王艷芳+周治剛+蔡燕燕
摘要:通過k0固結(jié)蠕變?cè)囼?yàn)探討飽和淤泥土在軸向加載和側(cè)向減載條件下的蠕變特性。由試驗(yàn)數(shù)據(jù)知:排水條件下,兩種應(yīng)力路徑的軸向蠕變規(guī)律基本一致,體積應(yīng)變明顯小于軸向應(yīng)變,且隨時(shí)間的延長(zhǎng)呈現(xiàn)一定程度的剪縮與剪脹交替性。Merchant和Burgers蠕變模型對(duì)淤泥土都有較好擬合精度。二者的蠕變參數(shù)EK、ηK、ηM均呈現(xiàn)隨應(yīng)力水平的增大而減小的變化規(guī)律,EM隨應(yīng)力水平的變化則較為平穩(wěn),無明顯增大或減小趨勢(shì),說明淤泥土的蠕變變形受黏彈模量影響較小,受土體黏滯系數(shù)及彈性模量影響較大。
關(guān)鍵詞:淤泥土;k0固結(jié);蠕變?cè)囼?yàn);Merchant模型;Burgers模型
中圖分類號(hào):TU435 文獻(xiàn)標(biāo)志碼:A 文章編號(hào):1672-1683(2017)02-0139-06
Abstract:The creep characteristic of saturated silt soil was studied through k0 consolidation creep tests under the conditions of axial loading and lateral lightening.The following results were found.First,the axial creep patterns of the two stress paths were basically consistent under the drainage conditions.The volume strains were much smaller than the axial strains.The volume strains showed an alternation between shear shrinkage and shear dilatancy with the passage of time.The Merchant and Burgers creep models both had good fitting accuracy.The creep parameter EM showed no significant increasing or decreasing trend with the increase of deviatoric stress level,but the other creep parameters EK,ηK,ηM of the two creep models decreased with the increase of deviatoric stress level.These findings suggested that the creep strain of silt soil is mildly influenced by viscoelastic modulus,but largely influenced by the viscous coefficient and elastic modulus.
Key words:silt soil;k0 consolidation;creep test;Merchant model;Burgers model
近年來,隨著軟土工程的迅速發(fā)展,關(guān)于軟黏土的蠕變特性研究取得了許多的成果[1-6]。目前對(duì)土體蠕變特性的試驗(yàn)研究多數(shù)基于常規(guī)的等向固結(jié)三軸試驗(yàn)進(jìn)行,而沒有考慮土體k0固結(jié)情況對(duì)其蠕變特性的影響。隨著對(duì)天然狀態(tài)k0固結(jié)土的研究不斷深入,人們逐漸認(rèn)識(shí)到各向異性對(duì)土體的蠕變性狀有較大影響[7-9]。有些學(xué)者對(duì)k0固結(jié)軟土的流變模型進(jìn)行了探討,但都僅考慮初始應(yīng)力誘發(fā)各向異性的影響,而沒有考慮土體剪切變形過程中各向異性的演化[10-12]。本文旨在通過三軸試驗(yàn)研究飽和土體在完成k0固結(jié)后且排水條件下的蠕變規(guī)律,并探討在軸向加載條件下和側(cè)向減載條件下土樣的蠕變特性有何差異。
1 三軸蠕變?cè)囼?yàn)
1.1 試驗(yàn)方案
