垂向拉起沉沒長方形塊之解析研究

Abstract

拉起問題為將沉沒於水中且靜置於底床之物體，由底床垂直拉起之問題。此 問題於海岸或水利工程中有許多應用，如水工構造物之移除、海底沈船打撈、潛 水艇操作等。實際經驗中，拉起之力量甚大，且耗時良久，直到某個轉捩點此力 量才會突然鬆懈，而能將物體順利拉起，此特徵也因此被稱為突破現象。若能認 識突破現象之物理機制，對於拉起物體之過程必然有益。 本研究利用史托氏流(Stokes flow) 描述縫隙中之流體，研究由不透水、不變形底床拉起物體之問題。此外，本研究還利用史托氏流描述縫隙中之流體，利 用Song and Huang (2000) 提出之層流多孔彈性理論於多孔介質，分別研究由 透水、不變形底床拉起物體之問題，以及透水、變形底床拉起物體之問題。史托 氏流完整呈現水平及垂直方向之動量方程式，Song and Huang 之層流多孔彈性 理論能反應出孔隙流之黏滯性，且其理論之邊界條件能保有流體之速度及應力連 續。 本研究第一階段求得二維、於不透水底床拉起物體之精確解。此解揭示了黏 附近似之壓力誤差，也驗證流場之流線與速度不受其大刀闊斧之近似所影響，是 不錯的近似方法。 本研究第二階段求得二維、於透水但不變形底床拉起物體之解，並利用Mei (1985)研究中之實驗驗證其合理性。此解呈現出許多於透水但不變形底床拉起物 體之物理機制，首要是拉起力量之改變以及突破現象，即研究拉起問題之初衷， 此外還有如流體之流線、壓力、剪力、渦度、黏滯性應等，完整呈現出此問題之 物理機制。此外，這些物理機制顯示出Mei 所採用之黏附近似、達西定律、以及滑移邊界條件(Beavers and Joseph (1967))很可能不適用於有孔隙之拉起問 題。 本研究最終求得二維、於透水可變形底床拉起物體之解。求解過程中，多孔 介質之流體與固體之動量方程可拆開分別求解，孔隙流體之解和由透水但不變形 底床拉起物體之解相同，也因此有同樣的建議。孔隙固體之解可呈現孔隙固體之 變形函數、變形量、有效應力等物理機制，揭示拉起過程中孔隙固體受影響之深 度可達拉起物體長度之半，以及孔隙固體有效應力只和孔隙壓力之分布有關。

Lift-up problem is a process during which an object immersed in fluid is initially extricated from a bed (Fig. 2-1). In ocean and offshore engineering, it has many applications such as removing hydraulic structures, salvaging sunken ships, and operating submarines. Based on field experience (Liu (1969)), the lifting force is considerably large and the operation time is extremely long. It is a process that slowly increases the gap between the object and the bed until a turning point when the object is abruptly unfastened. This is called breakout phenomenon. Because of it and the lifting force, it is helpful to ocean and offshore engineering if the mechanics of the problem can be understood. This study applies Stokes flow to the gap, investigating a lift-up problem with a rigid impermeable bed. Also, this study applies Stokes flow to the gap and Song and Huang’s (2000) laminar poroelasticity theory to the porous medium, analyzing problems with a rigid porous bed and a hard poroelastic bed, respectively. Stokes flow can react to the horizontal and vertical velocities, Song and Huang’s (2000) laminar poroelasticity theory can respond to the viscous effect of pore flow, and the complete boundary conditions can react to the continuity of velocity and stress. The first stage of this study provides the exact solution to the two-dimensional lift-up problem with a rigid impermeable bed. The exact solution reveals the tiny error of the pressure in adhesion approximation (Acheson (1990)), and verifies that the tiny error does not influence the kinematics of the flow and the dynamic force acting on the object. The second stage of this study proposes a more general solution to the two-dimensional lift-up problem with a rigid porous bed. The solution has been verified by Mei’s (1985) experiments, and reveals many mechanics of the problem. The dynamic force acting on the object and the breakout phenomenon are displayed, and other mechanics are demonstrated. In fact, they are the mechanics that cannot be presented by Mei’s (1985) approach, and suggest that adhesion approximation (Acheson (1990)), Darcy’s law, and Beavers and Joseph’s (1967) partial-slip flow might not be suitable to problems with porous beds. This study finally offers the solution to the two-dimensional lift-up problem with a hard poroelastic bed. The fluid and solid parts in the porous medium can be decoupled. The mechanics of the fluid is exactly the same as those in the problem with a rigid porous bed. Deformation lines, deformations and effective stresses of the solid in a hard poroelastic bed are revealed. The porous medium can be influenced to the depth of L , half the length of the object, and the solid effective stresses are only influenced by the pressure distribution in the porous medium.