深基坑開(kāi)挖卸荷對(duì)既有樁基側(cè)摩阻力影響分析

龔曉南+王繼成+伍程杰

文章編號(hào)：16742974(2014)06007007

收稿日期：20131125

基金項(xiàng)目：國(guó)家自然科學(xué)基金資助項(xiàng)目(51078377)

作者簡(jiǎn)介：龔曉南（1944-），男，浙江金華人，浙江大學(xué)教授，中國(guó)工程院院士，博士生導(dǎo)師

通訊聯(lián)系人，E-mail: xngong@hzcnc.com

摘 要：基坑開(kāi)挖卸荷導(dǎo)致工程樁樁側(cè)極限阻力降低.建立單樁模型，用Mindlin應(yīng)力解考慮開(kāi)挖引起的豎向有效應(yīng)力變化，分別計(jì)算開(kāi)挖前后的樁側(cè)極限阻力.通過(guò)某工程案例，將理論結(jié)果與其他結(jié)果相對(duì)比.最后分析了樁側(cè)阻力降低系數(shù)隨基坑開(kāi)挖深度、邊長(zhǎng)、長(zhǎng)寬比及樁長(zhǎng)的變化規(guī)律.結(jié)果表明：樁側(cè)阻力降低系數(shù)隨開(kāi)挖深度增加先減小而后緩慢增大，存在谷值臨界深度，隨開(kāi)挖邊長(zhǎng)、長(zhǎng)寬比增加先減小而后趨于穩(wěn)定；增加樁長(zhǎng)導(dǎo)致樁側(cè)阻力降低系數(shù)增大.



關(guān)鍵詞：基坑開(kāi)挖；Mindlin應(yīng)力解；豎向有效應(yīng)力；樁側(cè)阻力



中圖分類號(hào)：TU473.1 文獻(xiàn)標(biāo)識(shí)碼：A

Effect of Unloading on the Shaft Resistance 

of Existing Piles due to Deep Excavation



GONG Xiaonan1, WANG Jicheng1,2, WU Chengjie1



(1. Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang Univ, Hangzhou,

Zhejiang 310058, China;2. Taizhou Tocational and Technical College, Taizhou, Zhejiang 318000, China)

Abstract: The effect of excavationrelated unloading on the underlying soil will reduce the ultimate pile shaft resistance. In this study, Mindlin's stress solution was used to allow for the variation of vertical effective stresses induced by excavation around a single pile. The ultimate resistances of the pile shaft before and after the excavation were calculated. The results of theoretical calculation were compared with others through a case study. Furthermore, the variations of reduction factors for shaft resistance with excavation depth, excavation length, ratio of length to width and pile length were analyzed. The results showed that reduction factors for shaft resistance decreased firstly and then increased with the increase of excavation depth, and it decreased first and then tended to be stable with the increase of excavation length and ratio of length to width. With the increase of pile length, the reduction factors for shaft resistance increased.

Key words:excavation; Mindlins stress solution; vertical effective stress; pile shaft resistance



基坑開(kāi)挖一般在成樁之后，而基坑開(kāi)挖時(shí)由于土體卸載打破了原有的平衡狀態(tài)，引起坑底土體卸荷回彈，并導(dǎo)致樁體承載力折減，這已經(jīng)成為學(xué)者和工程師們的共識(shí).

酈建俊等[1-3]基于上海某變電站深基坑開(kāi)挖后抗拔樁的實(shí)例，通過(guò)理論研究、數(shù)值分析、現(xiàn)場(chǎng)實(shí)測(cè)等方法分析了分層軟土地基中抗拔樁在深開(kāi)挖條件下的承載特性；王衛(wèi)東等[4]通過(guò)理論研究以及數(shù)值分析，認(rèn)為基坑開(kāi)挖卸荷會(huì)引起抗拔樁承載力損失；范巍[5]通過(guò)有限元法系統(tǒng)地研究了深基坑開(kāi)挖過(guò)程中單樁和群樁的受力特性，通過(guò)某工程實(shí)例說(shuō)明了如何對(duì)抗拔樁和抗壓樁進(jìn)行驗(yàn)算；胡琦等[6]采用模型試驗(yàn)和數(shù)值方法分析了基坑開(kāi)挖對(duì)坑內(nèi)工程樁承載力和剛度的影響，認(rèn)為采用覆土條件下測(cè)得的樁體承載力和剛度值是不安全的；楊敏等[7]通過(guò)理論研究表明，基坑開(kāi)挖會(huì)引起樁體回彈和樁側(cè)正負(fù)摩阻力，樁體位移量隨著樁長(zhǎng)和樁徑的增加而減少，中性點(diǎn)隨著樁長(zhǎng)增加其深度位置逐漸下移；鄭剛等[8-10]先后通過(guò)數(shù)值方法和模型試驗(yàn)分析了開(kāi)挖對(duì)工程樁的承載特性的影響，認(rèn)為基坑開(kāi)挖對(duì)樁基承載力和樁基剛度分別產(chǎn)生最高達(dá)45%和75%的衰減，同時(shí)開(kāi)挖導(dǎo)致超長(zhǎng)樁側(cè)阻和端阻異步發(fā)揮現(xiàn)象明顯，對(duì)在非膨脹土和膨脹土中的摩擦型樁的樁基承載力產(chǎn)生不同影響；王成華等[11]通過(guò)分析認(rèn)為開(kāi)挖后樁身大部分處于受拉狀態(tài)，樁端附近受壓，樁側(cè)阻力從樁身中部開(kāi)始向下部發(fā)揮；而文獻(xiàn)[12]則通過(guò)工程實(shí)例分析了基坑開(kāi)挖對(duì)坑底基樁的影響.

