完全飽和多孔彈性固體不暢邊界解決方案

1、完全飽和多孔彈性固體不暢邊界解決方案 摘要給出了解析解合并無(wú)限的地層和一個(gè)有限的土層與一個(gè)阻礙層定位于細(xì)胞表面受到垂直點(diǎn)裝。拉氏變換和漢克爾變換采用相對(duì)于時(shí)間和徑向協(xié)調(diào),分別。解決方案其他分布載荷,包括循環(huán)荷載作用下,通過(guò)整合可以輕易得到這些圖像的點(diǎn)裝。在固結(jié)度,多余的孔隙水壓力、垂直總應(yīng)力、剪應(yīng)力分析了強(qiáng)化層的探討。這固結(jié)比的減小而增大之增加厚度層的阻礙。應(yīng)力的變化。鞏固層由于在固結(jié)耦合的過(guò)剩土壤孔隙水耗散和骨架變形。另外,Mandel-Cryer效果進(jìn)行了分析研究。關(guān)鍵詞固結(jié),妨礙邊界,拉氏變換,漢克爾變換 1介紹 提出了降水固結(jié)理論從連續(xù)的中基本方程1。這個(gè)理論,結(jié)合帳戶(hù)之間的耦合和孔隙

2、固體菌株水壓力消散,被稱(chēng)為“耦合整理理論”,這個(gè)問(wèn)題就復(fù)雜得多那些理想彈性固體。有許多的研究有關(guān)在分析解的方程降水27。一些采用數(shù)值方法811。上述假設(shè),表面的調(diào)查這是完全滲透或鞏固層滲透性。這表面會(huì)影響巖土工程如砂墊障礙用于預(yù)壓摩擦樁的長(zhǎng)度可以被視為一種阻礙層位于底層低于成堆。這些阻礙有足夠的剛度層在垂直的方向他們的變形中底層的鞏固可以忽略。謝一維固結(jié)等了五解決這個(gè)問(wèn)題。然而,二維這個(gè)問(wèn)題的解決方案尚未有報(bào)道12,13?；诶绽棺儞Q和漢克爾變換,的基本解,無(wú)限的鞏固一個(gè)有限層地層和阻礙邊界條件進(jìn)行了介紹。這些解決方案也延長(zhǎng)了那些圓形分布載荷。鞏固學(xué)位,超孔隙水壓力和應(yīng)力強(qiáng)化層進(jìn)行了分析,

3、并比較兩者之間將半無(wú)限地層和有限層執(zhí)行。 2控制方程和通用的解決方案 降水后1的基礎(chǔ)上,對(duì)軸對(duì)稱(chēng)問(wèn)題的控制方程一個(gè)完全飽和變形的各向同性和均勻推導(dǎo)了柱坐標(biāo)系堅(jiān)固表達(dá)為在ur(r,z,t)、烏斯(r,z,t)是徑向位移和嗎垂直位移,分別酚醛(r,z,t)是多余的孔隙壓力;G的剪切模量;五是泊松比;k系數(shù)的介質(zhì)的滲透性,e大宗材料和擴(kuò)張e =y(盧布)/年/ + ryuz yz/ r。其他的參數(shù)在Eqs。(1)-(3)得到用應(yīng)力-應(yīng)變關(guān)系表達(dá) 在srr(r,z,t),噓(r,z,t),山株仔(r,z,噸)和szr(r,z,t)是什么零應(yīng)力分量的散裝材料;錯(cuò)了(r,z,t),ehh(r,z,t),e

4、zz(r,z,噸)和ezr(r,z,t)是體積應(yīng)變組件。以下McNamee和吉布森14,徑向位移ur(r,z,t),垂直位移烏斯(r,z,t)和pf的超孔隙水壓力(r,z,t)可以用條件兩個(gè)函數(shù)和y的w方便所有參數(shù)長(zhǎng)度和時(shí)間方面選擇" R "為某一單位小麥籽粒的長(zhǎng)度、和“R2 / c”作為一個(gè)時(shí)間單位,分別。替代Eqs的。(八)-(10)在Eqs。(1)-(3)產(chǎn)量以下對(duì)于函數(shù)微分方程w與y拉普拉斯變換和漢高Eqs的。(11),(12)的結(jié)果下面的兩個(gè)常微分方程在whl是零和yhl漢克爾變換和嗎拉普拉斯變換的功能w,y,分別地;和f,p是漢克爾變換參數(shù)和拉氏變換參數(shù),分別。

