砂岩依時性力學特性研究及應用

蔡立盛(Li-Sheng Tsai)

指導教授 ： 鄭富書

共同指導教授 ： 林銘郎

國立臺灣大學/工學院/土木工程學研究所/博士(2005年)

https://doi.org/10.6342/NTU.2005.00891

摘要

由於台灣特殊之地質背景，在某些特定岩層中進行地下開挖工程時，極易遭遇即時之受剪膨脹與依時之擠壓變形等不利於大地工程施工之災害。此外，台灣島為板塊交接處之快速造山運動所形成，山勢陡且斷層多，具有非常豐富的溫泉資源。隨著大型公共工程逐漸往山區發展，因此有關溫泉區或高岩覆之地熱勢必為日後工程實務上需遭遇面對之課題。
為了釐清上述之問題，本研究針對砂岩材料即時與依時情形下力學行為進行研究，透過控制溫度、應力路徑、圍壓、應力狀態等條件進行一系列力學試驗。除釐清外在環境因子對其強度與變形性包括彈性、塑性及黏塑性之影響外，並針對塑性與黏塑性變形彼此間之關聯性進行深入之探討。根據實驗結果，建議一可同時適用於描述本土砂岩即時與依時力學行為之彈/黏塑組成模式。此外，亦撰寫一可搭配數值分析軟體ABAQUS之彈塑模式副程式，據以進行工程案例之分析與探討。
力學試驗包含即時與依時試驗兩種，圍壓之範圍為20~60 MPa，溫度範圍為室溫至120度。即時試驗以純剪應力路徑為主，搭配傳統三軸及三軸解壓應力路徑，以探討應力路徑之影響，潛變試驗則以純剪應力路徑，採多階潛變方式進行。綜合本研究的成果主要可分為四個部份，分別為：(1)砂岩之即時變形特徵；(2)砂岩之依時變形特徵；(3)彈/黏塑組成模式及(4)數值分析與應用。
砂岩之即時變形特徵方面，在120度之範圍內，溫度對強度及變形性之影響均不顯著。應力路徑對於強度影響亦不顯著，對變形性則有明顯之影響。彈性行為方面，與一般研究較不同者，本研究由不同體積應力之解壓再壓曲線發現剪應力作用下，彈性體積應變不僅與純剪應力存在非線性之偶合關係，且此關係亦和體積應力有關。不同圍壓之偶合關係，若以各別體積應力針對剪應力予以正規化，可得相當一致的變形趨勢，此結果有助於建立簡易且可描述其彈性行為之迴歸式。塑性行為方面，本研究發現砂岩之整體及塑性剪脹門檻均與體積應力無關，呈現定值。小於塑性剪脹門檻時，塑性應變增量呈線性方式增加，大於塑性剪脹門檻，則會呈指數型式快速增加。此外，本研究直接由砂岩材料之塑性應變計算其不可回復應力功並求得砂岩之降伏面。由於其與塑性流與均大致正交，顯示降伏面可以等同於塑性勢能面，亦即在即時情形下，砂岩可以採用諧合性準則。
砂岩之依時變形特徵方面，溫度對於其砂岩之強度及潛變量均無明顯之影響。有趣的是，砂岩材料潛變應力在低剪應力下時，呈現體積為潛變壓縮，高剪應力時則為潛變膨脹之行為。彈性行為方面，試驗結果與即時情形之結果相當一致。黏塑性行為方面，可發現黏塑潛脹門檻與塑性剪脹門檻相當地一致。此外在應力空間中，黏塑性流與塑性流之方向相當地一致，均大致與降伏面正交。因此，可推測砂岩材料之降伏面等於塑性勢能面等於黏塑勢能面。此項結果非常有助於建構簡易且可以同時描述砂岩即時與依時變形特徵之組成模式。
彈/黏塑模式方面，依據上述砂岩變形特性，本研究以彈/黏塑性力學理論為出發點建構一組成模式，在彈性模式係以翁孟嘉(2002)之高階格林彈性模式，進行修改而得，黏性模式係以Cristescu (1994)之模式為基礎發展而得，模式遵守諧和流動準則。針對不同體積應力、應力路徑等情況進行模擬後，本研究模式與實驗資料存在不錯的吻合，在對於不同種類砂岩之模擬分析後，其結果亦良好。
數值分析與應用方面，本研究撰寫一可搭配數值分析軟體ABAQUS之彈塑組成模式之副程式。彈性採用本研究之彈性模式，塑性則採翁孟嘉(2002)之塑性模式。針對所撰寫之程式，本研究首先進行數值三軸試驗之模擬加以驗證後，進行工程案例之分析探討，並與傳統上常用之線彈性模式及Drucker-Prager模式相互比較。分析結果顯示本研究撰寫之彈塑模式副程式可適當地定性描述隧道開挖後擠壓變形特徵。此外本模式分析所得變形量約為線彈性模式及Drucker-Prager模式之1.7~2.9倍，相對於線彈性模式過於低估，本模式之分析結果可更接近於實測之變形量。