基坑開(kāi)挖卸荷會(huì)引起樁側(cè)阻力和樁端阻力的減小，劉國(guó)彬等[13]通過(guò)引入殘余應(yīng)力系數(shù)概念，將其定義為豎向殘余應(yīng)力與未開(kāi)挖前豎向初始應(yīng)力之比，認(rèn)為在開(kāi)挖面以下某點(diǎn)其值趨近于1時(shí)，說(shuō)明其處于初始應(yīng)力狀態(tài)，沒(méi)有產(chǎn)生卸荷效應(yīng)，并建議把殘余應(yīng)力系數(shù)為0.95時(shí)的深度作為殘余應(yīng)力影響深度，根據(jù)上海地區(qū)大量工程實(shí)例得出了如下經(jīng)驗(yàn)關(guān)系式：

hr=H0.0612H+0.19.(1)

式中：H為基坑開(kāi)挖深度, m；hr為殘余應(yīng)力影響深度, m.通過(guò)計(jì)算可以發(fā)現(xiàn)，當(dāng)基坑開(kāi)挖深度H>5 m時(shí)，殘余應(yīng)力影響深度將小于2H，這說(shuō)明開(kāi)挖面2H深度以下土體中不產(chǎn)生卸荷效應(yīng)，也就不存在回彈變形.李超[14]通過(guò)研究認(rèn)為基坑大面積開(kāi)挖均勻卸荷的情況下，坑底土體回彈變形的極限深度為2H，并認(rèn)為實(shí)際工程中基坑回彈變形的極限深度為1.5H.伍程杰等[15]通過(guò)某工程案例的研究發(fā)現(xiàn)開(kāi)挖10 m后，有效樁長(zhǎng)為34 m的樁端阻力的損失僅為2.4%.龔曉南等[16]基于平面單樁模型，研究既有建筑下開(kāi)挖卸荷對(duì)原有樁基側(cè)摩阻力的影響，發(fā)現(xiàn)開(kāi)挖深度超過(guò)0.5倍樁長(zhǎng)時(shí)，樁側(cè)阻力損失超過(guò)50%.因此本文重點(diǎn)研究基坑開(kāi)挖在樁側(cè)產(chǎn)生的卸荷效應(yīng)，分析其對(duì)樁側(cè)阻力的影響.

本文建立基坑開(kāi)挖三維單樁模型，首先通過(guò)理論公式推導(dǎo)，得到考慮開(kāi)挖卸荷效應(yīng)的樁側(cè)極限阻力計(jì)算公式，然后通過(guò)某工程案例，分別與工程實(shí)測(cè)數(shù)據(jù)、有限元分析結(jié)果以及其他方法結(jié)果相對(duì)比，驗(yàn)證該理論方法的合理性，最后提出樁側(cè)阻力降低系數(shù)的概念，并將開(kāi)挖深度、邊長(zhǎng)與樁長(zhǎng)相比進(jìn)行歸一化，通過(guò)算例分析樁側(cè)阻力降低系數(shù)隨基坑開(kāi)挖深度、邊長(zhǎng)、長(zhǎng)寬比以及樁長(zhǎng)的變化規(guī)律.

1 樁側(cè)阻力計(jì)算

1.1 樁側(cè)豎向有效應(yīng)力

假設(shè)土體為彈性的，土體中作用矩形均布荷載的Mindlin應(yīng)力解由王士杰等[17]給出.如圖1所示，長(zhǎng)度為a，寬度為b的矩形均布荷載作用在均質(zhì)各向同性彈性半空間內(nèi)部深度h處，則角點(diǎn)下深度z處的豎向附加應(yīng)力為：

σ′z=p4π(1－μ)(1－μ)arctanabZ1R1+arctanabZ2R2+

abZ1R21+Z212r21r23R1+abh+3－4μZR22+Z222r22r24R2+

abhZZ2R322R22+r22r42+2R22+r24r44．(2)

式中：p為土體中作用的矩形均布荷載；μ為土體泊松比；Z1=Z－h(huán)；Z2=Z+h；r21=a2+Z21；r22=a2+Z22；r23=b2+Z21；r24=b2+Z22；R21=a2+b2+Z21；R22=a2+b2+Z22.



圖1Mindlin應(yīng)力解示意圖

Fig.1 Sketch of Mindlins stress solution

設(shè)單樁處于基坑中心，基坑開(kāi)挖長(zhǎng)度為2a，開(kāi)挖寬度為2b，不考慮樁體存在對(duì)土體應(yīng)力場(chǎng)的影響，則在深度h處卸載p引起計(jì)算點(diǎn)z處的豎向有效應(yīng)力減少為：

σz=4σ'z.(3)

在深度h處取微小高度dh的土體，開(kāi)挖這部分土體引起的卸載即其豎向有效重度γdh，其中γ為土體平均有效重度，即p=γdh，將其代入式(2)則得開(kāi)挖這部分土體引起計(jì)算點(diǎn)z處的豎向有效應(yīng)力減少量.因此開(kāi)挖地面下深度H范圍內(nèi)土體引起z處的豎向有效應(yīng)力減少為：

pt=∫H0σz.(4)

因此基坑開(kāi)挖卸荷后，地面下深度z處的豎向有效應(yīng)力為：

σv=γZ－pt.(5)

1.2 樁側(cè)極限阻力

黏性土中，樁側(cè)極限阻力的經(jīng)典計(jì)算公式由Chandler[18]和Burland[19]等給出：

fs=Kσvtan δ.(6)

式中:K為土體側(cè)壓力系數(shù);δ為樁土接觸面摩擦角.

張乾青等[20]統(tǒng)計(jì)了不同條件下的K/K0值，其中K0為靜止土壓力系數(shù)，認(rèn)為其比值在0.7~4.0之間.本文考慮基坑開(kāi)挖前樁土體系已充分固結(jié)密實(shí)，土體應(yīng)力場(chǎng)已達(dá)到平衡，因此開(kāi)挖卸荷前有：

K=1－sin φ,(7)

式中:φ為土層內(nèi)摩擦角，開(kāi)挖卸荷后樁土體系來(lái)不及達(dá)到新的平衡狀態(tài)，根據(jù)Zheng等[10]的建議，有：

K=1－sin φOCRsin φ.(8)

式中:OCR為土體超固結(jié)比，等于開(kāi)挖前后豎向有效應(yīng)力之比，成層土體計(jì)算時(shí)可取土層中點(diǎn)值為這層土體的超固結(jié)比值.