本文淤泥土取自于天津港碼頭遮簾式板樁碼頭工程項(xiàng)目區(qū)域,土樣的物理力學(xué)性質(zhì)參數(shù)如表1所示。由于碼頭工程區(qū)域土體變形主要受到軸向壓縮和側(cè)向卸荷兩種應(yīng)力路徑的作用[13],故本文取一定數(shù)量的淤泥土進(jìn)行飽和重塑土的軸向加載和側(cè)向減載的三軸排水蠕變?cè)囼?yàn)。試驗(yàn)之前先根據(jù)淤泥土的取樣深度完成土體的先期k0固結(jié)條件。本文淤泥土樣k0值取為0.45。
試驗(yàn)在改裝后的應(yīng)力控制式三軸儀上進(jìn)行,試樣直徑為39.1 mm,高度為80 mm。試驗(yàn)過程共分三步驟,以軸向加載條件下圍壓50 kPa土樣為例,第一步土樣在50 kPa圍壓荷載下完成等向固結(jié);第二步依據(jù)k0=0.45,緩慢增加軸壓至111 kPa并完成k0固結(jié);第三步為蠕變加載,每級(jí)荷載為緩慢增加軸壓20~40 kPa不等,如第一級(jí)為軸壓由111 kPa增至130 kPa后并保持軸壓不變,測(cè)定該級(jí)荷載下,土樣軸向變形及體積變形隨時(shí)間的變化量,待軸向變形達(dá)到蠕變穩(wěn)定標(biāo)準(zhǔn)后,進(jìn)入下一級(jí)蠕變荷載。具體蠕變?cè)囼?yàn)方案見表2。
由于目前為止,還沒有關(guān)于蠕變?cè)囼?yàn)的規(guī)范,對(duì)蠕變的穩(wěn)定標(biāo)準(zhǔn)也沒有統(tǒng)一的說法,一般認(rèn)為在10 000 s內(nèi)變形量小于0.01 mm,則認(rèn)為已達(dá)到穩(wěn)定[14]。如實(shí)際上觀察土樣在24 h內(nèi)變形量小于0.01 mm,則可以進(jìn)入下一級(jí)應(yīng)力水平試驗(yàn)[15-17]。此次蠕變?cè)囼?yàn)穩(wěn)定標(biāo)準(zhǔn)為:每一級(jí)蠕變荷載施加的同時(shí)開始記錄,當(dāng)時(shí)間為0.25 min、1.25 min、4 min、9 min、16 min、25 min、36 min、49 min、64 min、100 min、150 min、200 min、260 min、350 min、470 min、650 min時(shí)記錄百分表讀數(shù)及體變管讀數(shù),接下來一天內(nèi)進(jìn)行2~4次讀數(shù)。試樣連續(xù)24 h內(nèi)土樣軸向變形小于0.025 mm時(shí),認(rèn)為蠕變變形已穩(wěn)定,可以繼續(xù)下一級(jí)荷載的施加或結(jié)束試驗(yàn)。
1.2 試驗(yàn)結(jié)果分析
1.2.1 剪切蠕變
根據(jù)實(shí)驗(yàn)結(jié)果,采用線性疊加原理將分級(jí)荷載下的應(yīng)變-時(shí)間關(guān)系曲線轉(zhuǎn)換為分別荷載下的蠕變曲線,并依據(jù)εS=εa-1/3εV求解出各級(jí)荷載作用下剪應(yīng)變?nèi)渥兦€[18],見圖1、圖2。由于土體進(jìn)行排水蠕變?cè)囼?yàn)之前,先完成三軸k0固結(jié)試驗(yàn),故土體在第一級(jí)蠕變之前就存在初始的剪應(yīng)變和體積應(yīng)變,且變形量隨圍壓的增大而增加,土體先期k0固結(jié)變形值相較蠕變變形不可忽略,說明還原土體先期k0固結(jié)條件的必要性。
由圖1、圖2可看出,軸向加載和側(cè)向減載條件下,二者剪切蠕變趨勢(shì)基本一致,不管應(yīng)力水平地高低,均為穩(wěn)定衰減型,沒有出現(xiàn)等速蠕變或加速蠕變。軸向加載條件下,土樣破壞前蠕變分級(jí)的最大偏應(yīng)力水平為0.83,而側(cè)向減載條件下可達(dá)到更高偏應(yīng)力水平,最大值可達(dá)0.96。從圖1、圖2的對(duì)比分析可知,在較低偏應(yīng)力水平下,土體在分級(jí)加載時(shí)的瞬時(shí)變形值和蠕變變形值都不大,而較高偏應(yīng)力水平下,土樣分級(jí)加載時(shí)瞬時(shí)變形值和蠕變值均增大,且蠕變進(jìn)入衰減狀態(tài)需要時(shí)間也越長(zhǎng)見圖2(b),說明偏應(yīng)力水平越高,蠕變變形越不易達(dá)到穩(wěn)定。1.2.2 體積蠕變
不論是軸向加載條件還是側(cè)向減載條件,體積變形的蠕變?cè)隽侩S偏應(yīng)力水平的增加而增加,體積蠕變未出現(xiàn)加速蠕變,見圖3、圖4。體應(yīng)變隨圍壓的減小,表現(xiàn)出先剪縮后剪脹的交替趨勢(shì),且側(cè)向減載條件下比軸向加載條件下土體更易剪脹,說明土體在低圍壓下易剪脹。
