for the past few years. In addition, the extraction of groundwater has become one of the most rapid and convenient sources. There is no regulation of groundwater abstraction in the early days, which has led to overpumping of groundwater, thus causing land subsidence. Besides overwithdrawals, ground movement and loading of surface structures also have an impact on land subsidence. It is a matter of concern for engineering that external loading affects soil continuously. The Taiwan High Speed Rail Corporation has been observing the vertical displacement of the railroad pier closely. The latest observing results indicate that land subsidence in the Yunlin area is around 3 to 5 centimeters yearly, which poses security risk to the high-speed rail. Therefore, in order to address those engineering problems, the development an appropriate theoretical model to calculate the outcome of soil consolidation by means of a mathematical framework which can be used to describe the total settlement.

The purpose of this study is to investigate the subsidence of unsaturated soils under different waveforms of time-varying external loading. In this study, we apply the consolidation theory of poroelasticity developed by Lo et al. (2014) to discuss two different soils (i.e., clay and sand) with different initial water saturations (i.e., , , and ) and three different excitation frequencies (i.e., 0.1, 0.01, and 0.001) under full-permeable drainage conditions. The effects of two types of external loading on the excess pore water pressure and total settlement are discussed, and the results with respect to saturation and frequency are compared. The research results show that although initial water saturation has different trends under different external loading, the same results are found for both square wave and triangle wave. When at higher frequency a larger excess pore water pressure exists while, when at lower frequency a smaller excess pore water pressure occurs. Also, according to the concept of total stress, the result of the total settlement is opposite to the result of excess pore water pressure.

1. Biot, M. A. (1941). "General theory of three-dimensional consolidation." Journal of Applied Physics 12(2): 155-164.
2. Biot, M. A. and D. Willis (1957). "The elastic coeff cients of the theory of consolidation." J. appl. Mech 24: 594-60
3. Biot, M. A. (1962). "MECHANICS OF DEFORMATION AND ACOUSTIC PROPAGATION IN POROUS MEDIA." Journal of Applied Physics 33(4): 1482-+
4. Bishop, A.W. (1959). " The effective stress principle, Teknisk Ukeblad , Vol. 93,
859-863
5. Bishop, A.W. and Blight, G. (1963). "Some aspects of effective stress in saturated and partly saturated soils." Geotechnique 13(3): 177-197.
6. Conte, E. and A. Troncone (2006). "One-dimensional consolidation under general time-dependent loading." Canadian Geotechnical Journal 43(11): 1107-1116.
7. Deng, J. H., J. W. Lee and W. C. Lo (2019). "Closed-form solutions for one-dimensional consolidation in saturated soils under different waveforms of time-varying external loading." Journal of Hydrology 573: 395-405
8. Fredlund, D. G. and N. R. Morgenstern (1976). "CONSTITUTIVE RELATIONS FOR VOLUME CHANGE IN UNSATURATED SOILS." Canadian Geotechnical Journal 13(3): 261-276
9. Fredlund, D. G. and J. U. Hasan (1979). "ONE-DIMENSIONAL CONSOLIDATION THEORY - UNSATURATED SOILS." Canadian Geotechnical Journal 16(3): 521-531.
10. Hasan, J. U. and D. G. Fredlund (1977). Consolidation theory for unsaturated soils, American
11. Ho, L. and B. Fatahi (2016). "One-Dimensional Consolidation Analysis of Unsaturated Soils Subjected to Time-Dependent Loading." International Journal of Geomechanics 16(2): 04015052
12. Ho, L. and B. Fatahi (2016). "One-Dimensional Consolidation Analysis of Unsaturated Soils Subjected to Time-Dependent Loading." International Journal of Geomechanics 16(2): 04015052]
13. Lo, W. C., G. Sposito and E. Majer (2002). "Immiscible two-phase fluid flows in deformable porous media." Advances in Water Resources 25(8-12): 1105-1117.