文獻(xiàn)[20]經(jīng)過(guò)統(tǒng)計(jì)，認(rèn)為不同樁土條件下δ/φ在0.5~1.0之間.本文分析案例處于軟土地區(qū)，根據(jù)Potyondy[21]的建議，取δ=0.6φ.

因此開(kāi)挖卸荷前樁側(cè)單位面積極限阻力為：

fs=1－sin φγZtan 0.6φ.(9)

開(kāi)挖卸荷后樁側(cè)單位面積極限阻力為：

fs=1－sin φOCRsin φγZ－pttan 0.6φ.(10)

最終沿整個(gè)樁長(zhǎng)范圍內(nèi)積分得總的樁側(cè)阻力：

Qs=πd∫LfsdZ.(11)

式中:d為樁體直徑；L為樁長(zhǎng)，成層土體沿樁長(zhǎng)分段積分即可得到基坑開(kāi)挖前后樁側(cè)極限阻力.

2 案例分析與驗(yàn)證

為了驗(yàn)證1.2節(jié)提出的開(kāi)挖條件下樁側(cè)阻力理論計(jì)算式的合理性，本文建立三維有限元模型進(jìn)行數(shù)值分析，并將其結(jié)果與本文理論計(jì)算結(jié)果以及工程實(shí)測(cè)數(shù)據(jù)相對(duì)比.

2.1 工程概況

本文案例取自文獻(xiàn)[12]，該工程位于上海某地塊，由24層主樓和5層裙房組成，整體設(shè)3層地下室.基坑開(kāi)挖深度12.5~13 m，占地面積約4 771 m2，工程樁采用Φ700鉆孔灌注樁，有效樁長(zhǎng)30~37 m不等，鋼筋籠長(zhǎng)均為13 m，總樁數(shù)為278根，樁身混凝土C30，排樁圍護(hù)，3道內(nèi)支撐.場(chǎng)地土層分布及主要物理力學(xué)指標(biāo)見(jiàn)表1.

表1 土層物理力學(xué)參數(shù)

Tab.1 Physical and mechanical parameters of soil

層號(hào)

名稱

層厚

/m

γ(重度)

/(kN?m-3)

Es 0.1-0.2

(壓縮模量)/MPa

c

(有效黏聚力)

/kPa

φ

(有效內(nèi)

摩擦角)/(°)

μ

(泊松比)

①

②

③

④

⑤1a

⑤1b

⑥

⑦1a

⑦1b

填土

褐黃色粉質(zhì)黏土

灰色淤泥質(zhì)粉質(zhì)黏土

灰色淤泥質(zhì)黏土

灰色黏土

灰色粉質(zhì)黏土

暗綠色粉質(zhì)黏土

灰色粉細(xì)砂

草黃色粉細(xì)砂

1.4

2.0

5.4

7.7

7.8

14.0

3.3

3.1

8.6

18.3

18.4

17.4

17.0

17.9

18.1

19.9

19.4

19.1

2.53

4.17

3.49

2.42

3.52

5.03

7.41

13.76

10.95

0.0

17.9

14.0

13.0

21.0

20.0

31.0

15.5

12.0

25.9

19.8

9.6

10.2

13.6

15.1

13.6

23.9

26.2

0.33

0.33

0.33

0.33

0.33

0.33

0.33

0.30

0.30

2.2 有限元分析

本文采用PLAXIS 3D進(jìn)行數(shù)值模擬，建立三維單樁模型.分析時(shí)基坑開(kāi)挖深度H為13 m，將開(kāi)挖形狀近似處理為方形，邊長(zhǎng)為69 m，即2a=2b=69 m.單樁位于基坑中心，樁長(zhǎng)L取37 m.按照Randolph等[22]的理論單樁影響半徑為2.5×37 m×(1-0.33)=62 m，因此取模型邊長(zhǎng)為120 m，高為60 m，標(biāo)準(zhǔn)固定邊界.考慮地下水面在地表面，取土體平均有效重度為18kN/m3-10kN/m3=8 kN/m3，整體模型網(wǎng)格劃分及基坑開(kāi)挖后1/4模型剖面圖分別如圖2和圖3所示.



圖2整體模型網(wǎng)格劃分

Fig.2 Finite element mesh of entire model





圖3 開(kāi)挖后1/4模型剖面圖

Fig.3 Profile of 1/4 model after excavation



模型中土體、工程樁和圍護(hù)樁均采用實(shí)體單元，內(nèi)支撐采用梁?jiǎn)卧?各層土體水平分層、均質(zhì)各向同性.工程樁、圍護(hù)樁和內(nèi)支撐均為線彈性材料，彈性模量為30 GPa，泊松比為0.15.圍護(hù)墻厚度為1 m，入土深度為28 m.內(nèi)支撐為3道鋼筋混凝土對(duì)撐.土體為彈塑性材料，服從HS屈服準(zhǔn)則，具體參數(shù)見(jiàn)表1.用界面單元模擬樁土相互作用，引入強(qiáng)度折減因子來(lái)表征接觸面摩擦角取相應(yīng)土層摩擦角的折減，如此能與1.2節(jié)樁側(cè)阻力計(jì)算公式相吻合，取得較好的對(duì)比效果.具體模擬步驟如下：

1)激活樁和圍護(hù)結(jié)構(gòu)，模擬樁圍護(hù)體系重力加載，忽略初始位移場(chǎng)，保存初始應(yīng)力場(chǎng)；

2)模擬基坑開(kāi)挖施工，關(guān)閉開(kāi)挖區(qū)域土體，激活內(nèi)支撐，由于本文重點(diǎn)關(guān)注開(kāi)挖前后樁體承載性能，因此假定開(kāi)挖一步完成；

3)模擬單樁靜載試驗(yàn)的整個(gè)過(guò)程，分級(jí)施加軸向荷載，直至得到樁側(cè)阻力的極限值.

