砂土中單樁基礎(chǔ)沖刷的修正應(yīng)變楔計(jì)算①

楊曉峰,張陳蓉,黃茂松,袁聚云,高博雷

(1.同濟(jì)大學(xué)土木工程學(xué)院地下建筑與工程系,上海 200092; 2.同濟(jì)大學(xué)巖土及地下工程教育部重點(diǎn)實(shí)驗(yàn)室,上海 200092)

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砂土中單樁基礎(chǔ)沖刷的修正應(yīng)變楔計(jì)算①

楊曉峰1,2,張陳蓉1,2,黃茂松1,2,袁聚云1,2,高博雷1,2

(1.同濟(jì)大學(xué)土木工程學(xué)院地下建筑與工程系,上海 200092; 2.同濟(jì)大學(xué)巖土及地下工程教育部重點(diǎn)實(shí)驗(yàn)室,上海 200092)

由沖刷引起的深水結(jié)構(gòu)物樁基礎(chǔ)周圍土體損失致使基礎(chǔ)水平承載性能下降的問題越發(fā)受到重視。應(yīng)變楔方法假設(shè)樁前土體抵抗為三維楔形體,其尺寸發(fā)展與楔形體區(qū)域土體發(fā)揮的內(nèi)摩擦角有關(guān),從而得到水平受荷樁的p-y曲線。本文對(duì)應(yīng)變楔方法進(jìn)行修正和拓展,建立非線性位移假設(shè)以考慮樁前楔形體區(qū)域土體應(yīng)變沿深度的非均勻分布,將沖刷坑底以上土體的有效自重作用等效為豎向荷載,對(duì)楔形體的深度進(jìn)行修正,以解決楔形體方法只適用于地表水平的情況,得到砂土中單樁基礎(chǔ)沖刷的修正應(yīng)變楔計(jì)算方法;并通過與模型試驗(yàn)及三維有限元分析的對(duì)比來驗(yàn)證該方法的合理性。分析結(jié)果表明:沖刷深度增加會(huì)顯著降低樁基水平承載性能,沖刷深度3.2D和6.4D情況下的樁頂位移比平均值分別趨近于1.8和3.0;相比有限元方法,本文修正SW方法計(jì)算的p-y曲線結(jié)果與實(shí)測(cè)結(jié)果更為接近。

沖刷; 水平受荷樁; 修正應(yīng)變楔方法;砂土; p-y曲線

0　引言

橋梁基礎(chǔ)和海上風(fēng)電因水流沖刷會(huì)造成樁基周圍土體的損失,引起水平承載性能下降,甚至上部結(jié)構(gòu)的破壞,因此對(duì)沖刷條件下樁基礎(chǔ)水平承載性能的評(píng)估越來越受重視[1-5]。Ni等[2]將沖刷簡(jiǎn)單地模擬為整個(gè)土層的剝離,分析了砂土中不同沖刷深度對(duì)單樁水平承載力的損失。Achmus等[4]的有限元分析表明,沖刷深度對(duì)海上大直徑樁的水平位移和轉(zhuǎn)角有重大影響。Li等[5]研究了局部沖刷尺寸(沖刷深度、寬度和坡角)對(duì)海洋軟黏土中水平受荷單樁承載力的影響,認(rèn)為沖刷深度達(dá)到5倍樁徑時(shí)單樁水平承載力下降40%左右。Lin等[6]令沖刷條件下與Reese地表水平條件下的樁前楔形體土體極限抗力值相等,對(duì)Reese極限平衡方法[7]進(jìn)行修正,推導(dǎo)了沖刷條件下的p-y曲線,但該方法僅修正了Pu值。

與Reese方法不同,應(yīng)變楔(Strain Wedge)方法(以下簡(jiǎn)稱SW法)[8]將樁前楔形體的幾何尺寸發(fā)展與土體發(fā)揮的內(nèi)摩擦角建立聯(lián)系,使得樁側(cè)p-y曲線的開展與土體的非線性應(yīng)力應(yīng)變關(guān)系完全對(duì)應(yīng)。Xu等[9]基于SW法討論了Duncan-Chang和Mohr-Coulomb土體條件下p-y曲線的區(qū)別,而文獻(xiàn)[10]對(duì)SW方法的楔形體內(nèi)土體應(yīng)變均一化假設(shè)進(jìn)行了修正改進(jìn)。與Reese方法類似,SW方法只適用于地表水平的情況。本文參考了文獻(xiàn)[11]的楔形體等效深度修正,考慮了沖刷引起的樁周土體幾何形狀的改變,將修正SW方法應(yīng)用于沖刷條件下的水平受荷樁分析。

