以離心模型試驗及個別元素法評估正斷層和逆斷層錯動地表及地下變形

Use of Centrifuge Modeling and Distinct Element Method to Evaluate the Surface and Subsurface Deformation of Normal Faulting and Reverse Faulting

張有毅(Yu-Yi Chang)

指導教授 ： 李崇正 ； 黃文昭

國立中央大學/工學院/土木工程學系/博士(2013年)

摘要

本研究以離心模型和PFC2D數值模擬，分別在離心力場 1 g, 40 g及 80 g的試驗條件下，進行正斷層及逆斷層(斷層傾角60°的錯動模擬，了解不同斷層垂直錯動量，地表變形的發展、地下破裂跡之延伸及演化。另外亦探討地表淺基礎與正斷層及逆斷層的互制機制。
首先建立微觀力學的微觀參數(Kn及Ks)與連體力學的應力及應變關係，利用離心模型試驗升g過程中，試體床的地表沉陷，來校正及建立PFC2D數值模擬之合理參數值。利用校正過之參數，進行正逆斷層錯動的數值模擬。數值模擬所得60正傾角的正斷層或逆斷層錯動後之地表變形剖面與離心模型的試驗結果一致。因此本研究利用此組微觀參數，進行不同斷層傾角的正斷層及逆斷層錯動的數值模擬，建立不同斷層傾角的正斷層及逆斷層錯動的地表變形剖面及評估影響範圍。
利用Gompertz 函式來模擬不同斷層傾角的逆斷層，在不同垂直錯動量下之地表變形剖面。以Gompertz 函式模擬不同的斷層傾角所形成的地表變形剖面，可獲得不同的地表剖面參數。將地表剖面參數以回歸統計之方法作歸納，則可預估不同斷層傾角逆斷層錯動後地表的變形剖面及影響範圍。在基礎角變量為1/150及斷層推升高度(h)與土層厚度(H)之比值r=25%下，斷層傾角為22.5°、30°、37.5°、45°、52.5°、60°及67.5°其地表影響範圍分別為2.32H, 1.77H, 1.51H, 1.47H, 1.53H, 1.63H 及 1.66H。
在1g的離心正斷層模型試驗，上盤會產生地塹且下盤會呈現較陡之崖坡。正斷層錯動後地表之變形剖面受斷層傾角大小的影響，斷層傾角愈小地表變形之影響範圍愈大。在斷層陷落高度(h)與土層厚度(H)之比值rn=2.5%~25%時，斷層陷落後地表之主要影響距離Lp與斷層傾角(α)之關係可用二元二次方程式來表示。
淺基礎載重的大小會影響斷層錯動後，地下破裂跡的延伸地表變形剖面與方向及是否出露地表或出露的位置。於本研究之逆斷層試驗中驗證在基礎壓力為87.2 kPa (應力增量約為35kPa)時，不只有能力改變裂跡的延伸之方向，而且還有可能阻止斷層跡延伸至地表。地表斷層跡至淺基礎右側邊緣之距離為S，淺基礎寬度為B，地表及地下變形會隨S/B不同而呈現不同之變形型態。不論是正斷層或逆斷層試驗其結果均顯示基礎的旋轉量與基盤的推升或陷落量(h)、基礎的壓力(p)、基礎的寬度(B)及基礎的座落位置(S/B)有關。一般而言，基盤的推升或陷落量(h)大則基礎的旋轉量大、基礎的壓力(p)大則基礎的旋轉量小、基礎的寬度(B)大則基礎的旋轉量小、 基礎的座落位置S/B之比值介於0與1之間基礎會有較大之旋轉量。

關鍵字

正斷層及逆斷層 ； 地表變形剖面 ； PFC2D數值模型 ； 淺基礎 ； 離心模型

並列摘要

A series of centrifuge model tests and PFC2D numerical simulations on the normal faulting and reverse faulting (both with the dip angle of 60°) are conducted at the acceleration conditions of 1 g, 40 g, and 80 g. The evolution of the surface deformation profile, the subsurface deformation pattern and the development of fault trace are evaluated. In addition, the shallow foundation rested on the ground surface subject to normal and reverse faulting is conducted to evaluate the Fault Rupture-Soil-Foundation-Structure Interaction (FR-SFSI) in this study.
Based on the measured surface settlements of the centrifuge model tests in the stage of self-weight consolidation, a methodology of calibrating the micromechanical material parameters is proposed and used in the later numerical simulations. Using the calibrated parameters in the numerical simulations the derived ground surface profiles show good agreements with those ground surface profiles measured in the centrifuge tests. By using the calibrated parameters in the PFC2D numerical simulation, at the condition of different dip angles and different fault throw (h), the affected length on the ground surface after normal/reverse faulting can be evaluated.
A Gompertz equation is proposed to simulate ground surface deformation after reverse faulting. The different ground surface deformations at the different dip angles are evaluated by the PFC2D numerical simulation and the different parameters of Gompertz curve are obtained. By using the method of regression, the affected length on the ground surface can be predicted. At the condition of angular criteria η= 1/150 and the reverse fault throw (h) and soil layer thickness (H) ratio r=25%, the affected lengths on the ground surface are 2.32H, 1.77H, 1.51H, 1.47H, 1.53H, 1.63H and 1.66H for the fault dip angles of 22.5°, 30°, 37.5°, 45°, 52.5°, 60° and 67.5°, respectively.
The centrifuge normal fault modeling tested at the acceleration of 1 g level has a steeper fault scarp and forms the graben on the hanging wall ground surface. Since the profiles of ground surface deformation are affected by the dip angles, and a smaller dip angle results in a larger affected length on ground surface. At the ratio of falling throw and soil layer thickness (h/H), rn=2.5%~25%, the relationship between primary affected length Lp, and fault dip angle,α, can be expressed by a binary quadratic equation.
The profiles of ground surface deformation, the direction of fault rupture propagation and the position of the rupture emerge on the ground surface are affected by the bearing pressure of foundation. One of the centrifuge model tests in this study shows that, a heavy foundation (87.2kPa) not only has the ability of diverting the fault rupture, but also might have the ability of stopping the fault rupture emerging on the ground surface. The rotational angles of foundation are related to the various ratios of the distance from the rupture line emerging on the ground surface to the right margin of the foundation, S, and the width of the foundation (B), S/B. In general, the higher uplifting throw or falling throw has the tendency of the higher rotational angle of foundation, and the position of the foundation locates within the ratio of S/B=0 to S/B=1 has the higher rotational angle of foundation. During reverse faulting, the higher foundation bearing pressure has the lower rotational angle of foundation; the wider width of foundation has the lower rotational angle of foundation.

並列關鍵字

centrifuge modeling ； PFC2D numerical modeling ； normal faulting and reverse faulting ； ground surface deformation ； shallow foundation

參考文獻

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