2.3 計(jì)算結(jié)果對(duì)比分析

本文案例中的工程樁在基坑開(kāi)挖完成后，隨機(jī)抽取3根樁進(jìn)行堆載法靜載試驗(yàn)，其中一根試樁的樁頂荷載沉降曲線如圖4所示(對(duì)文[12]中圖3錯(cuò)誤加以糾正)，加載到800 kN時(shí)樁頂有快速沉降32 mm，之后又趨于正常，最終加載量為4 000 kN.經(jīng)過(guò)樁身取芯檢查，發(fā)現(xiàn)在樁頂下13 m處附近樁身被拉斷，產(chǎn)生20~40 mm的樁身間隙.根據(jù)文獻(xiàn)[12]，用慢速堆載法測(cè)試得樁身上部13 m段的極限承載力為1 200 kN.將本案例數(shù)據(jù)代入1.2節(jié)理論計(jì)算公式，并借助數(shù)值計(jì)算軟件，得到樁身上部13 m范圍內(nèi)的樁側(cè)極限阻力為1 090 kN，可見(jiàn)與實(shí)測(cè)結(jié)果還是有一定差距，相差9.2%，這是由于理論模型經(jīng)過(guò)了一系列假設(shè)簡(jiǎn)化以達(dá)到簡(jiǎn)明實(shí)用的目的，而實(shí)測(cè)數(shù)據(jù)受施工因素影響較大.通過(guò)2.2節(jié)建立的有限元模型，可以得到樁身上部13 m范圍內(nèi)的樁側(cè)極限阻力為1 130 kN，可見(jiàn)介于理論計(jì)算結(jié)果和實(shí)測(cè)結(jié)果之間.

Q/kN

圖4 樁頂實(shí)測(cè)荷載沉降曲線



Fig.4QS curve for pilehead form test results



表2是沿樁身各土層的樁側(cè)單位極限阻力的幾種計(jì)算結(jié)果的對(duì)比，從表中可以看出，本文2種方法的計(jì)算結(jié)果與規(guī)范推薦值和靜探指標(biāo)換算值的總體趨勢(shì)是一致的，然而越接近坑底開(kāi)挖面，本文2種方法的計(jì)算結(jié)果相對(duì)越小，與其他2種方法結(jié)果差別越大，這是由于本文2種方法都不同程度地考慮了開(kāi)挖卸荷效應(yīng)，而其他2種方法是沒(méi)有考慮的.另外，總體來(lái)說(shuō)有限元法計(jì)算結(jié)果比理論公式計(jì)算結(jié)果有所偏大.

表2 樁側(cè)單位極限阻力不同計(jì)算結(jié)果對(duì)比

Tab.2 Comparison of unit ultimate resistance of pile shaft

from different computing resultskPa 

土層名稱

規(guī)范推

薦值[23]

靜探指標(biāo)

換算值[12]

本文理論

公式法

本文有

限元法

④灰色淤泥質(zhì)黏土

⑤1a灰色黏土

⑤1b灰色粉質(zhì)黏土

⑥暗綠色粉質(zhì)黏土

⑦1a灰色粉細(xì)砂

27.5

55.5

55.5

36.3

36.025.0

42.5

70.0

46.0

46.0

14.5

37.6

57.9

31.1

36.6

15.1

40.0

59.8

33.7

37.9

3算例分析

為了進(jìn)一步分析基坑開(kāi)挖時(shí)各參數(shù)對(duì)樁基側(cè)摩阻力的影響程度，本算例假定彈性半空間內(nèi)為均質(zhì)土體，其物理力學(xué)參數(shù)見(jiàn)2.3節(jié)案例⑤1a灰色黏土層，水文條件及樁體同案例.定義樁側(cè)阻力降低系數(shù)α為開(kāi)挖后樁側(cè)極限阻力Q′s與開(kāi)挖前樁側(cè)極限阻力Qs之比.下面分析基坑在不同開(kāi)挖深度、開(kāi)挖邊長(zhǎng)、開(kāi)挖長(zhǎng)寬比以及樁長(zhǎng)時(shí)對(duì)α的影響.

3.1 開(kāi)挖深度

設(shè)定基坑開(kāi)挖為方形，開(kāi)挖邊長(zhǎng)為100 m，即2a=2b=100 m，下面分析樁側(cè)阻力降低系數(shù)隨H/L(開(kāi)挖深度與樁長(zhǎng)之比)的變化規(guī)律.

圖5是樁側(cè)阻力降低系數(shù)α隨H/L的變化曲線.從圖中可以看出，在同一樁長(zhǎng)條件下，隨著H/L增大即開(kāi)挖深度增加，樁側(cè)阻力降低系數(shù)開(kāi)始快速減小而后衰減速度變緩，約在H/L=0.6~1.0時(shí)達(dá)到最小值，然后α值又逐漸緩慢增大，這說(shuō)明隨開(kāi)挖深度增加樁側(cè)阻力降低系數(shù)存在一個(gè)谷值臨界深度，達(dá)到這個(gè)深度后土體卸載效應(yīng)減弱；在同樣大小的H/L值條件下，樁體越長(zhǎng)樁側(cè)阻力降低系數(shù)越

H/L

圖5樁側(cè)阻力降低系數(shù)隨H/L變化曲線

Fig.5 Variation in reduction factors

for shaft resistance withH/L



大，樁體越短α值越小，經(jīng)仔細(xì)對(duì)比還可發(fā)現(xiàn)開(kāi)挖深度相同時(shí)，樁體越長(zhǎng)α值越大，這說(shuō)明開(kāi)挖深度相同時(shí)增加樁長(zhǎng)有利于減小開(kāi)挖后樁側(cè)阻力的損失.

3.2 開(kāi)挖邊長(zhǎng)

設(shè)定基坑開(kāi)挖為方形，開(kāi)挖深度為10 m，即H=10 m，下面分析樁側(cè)阻力降低系數(shù)α隨2a/L或2b/L(開(kāi)挖邊長(zhǎng)與樁長(zhǎng)之比)的變化規(guī)律.

