未飽和土壤受到隨時間變化外部載重之一維壓密研究

李哲瑋

doi:10.6844/NCKU.2015.01120

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未飽和土壤受到隨時間變化外部載重之一維壓密研究

One-dimensional consolidation in unsaturated soils under an external time-varying loading

李哲瑋 , Ph.D　　Advisor：羅偉誠　　

英文 DOI： 10.6844/NCKU.2015.01120

孔彈性壓密理論；未飽和土壤；時變性載重； Poroelasticity theory of consolidation ； Unsaturated soil ； Time-varying loading

Abstract │ Reference (49) │ Altmetrics

Abstract 〈TOP〉

土壤壓密對於工程應用及災害防治常扮演關鍵的角色，尤其地層下陷的問題為台灣沿海及平原常見的地質災害。近年因乾旱所導致土壤壓密造成的災害更是需迫切解決的問題，因此應用數學解析解量化分析土壤壓密的結果，將能有效的提供工程師及決策者進行評估。本研究利用Lo et al. (2002)所發表的孔隙介質含兩項流體之動量方程式結合線性應力應變關係式(Lo et al., 2005)，並且依照前人研究土壤壓密的典型假設(Biot, 1941; Terzaghi, 1943)，將方程式的慣性項忽略所推導出的孔彈性壓密理論，並且根據Biot (1941)所提出的載重作用瞬間土體不排水的假設以及Lewallen and Wang(1998)應用載重效應(loading efficiency)所提出雙孔隙初始壓力而建立未飽和孔隙流體初始壓力，推導出土壤受到隨時間變化外部載重的孔隙流體壓力以及隨時間變化的總沉陷量。
不同土壤質地、水飽和度以及外部載重的震盪頻率會直接反應土壤受到外力作用時的特性，但由於目前較缺乏上述三點對於土壤壓密問題的完整研究，因此本研究將針對11種土壤分別模擬在3組邊界條件、4組初始水飽和度(0.7、0.8、0.9及1.0)以及4組無因次震盪頻率下(0、0.1、1及10)的壓密行為。結果顯示，初始水飽和度與土壤質地對於土壤壓密的過程極為重要，由孔隙水壓消散速率比較可發現，在初始水飽和度等於0.9且達到壓密穩定時，砂土的無因次孔隙水壓消散速率最快，其次依序為壤質砂土、砂質壤土、壤土、砂質黏壤土、坋質壤土、黏質壤土、砂質黏土、坋質黏壤土、坋質黏土以及消散速率最慢的黏土，並且發現與水有關的壓密係數為影響土壤消散速率快慢的主要因素；且在相同土壤下，初始水飽和度愈高孔隙水壓消散速率愈快；無論在任何的壓密時間，雙邊排水邊界的孔隙水壓消散速率比單邊排水快。當載重作用的初期，土壤的初始水壓受到水的載重效應影響，水的載重效應愈大則初始水壓愈高，而水的載重效應受到水飽和度直接的影響，因此，由上述可知，高飽和度的土壤會產生較大的初始孔隙水壓與較小的初始沉陷量，但也會產生較快的消散速率。當土壤受到隨時間變化外部載重作用時，若無因次震盪頻率大於1時，則無因次孔隙水壓的振幅會隨著水飽和度增加而減小，若無因次震盪頻率小於1時，載重作用的週期大於孔隙水壓消散的時間，因此水能夠快速的由邊界排出。由土壤的總沉陷量可知，土壤的沉陷量與土壤基質統體模數的倒數(compressibility)成正比的關係，且隨著無因次震盪頻率增加而減小。

Parallel Abstract 〈TOP〉

Soil consolidation plays an important role in practical applications related to the field of engineering as well as in disaster prevention. In particular, subsidence is a common problem in coastal regions and in the alluvial fans in Taiwan. Drought-induced soil consolidation has also become a problem. As consolidation proceeds, the excess pore fluid pressure decreases, and the effective stress increases, reducing pore spaces and consolidating the soil grains. Time-varying loading, a common phenomenon in practical geotechnical engineering problems, is significant during the process of soil consolidation. Analytical solutions for quantifying soil consolidation can provide useful information to engineers and policymakers.
This study applies a set of coupled partial differential equations of momentum balance for two-phase fluid flows in a deformable porous medium developed by Lo et al. (2002) and linear stress-strain relations (Lo et al., 2005) to formulate a poroelasticity theory of consolidation. Closed-form analytical solutions describing the excess pore air and water pressure and the total settlement in response to an external loading under three types of boundary drainage conditions are formulated by employing the Laplace transform. To establish the initial conditions, Biot’s assumption (1941) that water is not allowed to escape when the loading is instantly applied on a porous medium is used. The effects of water content, soil texture, and the dimensionless frequency on one-dimensional consolidation in unsaturated soils are then determined.
The results show that the dissipation of excess pore water pressure is significantly sensitive to soil texture, which is almost completed in very short elapsed time in sand, followed by loamy sand, sandy loam, loam, sandy clay loam, silt loam, clay loam, sandy clay, silty clay loam, silt clay, and clay at water saturation equal to 0.9. This trend is consistent with the coefficient of consolidation for water. Irrespective of the elapsed time, the excess pore water pressure always dissipates faster under full-permeable boundaries than under a semi-permeable boundary. For a given soil texture, the dissipation rate of excess pore water pressure is higher in wetter soil. In the early stage of consolidation, the initial pore water pressure is affected by the loading efficiency for water, which is strongly controlled by the initial water saturation. For soil consolidation under time-varying loading, the amplitude of excess pore water pressure is not only controlled by the initial water saturation but also by the dimensionless frequency. The transient response decays immediately and produces an increase in the rate of change of water pressure immediately after the application of the time-varying loading. In reference to the time-dependent total settlement, it is found that it has a positive relationship with the inverse of the soil bulk modulus.

Reference ( 49 ) 〈TOP〉

1.黃鈺涵、羅偉誠、陳主惠及李哲瑋，「非飽和砂土、坋質壤土及黏土於固定載重下壓密行為之理論與數值研究」，農業工程學報，第58卷第3期，pp. 66-81，2012。
連結：
2.Albers, B.,“Linear elastic wave propagation in unsaturated sands, silts, loams and clays,”Transp. Porous Media, Vol. 86, No. 2, pp. 567-587, 2011.
連結：
3.Ausilio, E., and Conte, E.,“Settlement rate of foundations on unsaturated soils,”Can. Geotech. J., Vol. 36, No. 5, pp. 940-946, 1999.
連結：
4.Barden, L.,“Consolidation of compacted and unsaturated clays,”Geotechnique, Vol. 15, No. 3, pp. 267-286, 1965.
連結：
5.Biot, M.A.,“General theory of three-dimensional consolidation,”J. Appl. Phys.,Vol 12, pp. 155-164, 1941.
連結：

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