5、Eqs解的。(13)和(14)是在c = f + 2 p。基于Eqs。(4),(16),解決方案為位移、孔隙水壓力、對(duì)軸對(duì)稱(chēng)變形的應(yīng)力有了完全的飽和多孔固體可以如下所述在表示了拉普拉斯變換重疊酒吧有關(guān)參數(shù)。3解半無(wú)限階層3.1基本解,點(diǎn)裝,如圖1、一個(gè)垂直荷載是應(yīng)用于點(diǎn)并無(wú)限的表面強(qiáng)化層,其中H阻礙的厚度層,k1和k2滲透系數(shù)的是阻礙層和嗎層的鞏固,分別。它假定了阻礙層有足夠的剛度,滲透而已發(fā)生在阻礙垂直層,并進(jìn)一步,那沒(méi)有剪應(yīng)力面為z = 0。然后,邊界條件的鞏固層表面的幾點(diǎn)建議通過(guò)在d(r)的階躍函數(shù)。利用拉普拉斯變換和零級(jí)漢克爾變換,Eqs。(22)-(24)重寫(xiě)為結(jié)合Eqs的解決方案。

6、(17)-(21)與邊界Eqs條件。(22)-(24)可以被獲得作為,以下基本解決方案點(diǎn)的階躍載荷3.2圓形分布載荷的的解決方案如圖。2、垂直循環(huán)加載強(qiáng)度問(wèn)是應(yīng)用于的圓形區(qū)域半徑R在飛機(jī)z = 0。利用拉普拉斯變換和漢克爾變換邊界條件的零的產(chǎn)量下列方程只是取代p0/2p根本的解決方案加載了這一點(diǎn)Eqs。(28)-(32),解決方案循環(huán)加載數(shù)據(jù)。4解有限層4.1基本解,點(diǎn)裝,如圖3所示,一個(gè)垂直荷載是應(yīng)用于點(diǎn)并表面形成一層有限鞏固。在本圖中,H阻礙層的厚度、h是厚的鞏固層等參數(shù)可被訪(fǎng)問(wèn)圖1 .它假定了基地的鞏固層基于一個(gè)光滑的、僵硬的,不透水介質(zhì)。然后,這架飛機(jī)摘要基于通用的解決方案Eqs。(1

7、7)-(21)和邊界Eqs條件。(25)-(27)和拉普拉斯變換方程漢克爾變換和零Eqs。(36)-(38),基本解有限層在拉氏域可以得到以下表格4.2圓形分布載荷的的解決方案類(lèi)似的分析解的圓形分布加載應(yīng)用于無(wú)限地層,如圖4)。圓形分布載荷的解決方法應(yīng)用在一個(gè)有限的層也可以是通過(guò)整合的基本原理點(diǎn)解一個(gè)圓形的區(qū)域,在加載5數(shù)值計(jì)算和分析(圓形分布載荷)大多數(shù)以上解決方案應(yīng)評(píng)估計(jì)算。在數(shù)值積分計(jì)劃,所有無(wú)窮積分對(duì)漢克爾變換參數(shù)外進(jìn)行評(píng)估利用辛普森統(tǒng)治和時(shí)域解采用近似計(jì)算拉普拉斯反公式Shapery建議15。垂直分布問(wèn)題的單位循環(huán)載荷應(yīng)用于無(wú)限和有限層地層都認(rèn)為,分別考慮下列參數(shù)H從0到5。在固結(jié)度

8、、孔隙水壓力垂直總應(yīng)力和剪切應(yīng)力進(jìn)行了分析。圖5顯示固結(jié)度函數(shù)的時(shí)間無(wú)因次時(shí)刻T的用ct / R2 = T。從中可以發(fā)現(xiàn)層厚度的阻礙影響認(rèn)識(shí)的合并兩個(gè)階層和有限層,并鞏固的有限層,遠(yuǎn)快于常用的半無(wú)限階層起阻礙層定位在鞏固層,阻礙滲透鞏固的層。作為結(jié)果,鞏固率減小厚度的增加阻礙層。如果阻礙層厚度為零上邊界的層,然后變成全鞏固滲透。超孔隙水壓力的無(wú)因次酚醛/ qz = 0.5在中心區(qū)域的加載對(duì)T被顯示出在圖6。這Mandel-Cryer可以明顯地看到效果圖形。pf的峰值出現(xiàn)在T / q從0.01上升到0.1,它隨著厚度的增加層的阻礙。無(wú)因次垂直的變化總應(yīng)力法山株仔/ q在整理是如圖。7 .可以看出