本文將砂土中的修正應(yīng)變楔方法推廣到考慮沖刷坑幾何尺寸的非水平地表?xiàng)l件下,基于坑底以上楔形體的自重荷載得到?jīng)_刷條件下的楔形體等效深度,分析沖刷深度對(duì)單樁水平承載性能的影響,并與模型試驗(yàn)的結(jié)果以及有限元分析進(jìn)行對(duì)比驗(yàn)證。

1　應(yīng)變楔模型的修正

在水平荷載下,將樁周土體作用等效成彈性地基梁上的非線性彈簧,樁土系統(tǒng)的平衡方程為:

(1)

式中:EI為樁身抗彎剛度;y為樁身水平位移;z為地表以下深度;地基反力模量k=p/y,p為單位樁長(zhǎng)提供的土體抗力。

樁頂受水平荷載時(shí),樁前土體處于被動(dòng)受壓狀態(tài),應(yīng)變楔模型[8]假定在樁前形成三維被動(dòng)土楔,其幾何形態(tài)由扇形角φm、底角βm和楔形體最大深度H進(jìn)行描述,如圖1所示。隨著外荷載的增大,楔形體的尺寸和內(nèi)部應(yīng)力應(yīng)變狀態(tài)隨之發(fā)展。根據(jù)樁前楔形體土體局部平衡條件和單樁的樁土系統(tǒng)平衡條件進(jìn)行求解,得到單樁在水平荷載下的響應(yīng)和相應(yīng)的p-y曲線。

圖1　應(yīng)變楔模型Fig.1　Basic strain wedge model

應(yīng)變楔模型假定被動(dòng)楔對(duì)應(yīng)的樁身水平位移沿深度線性變化(圖2),該假設(shè)使得楔形體內(nèi)水平向土體應(yīng)變大小一樣。修正應(yīng)變楔方法對(duì)樁身變形的開展引入了非線性假設(shè)(圖3),具體實(shí)現(xiàn)如下:將樁和應(yīng)變楔土體沿深度均勻分層,各子層上下界面處的樁身位移分別與該層的樁身偏轉(zhuǎn)角及水平土體應(yīng)變建立聯(lián)系,以考慮楔形體內(nèi)土體應(yīng)變沿深度的發(fā)展變化。假定子層厚度為h,單樁在第i層的上下界面處位移分別為yi-1和yi,則第i層單樁偏移角δi與樁身位移的關(guān)系為:

(2)

樁身偏轉(zhuǎn)角與土體水平應(yīng)變的關(guān)系[8]為:

(3)

式中:εvi為土體的豎向應(yīng)變,εvi=-υεi,υ為土體的泊松比。θmi為βmi的補(bǔ)角,θmi=45°-φmi/2。

圖2　樁身線性位移示意圖[8]Fig.2　Linear displacement assumption of a laterally loaded pile in the SW model[8]

圖3　修正應(yīng)變楔模型的樁身非線性位移假定[10]Fig.3　Nonlinear displacement assumption of a laterally loaded pile in the modified SW model[10]

2　沖刷條件下的楔形體等效

沖刷是水流對(duì)土體的一種侵蝕行為,會(huì)引起樁基礎(chǔ)周圍土體損失而形成局部沖刷坑。典型沖刷坑剖面如圖4所示,由沖刷坑深度Sd、沖刷寬度Sw和沖刷坑坡角θ加以描述。當(dāng)Sw=∞時(shí)為最不利情況,即沖刷深度范圍內(nèi)土層全部被剝蝕。

圖4　沖刷坑剖面示意圖[6]Fig.4　The profile of a scour hole[6]