圖6是樁側(cè)阻力降低系數(shù)α隨2a/L或2b/L的變化曲線.從圖中可以看出，在同一樁長(zhǎng)條件下，隨著2a/L增大即開(kāi)挖邊長(zhǎng)增加，樁側(cè)阻力降低系數(shù)開(kāi)始快速減小而后衰減速度變緩并趨于穩(wěn)定，當(dāng)2a/L>4時(shí)α值變化很小,基本穩(wěn)定，這說(shuō)明達(dá)到一定開(kāi)挖寬度后土體卸載對(duì)其影響程度已穩(wěn)定，同樣說(shuō)明群樁基礎(chǔ)基坑開(kāi)挖后，中心樁的樁側(cè)阻力損失大于邊角樁，樁位與基坑邊距大于2倍樁長(zhǎng)的各基樁其損失相差很??；在同樣大小的2a/L值條件下，樁體越長(zhǎng)樁側(cè)阻力降低系數(shù)越大，樁體越短α值越小，經(jīng)仔細(xì)對(duì)比還可發(fā)現(xiàn)開(kāi)挖邊長(zhǎng)相同時(shí)，樁體越長(zhǎng)α值越大，這說(shuō)明開(kāi)挖邊長(zhǎng)相同時(shí)增加樁長(zhǎng)有利于減小開(kāi)挖后樁側(cè)阻力的損失.

2a/L或2b/L

圖6樁側(cè)阻力降低系數(shù)隨2a/L

或2b/L變化曲線



Fig.6 Variation in reduction factors for shaft 

resistance with2a/Lor2b/L



3.3 開(kāi)挖長(zhǎng)寬比

設(shè)定基坑開(kāi)挖深度為10 m，即H=10 m，樁長(zhǎng)L=40 m，下面分析樁側(cè)阻力降低系數(shù)α隨2a/2b (開(kāi)挖長(zhǎng)度與寬度之比)的變化規(guī)律.

圖7是樁側(cè)阻力降低系數(shù)α隨2a/2b的變化曲線.從圖中可以看出，在同一開(kāi)挖寬度條件下，隨著2a/2b增大即開(kāi)挖長(zhǎng)寬比增加，樁側(cè)阻力降低系數(shù)開(kāi)始急劇減小而后基本不變，當(dāng)2a/2b>3時(shí)α值變化非常小，這說(shuō)明達(dá)到一定開(kāi)挖長(zhǎng)寬比后土體卸載對(duì)其影響程度已幾乎不變；在同樣大小的2a/2b值條件下，開(kāi)挖寬度越大樁側(cè)阻力降低系數(shù)越小，開(kāi)挖寬度越小α值越大，經(jīng)仔細(xì)對(duì)比還可發(fā)現(xiàn)開(kāi)挖長(zhǎng)度相同時(shí)，開(kāi)挖寬度越大α值越小，這說(shuō)明增加開(kāi)挖長(zhǎng)度或?qū)挾龋_(kāi)挖后樁側(cè)阻力的損失增大.

2a/2b

圖7 樁側(cè)阻力降低系數(shù)隨2a/2b變化曲線

Fig.7 Variation in reduction factors 

for shaft resistance with2a/2b



4結(jié) 論

本文首先推導(dǎo)了開(kāi)挖條件下樁側(cè)豎向有效應(yīng)力的計(jì)算公式，并基于經(jīng)典的黏性土中樁側(cè)阻力公式給出了開(kāi)挖前后樁側(cè)極限阻力計(jì)算方法.然后通過(guò)一個(gè)工程實(shí)例，將本文理論計(jì)算結(jié)果與工程實(shí)測(cè)數(shù)據(jù)、有限元分析結(jié)果以及其他方法得到的結(jié)果相對(duì)比，驗(yàn)證了本文理論方法的可靠性.最后應(yīng)用本文的理論計(jì)算方法，分析了工程樁在不同基坑開(kāi)挖深度、開(kāi)挖邊長(zhǎng)、開(kāi)挖長(zhǎng)寬比以及樁長(zhǎng)時(shí)樁側(cè)阻力降低系數(shù)的變化規(guī)律.本文通過(guò)理論公式推導(dǎo)，結(jié)合具體工程案例，比較理論結(jié)果和其他結(jié)果，并通過(guò)算例進(jìn)行參數(shù)討論，得出如下結(jié)論：

1)通過(guò)案例分析，本文理論計(jì)算結(jié)果與實(shí)測(cè)數(shù)據(jù)較接近，樁側(cè)阻力偏小，其作為工程前期對(duì)工程樁承載特性的預(yù)判，不失為一種可取的方法.

2)樁長(zhǎng)相等時(shí)，樁側(cè)阻力降低系數(shù)隨開(kāi)挖深度增加先快速減小而后緩慢增大，約在H/L=0.6~1.0時(shí)達(dá)到最小值，即α存在谷值臨界深度.

3)樁長(zhǎng)相等時(shí)，樁側(cè)阻力降低系數(shù)隨開(kāi)挖邊長(zhǎng)增加先快速減小而后趨于穩(wěn)定，當(dāng)2a/L>4時(shí)α值變化很小，群樁基礎(chǔ)中心樁α值小于邊角樁，與基坑邊距大于2L的各基樁其α值相差很小.

4)開(kāi)挖寬度相等時(shí)，樁側(cè)阻力降低系數(shù)隨開(kāi)挖長(zhǎng)寬比增加先急劇減小而后基本不變，當(dāng)2a/2b>3時(shí)α值變化非常??；開(kāi)挖長(zhǎng)度相等時(shí)，開(kāi)挖寬度越大α值越小.

5)增加樁長(zhǎng)有利于減小開(kāi)挖后樁側(cè)阻力損失；增大開(kāi)挖長(zhǎng)度或?qū)挾葘?dǎo)致開(kāi)挖后樁側(cè)阻力的損失增大.