14. Lo, W. C., G. Sposito and E. Majer (2005). "Wave propagation through elastic porous media containing two immiscible fluids." Water Resources Research 41(2): 20
15. Lo, W. C., C. L. Yeh and C. T. Tsai (2007). "Effect of soil texture on the propagation and attenuation of acoustic wave at unsaturated conditions." Journal of Hydrology 338(3-4): 273-284
16. Lo, W. C., C. L. Yeh and C. D. Jan (2008). "Effect of soil texture and excitation frequency on the propagation and attenuation of acoustic waves at saturated conditions." Journal of Hydrology 357(3-4): 270-281
17. Lo, W. C., G. Sposito and Y. H. Huang (2012). "Modeling seismic stimulation: Enhanced non-aqueous fluid extraction from saturated porous media under pore-pressure pulsing at low frequencies." Journal of Applied Geophysics 78: 77-84.
18. Lo, W.-C. and G. Sposito (2013). "Acoustic waves in unsaturated soils." Water Resources Research 49(9): 5674-5684
19. Lo, W. C., G. Sposito and H. H. Chu (2014). "Poroelastic Theory of Consolidation in Unsaturated Soils." Vadose Zone Journal 13(5): 12
20. Lo, W.-C., G. Sposito, J.-W. Lee and H. Chu (2016). "One-dimensional consolidation in unsaturated soils under cyclic loading." Advances in Water Resources 91: 122-137.
21. Miao, L., F. Wang and X. Wang (2010). "One Dimensional Consolidation of Double-Layered Foundation with Multi-Level Load." Marine Georesources & Geotechnology 28(1): 1-24.
22. Schiffman, R. L. (1958). "Consolidation of soil under time-dependent loading and varying permeability." Proceedings Highway Research Board 37(37): 584-617.
23. Schrefler, B. and Xiaoyong, Z. (1993). "A fully coupled model for water flow and airflow in deformable porous media." Water Resources Research 29(1): 155-167.
24. Terzaghi, K. (1925). Erdbaumechanik auf bodenphysikalischer Grundlage, F. Deuticke.
25. Terzaghi, K. (1943). "Theoretical soil mechanics. johnwiley & sons." New York: 11-15.
26. Tuncay, K. and M. Y. Corapcioglu (1996). "Body waves in poroelastic media saturated by two immiscible fluids." Journal of Geophysical Research-Solid Earth 101(B11): 25149-25159
27. Van Genuchten, M. T. (1980). "A closed‐form equation for predicting the hydraulic conductivity of unsaturated soils." Soil science society of America journal 44(5): 892-898.
28. Van Genuchten, M. T., F. Leij and L. Lund (1992). Indirect methods for estimating the hydraulic properties of unsaturated soils, Citeseer.
29. Wang, K. L. and E. E. Davis (1996). "Theory for the propagation of tidally induced pore pressure variations in layered subseafloor formations." Journal of Geophysical Research-Solid Earth 101(B5): 11483-11495
30. Wang, H. F. (2017). Theory of linear poroelasticity with applications to geomechanics and hydrogeology, Princeton university press
31. Xu, C. J., Q. Z. Chen, L. J. Liang and X. Z. Fan (2018). "Analysis of consolidation of a soil layer with depth-dependent parameters under time-dependent loadings." European Journal of Environmental and Civil Engineering 22: s200-s212.
32. Yamamoto, T., H. L. Koning, H. Sellmeijer and E. V. Van Hijum (1978). "On the response of a poro-elastic bed to water waves." Journal of Fluid Mechanics 87(1): 193-206
33. Zienkiewicz, O. C., C. T. Chang and P. Bettess (1980). "DRAINED, UNDRAINED, CONSOLIDATING AND DYNAMIC BEHAVIOR ASSUMPTIONS IN SOILS." Geotechnique 30(4): 385-395.
34. 李哲瑋, 羅偉誠, 陳主惠, 葉昭龍 and 葉信富 (2015). "水飽和度及土壤質地對未飽和土壤壓密過程之影響評估." 農業工程學報 61(2): 1-27.
35. 鄧教弘, 李哲瑋, 羅偉誠 and 王常勉 (2016). 載重效率對於未飽和土壤壓密過程之影響評估