9、垂直總應(yīng)力變化,在整理因?yàn)轳詈系目紫端南呐c土骨架變形。峰值的總數(shù)壓力的價(jià)值也出現(xiàn)T,是在0.01到0.1之間波動(dòng)。很少有一個(gè)區(qū)別這兩者之間的總應(yīng)力強(qiáng)化層的地層和有限無(wú)限層。剪切應(yīng)力在z / R = 0.5和R / R = 1不同阻礙層厚度如圖第八。厚度阻礙層的剪切應(yīng)力幾乎不能影響如果鞏固層的厚度的阻礙層是大的,剪切應(yīng)力增加而增加在阻礙層的厚度對(duì)同一鞏固時(shí)間。相似的變化對(duì)垂直的總應(yīng)力法在整合,最大剪切應(yīng)力鞏固層出現(xiàn)在關(guān)于T = 0.1。分布剪切應(yīng)力的在飛機(jī)z = 0.5被顯示在圖9。它的最大剪切應(yīng)力達(dá)到價(jià)值的r / r是1。6結(jié)論,并討論顯式解拉普拉斯轉(zhuǎn)換的位移,壓力和孔隙水壓力的semii

10、nfinite方程地層和有限層與一個(gè)阻礙邊界并受垂直點(diǎn)加載,分別。這些方案還延伸到處理循環(huán)分布載荷。阻礙延誤的層的鞏固層,其厚度影響孔隙水之間壓力和應(yīng)力的強(qiáng)化層。鞏固有限層,遠(yuǎn)快于常用的半無(wú)限對(duì)同一載和地層滲透率的條件。這固結(jié)比的減小而增大之增加厚度層的阻礙。超孔隙水壓力的,Mandel-Cryer的效果可能會(huì)提出了一種用所提出的解決方案,并對(duì)它發(fā)生在T = 0.01 -0.1。因?yàn)槟壳暗慕鉀Q方案考慮耦合的過(guò)剩土壤孔隙水耗散和骨架變形垂直的總應(yīng)力變化的鞏固層的期間合并以及它的剪切應(yīng)力。剪切力在邊緣的圓形分布載荷的應(yīng)用比別的地方在鞏固層。參考1。答:一般理論降水的三維米合并。J應(yīng)用研究,1941

11、,14(1):155-1642。McNamee J,吉普森R e平面應(yīng)變和軸對(duì)稱(chēng)問(wèn)題合并的一個(gè)Semi-infinity粘土地層。問(wèn)J機(jī)甲和應(yīng)用數(shù)學(xué),1960,8(2):210-2273。吉布森R E,Schiffman R L、Pu年代軸對(duì)稱(chēng)平面應(yīng)變和>固結(jié)粘土層的滲透性在平坦基地。問(wèn)J.應(yīng)用數(shù)學(xué)作業(yè)線(xiàn),1970,13(4):505-5194。你Puswewala G,拉賈帕克薩R K·d·軸對(duì)稱(chēng)N的基本原理解決方案完全飽和多孔彈性固體。智力JEngng雜志,1988,26(5):419-4365。固結(jié)解析解多層基礎(chǔ)受軸對(duì)稱(chēng)加載。J巖土工程,1992,20:民俗6。

12、黃C Z,小y為二維解析解固結(jié)問(wèn)題。J.巖土工程,1996,18:47 54個(gè)臨床微生物7。王建民龔振青,方S .解決軸對(duì)稱(chēng)狀態(tài)向量降水問(wèn)題推導(dǎo)整合多層介質(zhì)。力學(xué)研究通訊,2001,28:671-6778。王建民J .,劉G R,林p .數(shù)值分析降水的整合徑向點(diǎn)插值方法的過(guò)程。國(guó)際固體和結(jié)構(gòu)雜志,2002(2):1 557-1 5739。公園鉀H、巴納吉P .三維土固結(jié)開(kāi)始通過(guò)特定的采用整體。月第一版。方法應(yīng)用Engrg作業(yè)線(xiàn),2002,18(1):3 233-3 25510。Cavalcanti C,Telles J C樓降水固結(jié)理論- - - - - -應(yīng)用邊界元法與時(shí)間無(wú)關(guān)的基本解決方案

13、飽和介質(zhì)。為推導(dǎo)工程分析與邊界元素,2003,27:145-15711分。陳R P,周哦,王H Z,吳昱。一維非線(xiàn)性多層土固結(jié)微分求積方法。電腦和巖土、2005年,32:358-36912。謝一維固結(jié)分析K .分層土壤阻礙的界限。J.浙江大學(xué),1996,19(1):30。567-575(中文)13歲。謝鉀H,謝X Y,對(duì)一維固結(jié)理論高Xtwo-layered土壤排水的部分邊界。電腦和巖土,1999,24:265-27814。McNamme J,吉普森R e位移函數(shù)和線(xiàn)性變換通過(guò)應(yīng)用于多孔彈性介質(zhì)擴(kuò)散。問(wèn)J機(jī)甲應(yīng)用數(shù)學(xué),1970,13:89-11115。答:近似方法Shapery R變換反演粘彈

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