參考文獻(xiàn)

［1］ 酈建俊, 黃茂松, 木林隆, 等. 分層地基中擴(kuò)底樁抗拔承載力的計(jì)算方法研究[J]. 巖土力學(xué), 2008, 29(7): 1997-2004.

LI Jianjun, HUANG Maosong, MU Linlong, et al. Research on computation methods of uplift capacity of enlarged base pile in layered soils[J]. Rock and Soil Mechanics, 2008, 29(7): 1997-2004. (In Chinese)

[2] 酈建俊. 深層開(kāi)挖條件下抗拔樁的承載特性研究[D]. 上海: 同濟(jì)大學(xué)土木工程學(xué)院, 2008: 3-5.

LI Jianjun. Study on bearing behavior of uplift piles under deep excavation[D]. Shanghai: College of Civil Engineering, Tongji University, 2008: 3-5. (In Chinese)

[3] 酈建俊, 黃茂松, 王衛(wèi)東, 等. 軟土地基中擴(kuò)底抗拔中長(zhǎng)樁的極限承載力分析[J]. 巖土力學(xué), 2009, 30(9): 2643-2651.

LI Jianjun, HUANG Maosong, WANG Weidong, et al. Analysis of uplift capacity of long enlargedbase pile in soft soil ground[J]. Rock and Soil Mechanics, 2009, 30(9): 2643-2651. (In Chinese)

[4] 王衛(wèi)東, 吳江斌. 深開(kāi)挖條件下抗拔樁分析與設(shè)計(jì)方法[J].建筑結(jié)構(gòu)學(xué)報(bào), 2010, 31(5): 202-208.

WANG Weidong, WU Jiangbin. Design and analysis of uplift pile under deep excavation[J]. Journal of Building Structures, 2010, 31(5): 202-208. (In Chinese)

[5] 范巍. 大面積深基坑開(kāi)挖過(guò)程中樁基受力特性研究[D]. 上海: 上海交通大學(xué)土木工程系, 2007: 9-10.

FAN Wei. Behavior of pile foundation during largescale deep excavation[D]. Shanghai: Department of Civil Engineering, Shanghai Jiaotong University, 2007: 9-10. (In Chinese)

[6] 胡琦, 凌道盛, 陳云敏, 等. 深基坑開(kāi)挖對(duì)坑內(nèi)基樁受力特性的影響分析[J]. 巖土力學(xué), 2008, 29(7): 1965-1970.

HU Qi, LING Daosheng, CHEN Yunmin, et al. Study of loading characters of pile foundation due to unloading of deep foundation pit excavation[J]. Rock and Soil Mechanics, 2008, 29(7): 1965-1970. (In Chinese)

[7] 楊敏, 逯建棟. 深開(kāi)挖基坑回彈引起的坑中樁受力與位移計(jì)算[J]. 同濟(jì)大學(xué)學(xué)報(bào):自然科學(xué)版, 2010, 38(12): 1730-1735.

YANG Min, LU Jiandong. A calculation of behavior of underpinning pile subject to excavation of deep foundation pit[J]. Journal of Tongji University: Natural Science, 2010, 38(12): 1730-1735. (In Chinese)

[8] ZHENG G, DIAO Y, NG C W W. Parametric analysis of the effects of stress relief on the performance and capacity of piles in nondilative soils[J]. Canadian Geotechnical Journal, 2012, 48(9): 1354-1363.

[9] 鄭剛, 張立明, 刁鈺. 開(kāi)挖條件下坑底工程樁工作性狀及沉降計(jì)算分析[J]. 巖土力學(xué), 2011, 32(10): 3089-3096.

ZHENG Gang, ZHANG Liming, DIAO Yu. Analysis of working performance of piles beneath excavation bottom and settlement calculation[J]. Rock and Soil Mechanics, 2011, 32(10): 3089-3096. (In Chinese)

[10]ZHENG G, PENG S Y, NG C W W, et al. Excavation effects on pile behaviour and capacity[J]. Canadian Geotechnical Journal, 2012, 49(12): 1347-1356.

[11]王成華, 劉慶晨. 考慮基坑開(kāi)挖影響的群樁基礎(chǔ)豎向承載性狀數(shù)值分析[J]. 巖土力學(xué), 2012, 33(6): 1851-1856.

WANG Chenghua, LIU Qingchen. Numerical analysis of vertical bearing behavior of group pile foundation considering pit excavation effect[J]. Rock and Soil Mechanics, 2012, 33(6): 1851-1856. (In Chinese)

[12]朱火根, 孫加平. 上海地區(qū)深基坑開(kāi)挖坑底土體回彈對(duì)工程樁的影響[J]. 巖土工程界, 2005, 8(3): 43-46.

ZHU Huogen, SUN Jiaping. Effect of basal soil heave on piles during deep excavation in Shanghai[J]. Geotechnical Engineering World, 2005, 8(3): 43-46. (In Chinese)

[13]劉國(guó)彬, 黃院雄, 侯學(xué)淵. 基坑回彈的實(shí)用計(jì)算法[J] ．土木工程學(xué)報(bào), 2000, 33(4): 61-67.

LIU Guobin, HUANG Yuanxiong, HOU Xueyuan. A practical method for calculating a heave of excavated foundation[J]. China Civil Engineering Journal, 2000, 33(4): 61-67. (In Chinese)

[14]李超. 樁式基礎(chǔ)托換在地下加層工程中的應(yīng)用研究[D]. 南京: 東南大學(xué)土木工程學(xué)院, 2008: 55-59.

LI Chao. Study on the application of pile foundation underpinning in the basementaddition of existing buildings[D]. Nanjing: College of Civil Engineering, Southeast University, 2008: 55-59. (In Chinese)

[15]伍程杰, 龔曉南, 俞峰, 等. 既有高層建筑地下增層開(kāi)挖樁端阻力損失[J]. 浙江大學(xué)學(xué)報(bào):工學(xué)版，2014，48（4）：671-678.