關鍵字

砂岩 ； 塑性 ； 黏塑性

並列摘要

Due to a special geological background in Taiwan, several unsuccessful cases, concerned with tunneling through special strata, had been occurred. Calamities, induced by severe squeezing and raveling, were encountered during tunnel construction, and it increases the cost and the construction time of the project. Base on the previous study, squeezing problem may be caused by the following mechanics characteristic of sandstones, including wetting deterioration, shear dilation, and significant creep behavior.
In order to evaluate the immediately and time-dependent deformational characteristics of Sandstone, five kinds of sandstone in western Taiwan were selected as experimental materials in this research. A series of hydrostatic and triaxial compressive tests were performed through pure shear stress path loading to distinguish deformation resulted from pure hydrostatic stress or pure shear stress. Especially in triaxial compressive test, the creep test was performed as well by following a step-wise loading procedure. Afterward the measured deformations were decomposed into elastic and irreversible, included plastic and creep part, components. In addition, further discussions on the relation between yield surface, plastic potential surface and viscoplastic potential surface were conducted. The results indicate that, (1) similar to other soil-like geo-materials, the sandstone has plastic and viscoplastic strain before the stress path reaching the failure envelope, and significant volumetric dilation is induced especially when stress path approaching the failure envelope; (2) apparent coupling behavior exists volumetric strain not only relates to shear stress but also involved in volumetric stress; (3) similar direction exists between plastic flow and viscoplastic flow; (4) base on irreversible stress work theory, the behavior of sandstone is satisfied with the associate flow rule, e.g. the yield surface ,plastic potential surface and viscoplastic potential surface are all the same one.
According to the test results, an elastic/viscoplastic constitutive model is proposed, and it comprises nonlinear elastic deformation, related to Hyperelastic model, and viscoplastic deformation, modified from Cristescu (1994). After comparing the experimental results with the predictions, it is shown that the proposed model reveals well the elastic, plastic and creep behaviors of sandstone under hydrostatic and triaxial loadings.
Given the distinct deformation behavior of sandston, especially shear dilation, influences of such behavior on the tunnel sidewall deformation was assessed by numerical analysis using finite element code. The numerical analysis indicates that the tunnel leads to a greatest inward displacement, which is resulted from the shear dilation prior to failure state.

並列關鍵字

sandstone ； plastic ； viscoplastic

參考文獻

[24] 陳正旺 (2005)，車籠埔斷層周圍岩石力學特性之初探，國立台灣大學土木工程研究所碩士論文。

[37] 鄭富書、黃燦輝、林銘郎 (2000)，台灣隧道工程老問題之新探討－軟岩之力學特性，地工技術，第79期，第81-90頁

[9] 林子平 (1985)，南港砂岩工程性質之影響因素研究，國立台灣大學地質學研究所碩士論文。

[40] Afrouz, A. and Harvey, J. M. (1974), Rheology of Rocks within the Soft to Medium Strength Range, Int. J. Rock Mech. Min. Sci., Vol. 11, No. 7, pp. 281-290.

[42] Bell, F. G. (1978), The physical and mechanical properties of the Fell Sandstones Northumberland England, Engineering Geology Vol. 12, pp. 1-29.