體積變形在加卸載初期變化并不大,進(jìn)入蠕變階段后保持一個(gè)相對(duì)穩(wěn)定的蠕變速率,且這種穩(wěn)定蠕變的速率很難減小,說明淤泥土的體變相較荷載的施加,存在滯后現(xiàn)象,且體積蠕變不像剪切蠕變,能較快進(jìn)入衰減蠕變階段,反而會(huì)保持相對(duì)較長(zhǎng)的穩(wěn)定蠕變階段。本文由于時(shí)間原因,未制定體積蠕變穩(wěn)定標(biāo)準(zhǔn),試驗(yàn)荷載的分級(jí)加載以土體軸向變形速率作為穩(wěn)定控制標(biāo)準(zhǔn)。故從體積蠕變曲線上看體積蠕變速率相較剪切蠕變速率較難達(dá)到蠕變穩(wěn)定標(biāo)準(zhǔn)。若體積存在剪脹趨勢(shì),則體積蠕變變形更不易達(dá)到穩(wěn)定。
2 蠕變模型
2.1 蠕變模型介紹
采用理論模型三單元的Merchant和四單元的Burgers模型進(jìn)行淤泥土蠕變特性的模擬[19-20](圖5),Merchant模型由胡克彈簧和Kelvin體串聯(lián)而成,其應(yīng)力應(yīng)變本構(gòu)關(guān)系式為
對(duì)于Merchant模型,在應(yīng)力σ,加載時(shí)間t和應(yīng)變?chǔ)牛╰)均已知情況下,需要確定的參數(shù)為EM、EKηK,而對(duì)于burgers模型有參數(shù)EM、ηM、EK、ηK。
2.2 蠕變參數(shù)的反演
根據(jù)實(shí)驗(yàn)結(jié)果,采用線性疊加原理將分級(jí)荷載下的應(yīng)變-時(shí)間關(guān)系曲線轉(zhuǎn)換為分別荷載下的蠕變曲線,并根據(jù)式(2)和式(4),利用Levenberg-Marquart(麥夸特)迭代方法,尋求方程組最優(yōu)解,反演得相關(guān)蠕變參數(shù)。列出淤泥土在σ3=100 kPa軸向加載條件下兩種蠕變模型各參數(shù)的反演結(jié)果見表2。
從表2數(shù)據(jù)和圖6計(jì)算曲線的擬合精度對(duì)比可看出,Merchant和Burgers模型對(duì)淤泥土有較好的適應(yīng)性。單從相關(guān)系數(shù)R來評(píng)價(jià)擬合精度時(shí),Burgers模型要比Merchant模型好。從圖6可看出低應(yīng)力水平時(shí),S<0.8時(shí),兩個(gè)模型均能達(dá)到較好擬合效果,S>0.8時(shí),Merchant模型蠕變速率過早減慢,而Burgers模型蠕變速率則隨時(shí)間幾乎穩(wěn)定不變,不太符合土體的衰減蠕變特征。故二者在高應(yīng)力水平時(shí),擬合效果均存在不足。
2.3 蠕變參數(shù)分析
圖7和圖8描述了淤泥土Merchant和Burgers模型蠕變參數(shù)隨應(yīng)力水平的關(guān)系圖。由圖可知兩個(gè)模型的蠕變參數(shù)參數(shù)EK、ηK、ηM均呈現(xiàn)隨應(yīng)力水平的增大而減小的變化規(guī)律,EM隨應(yīng)力水平的變化則較為平穩(wěn),無明顯增大或減小趨勢(shì)。說明淤泥土的蠕變變形受粘彈模量影響較小,受土體黏滯系數(shù)及彈性模量影響較大。這種影響效應(yīng)隨應(yīng)力水平增大而減弱。
3 結(jié)論
關(guān)于淤泥土蠕變特性的研究成果較多,本文在還原土體先期固結(jié)條件基礎(chǔ)上研究淤泥土的排水蠕變特性。將試驗(yàn)成果與已有的蠕變理論相結(jié)合做相關(guān)蠕變特性分析。由試驗(yàn)結(jié)果及相關(guān)分析可得以下結(jié)論。
(1)針對(duì)兩種應(yīng)力路徑的排水蠕變?cè)囼?yàn),不論軸向加載還是側(cè)向減載蠕變規(guī)律基本一致,即在應(yīng)力水平較低時(shí),蠕變變形很小,隨著應(yīng)力水平的提高,蠕變變形亦隨之增加。
(2)土體體應(yīng)變明顯小于剪應(yīng)變,且隨時(shí)間增加呈現(xiàn)一定程度的剪縮與剪脹交替性。側(cè)向減載條件下,土體更易發(fā)生剪脹。從體變隨時(shí)間關(guān)系曲線可以看出,當(dāng)沒有發(fā)生剪脹時(shí),體積變形較容易穩(wěn)定,一旦發(fā)生剪脹現(xiàn)象,體應(yīng)變較難穩(wěn)定。
(3)低應(yīng)力水平下,Merchant和Burgers蠕變模型對(duì)淤泥土都有較好擬合精度。蠕變參數(shù)EK、ηK、ηM均呈現(xiàn)隨應(yīng)力水平的增大而減小的變化規(guī)律,EM隨應(yīng)力水平的變化則較為平穩(wěn),無明顯增大或減小趨勢(shì),說明淤泥土的蠕變變形受黏彈模量影響較小,受土體黏滯系數(shù)及彈性模量影響較大。
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