WU Chengjie, GONG Xiaonan, YU Feng, et al. Loss of pile base resistance induced by further excavation beneath existing highrise buildings[J]. Journal of Zhejiang University: Engineering Science, 2014，48（4）：671-678. (In Chinese)

[16]龔曉南, 伍程杰, 俞峰, 等. 既有地下室增層開(kāi)挖引起的樁基側(cè)摩阻力損失分析[J]. 巖土工程學(xué)報(bào), 2013, 35(11): 1957-1964.

GONG Xiaonan, WU Chengjie, YU Feng,et al. Shaft resistance loss of piles due to excavation beneath existing basements[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(11): 1957-1964. (In Chinese)

[17]王士杰, 張 梅, 張吉占. Mindlin應(yīng)力解的應(yīng)用理論研究[J]. 工程力學(xué), 2001, 18(6): 141-148.

WANG Shijie, ZHANG Mei, ZHANG Jizhan. Study on the application of theory of Mindlins stress solution[J]. Engineering Mechanics, 2001, 18(6): 141-148. (In Chinese)

[18]CHANDLER R J. The shaft friction of piles in cohesive soils in terms of effective stresses[J]. Civil Engineering and Public Works Review, 1968, 63: 48-51.

[19]BURLAND J B. Shaft friction of piles in clay-a simple fundamental approach[J]. Ground Engineering, 1973, 6(3): 30-42.

[20]張乾青, 李術(shù)才, 李利平, 等. 考慮側(cè)阻軟化和端阻硬化的群樁沉降簡(jiǎn)化算法[J]. 巖石力學(xué)與工程學(xué)報(bào), 2013, 32(3): 615-624.

ZHANG Qianqing, LI Shucai, LI Liping, et al. Simplified method for settlement prediction of pile groups considering skin friction softing and end resistance hardening[J]. Chinese Journal of Rock Mechanics and Engineering, 2013, 32(3): 615-624. (In Chinese)

[21]POTYONDY J G. Skin friction between various soils and construction materials[J]. Geotechnique, 1961, 11(4): 339-345.

[22]RANDOLPH M F, WROTH C P. An analysis of the vertical deformation of pile groups[J]. Geotechnique, 1979, 29(4): 423-439.

[23]DGJ08372012巖土工程勘察規(guī)范[S]. 上海: 上海市城鄉(xiāng)建設(shè)和交通委員會(huì), 2012: 134-135.

DGJ08372012 Code for investigation of geotechnical engineering[S]. Shanghai: Shanghai Urban Construction and Communications Commission, 2012: 134-135. (In Chinese)

[10]ZHENG G, PENG S Y, NG C W W, et al. Excavation effects on pile behaviour and capacity[J]. Canadian Geotechnical Journal, 2012, 49(12): 1347-1356.

[11]王成華, 劉慶晨. 考慮基坑開(kāi)挖影響的群樁基礎(chǔ)豎向承載性狀數(shù)值分析[J]. 巖土力學(xué), 2012, 33(6): 1851-1856.

WANG Chenghua, LIU Qingchen. Numerical analysis of vertical bearing behavior of group pile foundation considering pit excavation effect[J]. Rock and Soil Mechanics, 2012, 33(6): 1851-1856. (In Chinese)

[12]朱火根, 孫加平. 上海地區(qū)深基坑開(kāi)挖坑底土體回彈對(duì)工程樁的影響[J]. 巖土工程界, 2005, 8(3): 43-46.

ZHU Huogen, SUN Jiaping. Effect of basal soil heave on piles during deep excavation in Shanghai[J]. Geotechnical Engineering World, 2005, 8(3): 43-46. (In Chinese)

[13]劉國(guó)彬, 黃院雄, 侯學(xué)淵. 基坑回彈的實(shí)用計(jì)算法[J] ．土木工程學(xué)報(bào), 2000, 33(4): 61-67.

LIU Guobin, HUANG Yuanxiong, HOU Xueyuan. A practical method for calculating a heave of excavated foundation[J]. China Civil Engineering Journal, 2000, 33(4): 61-67. (In Chinese)

[14]李超. 樁式基礎(chǔ)托換在地下加層工程中的應(yīng)用研究[D]. 南京: 東南大學(xué)土木工程學(xué)院, 2008: 55-59.

LI Chao. Study on the application of pile foundation underpinning in the basementaddition of existing buildings[D]. Nanjing: College of Civil Engineering, Southeast University, 2008: 55-59. (In Chinese)

[15]伍程杰, 龔曉南, 俞峰, 等. 既有高層建筑地下增層開(kāi)挖樁端阻力損失[J]. 浙江大學(xué)學(xué)報(bào):工學(xué)版，2014，48（4）：671-678.

WU Chengjie, GONG Xiaonan, YU Feng, et al. Loss of pile base resistance induced by further excavation beneath existing highrise buildings[J]. Journal of Zhejiang University: Engineering Science, 2014，48（4）：671-678. (In Chinese)

[16]龔曉南, 伍程杰, 俞峰, 等. 既有地下室增層開(kāi)挖引起的樁基側(cè)摩阻力損失分析[J]. 巖土工程學(xué)報(bào), 2013, 35(11): 1957-1964.

GONG Xiaonan, WU Chengjie, YU Feng,et al. Shaft resistance loss of piles due to excavation beneath existing basements[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(11): 1957-1964. (In Chinese)

[17]王士杰, 張 梅, 張吉占. Mindlin應(yīng)力解的應(yīng)用理論研究[J]. 工程力學(xué), 2001, 18(6): 141-148.

WANG Shijie, ZHANG Mei, ZHANG Jizhan. Study on the application of theory of Mindlins stress solution[J]. Engineering Mechanics, 2001, 18(6): 141-148. (In Chinese)

[18]CHANDLER R J. The shaft friction of piles in cohesive soils in terms of effective stresses[J]. Civil Engineering and Public Works Review, 1968, 63: 48-51.