應(yīng)變楔方法[8]僅適用于地表水平的情況,為此需要進(jìn)行修正。在整個(gè)水平加載過程中,針對(duì)沖刷坑的幾何形態(tài)和楔形體的發(fā)展?fàn)顟B(tài),將坑底以上土體的自重作用等效為豎向荷載,推導(dǎo)等效深度hs,建立等效應(yīng)變楔模型(圖5)。等效深度hs的求解具體見文獻(xiàn)[11]。得到等效深度hs后,結(jié)合修正應(yīng)變楔模型的求解,以實(shí)現(xiàn)應(yīng)變楔模型在沖刷條件下的推廣。

圖5　沖刷條件下等效應(yīng)變楔模型[11]Fig.5　The equivalent strain wedge model under scour[11]

3　算例驗(yàn)證

高博雷[12]進(jìn)行了砂土中沖刷條件下單樁水平響應(yīng)的1g模型試驗(yàn)。試驗(yàn)用土為中密細(xì)砂,砂土物理指標(biāo)見表1。模型樁的尺寸和材料參數(shù)見表2。本文選取無沖刷和沖刷深度分別為3.2D和6.4D的三組試驗(yàn)進(jìn)行分析,沖刷坡角20°,沖刷寬度為零,加載點(diǎn)位于沖刷前地表以上0.16 m處,無沖刷時(shí)樁身入土深度0.69 m。為驗(yàn)證計(jì)算的可靠性,對(duì)試驗(yàn)結(jié)果進(jìn)行三維有限元數(shù)值模擬,計(jì)算范圍:水平方向取30倍樁徑,豎直方向樁端向下取10倍樁徑。砂土采用MC材料模擬,樁土接觸面摩擦系數(shù)u=tan(φ/2)[6]。對(duì)無沖刷結(jié)果進(jìn)行反演,得到砂土彈模0.3 MPa,泊松比0.3。為保證收斂性,黏聚力取0.5 kPa。考慮到對(duì)稱性,有限元模型取一半,見圖6。

表1　砂土參數(shù)

表2　模型樁參數(shù)

圖6　考慮沖刷的有限元模型Fig.6　Finite element model considering scouring

圖7分別給出了三組試驗(yàn)的荷載位移曲線,11.76 N水平荷載時(shí)的樁身彎矩分布和樁身變形分布,并給出了本文計(jì)算方法和有限元計(jì)算結(jié)果。由圖可見,隨著沖刷深度的增大,樁身水平承載性能明顯降低,樁身所承受的最大彎矩顯著增加,最大彎矩位置也向更深土層移動(dòng)。

圖8給出了11.76 N和27.44 N兩種荷載水平下不同沖刷深度時(shí)加載點(diǎn)處的樁身水平位移。由圖可見:荷載一定時(shí),樁頂位移隨著沖刷深度的增大而加速增長(zhǎng);荷載水平較小(11.76 N)時(shí)各計(jì)算結(jié)果吻合較好,而荷載水平較大(27.44 N)時(shí),修正SW法計(jì)算的水平位移偏大,尤其是沖刷深度6.4D時(shí)。

圖7　樁身荷載位移、彎矩分布及變形曲線Fig.7　Curves of load-displacement,bending moment distribution,and deformation of the pile

圖8　樁頂位移隨沖刷深度的變化Fig.8　Displacements at pile head versus scour depths

圖9給出了不同荷載下的樁頂位移比。位移比即某一荷載下所得樁頂位移值與相應(yīng)無沖刷情況下位移的比值。相同荷載下,沖刷深度6.4D情況比3.2D情況的位移比大,但是隨著荷載的增大位移比趨于穩(wěn)定,沖刷深度3.2D和6.4D時(shí)平均位移比分別趨近于1.8和3.0左右。

圖9　不同水平荷載下的位移比Fig.9　Ratios of displacements at pile head versus lateral load

圖10給出了地表下6.9D處不同沖刷情況下的p-y曲線。由圖可見,隨著沖刷深度的增大,實(shí)測(cè)值和修正SW方法p-y曲線的初始斜率和相同位移水平下的土體抗力均有明顯降低且成增速下降。有限元計(jì)算得到的各沖刷深度下p-y曲線的初始斜率變化不大,僅影響了極限值。

