【正文】
有嚴(yán)格損失的。 不需要用任何特殊的方式通過( 3)式和( 4)式把 Aij? ,AiT 和 AijX? 聯(lián)系在一起。 內(nèi)部作用法則: 上邊界和下邊界原理都建立在內(nèi)部作用原則的基礎(chǔ)上,在發(fā)生坍塌前,給定了假設(shè)的小變形,內(nèi)部作用等式是可以運(yùn)用的,并且可以用以下的關(guān)系來表達(dá): 39。Pij ij ijGF? ? ??????? (2) 這里, ? 是非負(fù)的塑性比值,也就是當(dāng)發(fā)生塑性變形時的正直。( ) 0ijF? ? (1) 這里, F 是應(yīng)變函數(shù), 39。公認(rèn)的力學(xué)理論包括剛體的轉(zhuǎn)動和持續(xù)變形。 這篇文章的目的有兩個:( 1)就有效應(yīng)力而言,為土坡在孔隙水壓力作用下的極限分析提出了一個有限元的公式;( 2)通過比較Bishop的上下邊界解來核實(shí)土坡穩(wěn)定性分析方法在被 Bishop簡化的極限平衡法所得的解與簡單坡中 不考慮孔隙水壓力作用,上下 邊界所得的解相比較。它表示孔隙水壓力在內(nèi)部摩擦力等于零時的分析沒有影響,這就證實(shí)了用總應(yīng)力分析時 0?? 。在他們的理論中,孔隙水壓力被看作是內(nèi)力,在給定的滑坡機(jī)理下,它對降低內(nèi)部能量消散是有影響的。相似的 方法可以用于明確說明孔隙水壓力作用下的極限分析。在過去,對于土坡穩(wěn)定性的應(yīng)用,大多數(shù)研究工作都集中在上邊界法上,這是因?yàn)橥ㄟ^求解下邊界適合靜態(tài)允許應(yīng)力場方程的解是一項(xiàng)很困難的任務(wù)。就簡單而言,下邊界荷載作用下,滑動不會發(fā)生,但是如果下邊界受到外加荷載的作用,則滑動可能立即發(fā)生。在極限平衡法中,平衡方程 并不是對土體的每一點(diǎn)都適用的。由于它的簡單,在實(shí)踐中,極限平衡法是最被廣泛使用的。站在實(shí)踐的立場上,穩(wěn)定性的最基本關(guān)注點(diǎn)應(yīng)該是土體破壞條件。按照傳統(tǒng)的說法,在土力 學(xué)中,彈性理論是用來建立變形微分方程的,就象塑性理論是用來建立穩(wěn)定性問題的微分方程一樣 。作者對從不同地下水形式下簡單土坡的極限分析所得的結(jié)果與極限平衡法中所得的結(jié)果作了比較。在這篇文章中,三點(diǎn)確定的三角形三邊有限元法被利用與構(gòu)造在下邊界分析中的靜態(tài)允許應(yīng)力場和上邊界分析中的 速度 場。 ij? = actual stain rate。 that is, only plastic deformation occurs during plastic flow, and ij? = Pij? .This makes limit analysis a simple method to solve stability problems, without loss of rigor, assuming rigid perfect plasticity. Lowerbound Theorem If the stress field within the soil mass is stable and statically admissible, then collapse does not occur。Aij?= effective stress tensor in equilibrium with AiT and AijX 。 AijX? = body forces not including seepage and buoyancy forces。39。ij? ) = 0 (1) Where F( 39。附:英文翻譯 LIMIT ANALYSIS OF SOIL SLOPES SUBJECTED TO POREWATER PRESSURES By , assoicite member, ASCE ,and ., member,ASCE ABSTRACT: the limitequilibrium method is monly, used for slope stability analysis. However, it is well known that the solution obtained from the limitequilibrium method is not rigorous, because neither static nor kinematic admissibility conditions are satisfied. Limit analysis takes advantage of the lowerand upperbound theorem of plasticity to provide relatively simple but rigorous bounds on the true solution. In this paper, three nodded linear triangular finite elements are used to construct both statically admissible stress fields for lowerbound analysis and kinematically admissible velocity fields for upperbound analysis. By assuming linear variation of nodal and elemental variables the determination of the best lowerand upperbound solution maybe set up as a linear programming problem with constraints based on the satisfaction of static and kinematic admissibility. The effects of prowater pressure are considered and incorporated into the finiteelement formulations so that effective stress analysis of saturated slope may be done. Results obtained from limit analysis of simple slopes with different groundwater patterns are pared with those obtained from the limitequilibrium method. INTRODUCTION Stability and deformation problem in geotechnical engineering are boundaryvalue problem。 and (2) to check the accuracy of Bishop’s simplified method for slope stability analysis by paring Bishop’s solution with lowerand upperbound solution. The present study is an extension of previous research, where Bishop’s simplified limitequilibrium solutions are pared with lowerand upperbund solutions for simple slopes without considering the effect of porewater pressure. In the present paper, the effect of porewater pressure is cons