[19]BURLAND J B. Shaft friction of piles in clay-a simple fundamental approach[J]. Ground Engineering, 1973, 6(3): 30-42.

[20]張乾青, 李術(shù)才, 李利平, 等. 考慮側(cè)阻軟化和端阻硬化的群樁沉降簡(jiǎn)化算法[J]. 巖石力學(xué)與工程學(xué)報(bào), 2013, 32(3): 615-624.

ZHANG Qianqing, LI Shucai, LI Liping, et al. Simplified method for settlement prediction of pile groups considering skin friction softing and end resistance hardening[J]. Chinese Journal of Rock Mechanics and Engineering, 2013, 32(3): 615-624. (In Chinese)

[21]POTYONDY J G. Skin friction between various soils and construction materials[J]. Geotechnique, 1961, 11(4): 339-345.

[22]RANDOLPH M F, WROTH C P. An analysis of the vertical deformation of pile groups[J]. Geotechnique, 1979, 29(4): 423-439.

[23]DGJ08372012巖土工程勘察規(guī)范[S]. 上海: 上海市城鄉(xiāng)建設(shè)和交通委員會(huì), 2012: 134-135.

DGJ08372012 Code for investigation of geotechnical engineering[S]. Shanghai: Shanghai Urban Construction and Communications Commission, 2012: 134-135. (In Chinese)

[10]ZHENG G, PENG S Y, NG C W W, et al. Excavation effects on pile behaviour and capacity[J]. Canadian Geotechnical Journal, 2012, 49(12): 1347-1356.

[11]王成華, 劉慶晨. 考慮基坑開(kāi)挖影響的群樁基礎(chǔ)豎向承載性狀數(shù)值分析[J]. 巖土力學(xué), 2012, 33(6): 1851-1856.

WANG Chenghua, LIU Qingchen. Numerical analysis of vertical bearing behavior of group pile foundation considering pit excavation effect[J]. Rock and Soil Mechanics, 2012, 33(6): 1851-1856. (In Chinese)

[12]朱火根, 孫加平. 上海地區(qū)深基坑開(kāi)挖坑底土體回彈對(duì)工程樁的影響[J]. 巖土工程界, 2005, 8(3): 43-46.

ZHU Huogen, SUN Jiaping. Effect of basal soil heave on piles during deep excavation in Shanghai[J]. Geotechnical Engineering World, 2005, 8(3): 43-46. (In Chinese)

[13]劉國(guó)彬, 黃院雄, 侯學(xué)淵. 基坑回彈的實(shí)用計(jì)算法[J] ．土木工程學(xué)報(bào), 2000, 33(4): 61-67.

LIU Guobin, HUANG Yuanxiong, HOU Xueyuan. A practical method for calculating a heave of excavated foundation[J]. China Civil Engineering Journal, 2000, 33(4): 61-67. (In Chinese)

[14]李超. 樁式基礎(chǔ)托換在地下加層工程中的應(yīng)用研究[D]. 南京: 東南大學(xué)土木工程學(xué)院, 2008: 55-59.

LI Chao. Study on the application of pile foundation underpinning in the basementaddition of existing buildings[D]. Nanjing: College of Civil Engineering, Southeast University, 2008: 55-59. (In Chinese)

[15]伍程杰, 龔曉南, 俞峰, 等. 既有高層建筑地下增層開(kāi)挖樁端阻力損失[J]. 浙江大學(xué)學(xué)報(bào):工學(xué)版，2014，48（4）：671-678.

WU Chengjie, GONG Xiaonan, YU Feng, et al. Loss of pile base resistance induced by further excavation beneath existing highrise buildings[J]. Journal of Zhejiang University: Engineering Science, 2014，48（4）：671-678. (In Chinese)

[16]龔曉南, 伍程杰, 俞峰, 等. 既有地下室增層開(kāi)挖引起的樁基側(cè)摩阻力損失分析[J]. 巖土工程學(xué)報(bào), 2013, 35(11): 1957-1964.

GONG Xiaonan, WU Chengjie, YU Feng,et al. Shaft resistance loss of piles due to excavation beneath existing basements[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(11): 1957-1964. (In Chinese)

[17]王士杰, 張 梅, 張吉占. Mindlin應(yīng)力解的應(yīng)用理論研究[J]. 工程力學(xué), 2001, 18(6): 141-148.

WANG Shijie, ZHANG Mei, ZHANG Jizhan. Study on the application of theory of Mindlins stress solution[J]. Engineering Mechanics, 2001, 18(6): 141-148. (In Chinese)

[18]CHANDLER R J. The shaft friction of piles in cohesive soils in terms of effective stresses[J]. Civil Engineering and Public Works Review, 1968, 63: 48-51.

[19]BURLAND J B. Shaft friction of piles in clay-a simple fundamental approach[J]. Ground Engineering, 1973, 6(3): 30-42.

[20]張乾青, 李術(shù)才, 李利平, 等. 考慮側(cè)阻軟化和端阻硬化的群樁沉降簡(jiǎn)化算法[J]. 巖石力學(xué)與工程學(xué)報(bào), 2013, 32(3): 615-624.

ZHANG Qianqing, LI Shucai, LI Liping, et al. Simplified method for settlement prediction of pile groups considering skin friction softing and end resistance hardening[J]. Chinese Journal of Rock Mechanics and Engineering, 2013, 32(3): 615-624. (In Chinese)

[21]POTYONDY J G. Skin friction between various soils and construction materials[J]. Geotechnique, 1961, 11(4): 339-345.

[22]RANDOLPH M F, WROTH C P. An analysis of the vertical deformation of pile groups[J]. Geotechnique, 1979, 29(4): 423-439.

[23]DGJ08372012巖土工程勘察規(guī)范[S]. 上海: 上海市城鄉(xiāng)建設(shè)和交通委員會(huì), 2012: 134-135.

DGJ08372012 Code for investigation of geotechnical engineering[S]. Shanghai: Shanghai Urban Construction and Communications Commission, 2012: 134-135. (In Chinese)