圖10　地表下6.9D深度處的p-y曲線Fig.10　p-y curves at a depth of 6.9D

4　結(jié)論

(1)沖刷條件下建立的分析水平受荷樁的修正應(yīng)變楔方法是常規(guī)應(yīng)變楔方法的進(jìn)一步推廣,通過模型試驗(yàn)和有限單元法驗(yàn)證了其有效性。

(2)沖刷深度的增加對(duì)樁水平承載力性能的下降作用明顯。本文計(jì)算得到?jīng)_刷深度3.2D和6.4D情況下的樁頂位移比呈逐漸下降趨勢(shì),分別趨近于平均值1.8和3.0。

(3)相比有限元計(jì)算的p-y曲線結(jié)果,本文修正SW方法與實(shí)測(cè)結(jié)果更為接近。

References)

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[2]Ni S H,Huang Y H,Lo K F.Numerical Investigation of the Scouring Effect on the Lateral Response of Piles in Sand[J].Journal of Performance of Constructed Facilities,2011,26(3):320-325.

[3]Prendergast L J,Gavin K.A Review of Bridge Scour Monitoring Techniques[J].Journal of Rock Mechanics and Geotechnical Engineering,2014,6(2):138-149.

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[5]Li F,Han J,Lin C.Effect of Scour on the Behavior of Laterally Loaded Single Piles in Marine Clay[J].Marine Georesources & Geotechnology,2013,31(3):271-289.

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[7]Reese L C,Cox W R.Analysis of Laterally Loaded Piles in Sand[C]//Offshore Technology in Civil Engineering@ sHall of Fame Papers from the Early Years.ASCE,1974,95-105.

[8]Ashour M,Norris G,Pilling P.Lateral Loading of a Pile in Layered Soil Using the Strain Wedge Model[J].Journal of Geotechnical and Geoenvironmental Engineering,1998,124(4):303-315.

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[11]楊曉峰,張陳蓉,袁聚云.砂土中考慮沖刷的水平受荷樁等效應(yīng)變楔方法[J].巖土力學(xué),2015,36(10):2946-2950.

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Modified Strain Wedge Calculation of Single Pile in Sand under Scour

YANG Xiao-feng1,2,ZHANG Chen-rong1,2,HUANG Mao-song1,2,YUAN Ju-yun1,2,GAO Bo-lei1,2

(1.Department of Geotechnical Engineering,College of Civil Engineering,Tongji University,Shanghai 200092,China;2.Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education,Tongji University,Shanghai 200092,China)

Scour can induce soil loss around the pile foundations of engineering structures in deep water and the degeneration of the lateral bearing capacity of pile foundations caused by scour is being paid more and more attention.The strain wedge (SW)method is an effective p-y curve technique for predicting the response of piles under lateral loading.It assumes that a three-dimensional passive soil wedge forms to resist the movement of a laterally loaded pile and that the dimensions and mobilized friction angle of the soil wedge develop as the lateral load increases.However,in order to improve and extend the ability of the SW method,a modified SW method is developed which introduces the assumption of nonlinear lateral deflection of the pile resulting in non-uniform soil strain,rather than uniform strain in the soil wedge.In addition,by equating the soil weight above the bottom of the scour hole to a vertical load,the problem of the SW method being only suitable for horizontal ground surfaces is solved.The validity of the method is confirmed by the measured results of a model test and the finite element method.Results show that the lateral bearing capacity of the pile sharply declines as scour depth increases.The average ratio of lateral displacements at the pile head tended to 1.8 and 3.0 when scour depths were 3.2D and 6.4D (D=outer diameter of pile),respectively.Compared with the results of p-y curves from the finite element method,the results from the modified SW method are much more satisfactory than those measured.

scour; laterally loaded piles; modified strain wedge method; sand soil; p-y curve

2016-04-26

國(guó)家973計(jì)劃課題(2013CB036304)，國(guó)家自然科學(xué)基金項(xiàng)目(51378392)

楊曉峰(1986-)，男，博士研究生，從事樁基工程研究。E-mail:xiaofengsile@163.com。通信作者：張陳蓉(1982-)，女，副研究員，主要從事樁基工程科研與教學(xué)工作。E-mail:zcrong33@#edu.cn。

TU473

A

1000-0844(2016)04-0549-05

10.3969/j.issn.1000-0844.2016.04.0549