簡諧SH波作用下管樁的振動特性

劉林超，肖琪聃，閆啟方，劉滕

(信陽師范學院 土木工程學院，河南 信陽 464000)

?

簡諧SH波作用下管樁的振動特性

劉林超，肖琪聃，閆啟方，劉滕

(信陽師范學院 土木工程學院，河南 信陽 464000)

管樁；SH波；振動特性；動力放大因子

樁基作為一種重要的基礎形式通常要承受地震激勵、海洋荷載、動力機器荷載等動態(tài)激勵的作用，有關樁基振動特性的研究近幾十年來受到了足夠的重視并取得了一定的研究成果[1-7]，以往這些研究都是考察實芯樁的振動特性。管樁作為近年來才出現(xiàn)的一種樁基形式，由于具有抗彎抗拉性能好、強度和承載力高、耐久性好且造價較低等諸多優(yōu)點而被廣泛應用到眾多工程領域。為了給樁基設計、施工、檢測等提供理論依據(jù)，近幾年來，針對管樁的振動特性的研究越來越受到關注，丁選明等[8]給出了瞬態(tài)集中荷載作用下大直徑管樁的時域解析解，鄭長杰等[9-10]針對粘彈性地基中現(xiàn)澆大直徑管樁的縱向振動及扭轉振動進行了研究，吳文兵等[11]考慮土塞效應運用附加質量法對成層地基中管樁的縱向振動進行了研究，劉林超等[12]針對飽和土中管樁的水平振動運用多孔介質理論進行了研究。

1 簡諧SH波作用下樁周土和樁芯土的水平位移

考察圖1所示的管樁在沿y方向簡諧水平剪切波(SH波)作用下的振動問題，且簡諧SH波滿足

(1)

圖1 管樁土相互作用模型Fig. 1 The interaction model of pipe pile-

樁周土

(2)

(3)

樁芯土

(4)

(5)

(6)

(7)

(8)

(9)

考慮邊界條件式(7)和式(9)，設式(6)和式(8)的解分別為

(10)

(11)

(12)

(13)

進而可以得到簡諧SH波作用下引起的樁周土和樁芯土體的水平位移分別為

(14)

(15)

2 水平簡諧荷載作用下樁周土和樁芯土振動求解

樁周土

(ωOzeiωt)+

(16)

(17)

樁芯土

(ωIzeiωt)+

(18)

(19)

令

(20)

對式(16)～(19)進行無量綱運算并整理可得

φO=0

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(28)

(29)

(30)

考慮式(14)、式(15)和式(27)～式(30)可以得到簡諧SH波和樁頂水平集中荷載共同作用下產(chǎn)生的樁周土和樁芯土的水平位移分別為

(31)

(32)

(33)

(34)

考慮管樁與樁周土和樁芯土接觸面處的位移連續(xù)條件，可有如下連續(xù)性邊界條件

(35)

(36)

BOk=COkAOk，AIk=DkAOk，BIk=CIkDkAOk

(37)

3 簡諧SH波和水平集中荷載作用下管樁振動求解

由樁周土和樁芯土徑向位移和環(huán)向位移，可以求得樁周土和樁芯土無量綱化的徑向應力和環(huán)向應力σOr、τOrθ、σIr、τIrθ，進而可以得到樁周土和樁芯土對管樁的水平作用力。單位厚度樁周土對管樁的無量綱化水平作用力幅值為

θ=

(38)

單位厚度樁芯土對管樁的無量綱化水平作用力幅值為

θ=

(39)

由式(37)知樁周土和樁芯土對管樁的共同作用力為

(40)

由于管樁同樣作簡諧振動，以單位樁長為研究對象，考慮式(40)可以建立無量綱化的管樁的水平振動方程為

(41)

(42)

Ap1、Ap2、Ap3、Ap4為待定系數(shù)。由于管樁樁底為基巖，可建立管樁樁頂和樁底的邊界條件為

(43)

P0為無量綱化的樁頂簡諧水平集中荷載幅值。由管樁樁頂和樁底的邊界條件可以確定待定系數(shù)

(44)

由式(31)可知，

(45)

考慮管樁與樁周土的連續(xù)性條件可得

(46)

對式(46)兩端運用三角函數(shù)的正交性可得

(47)

式(47)中

(48)

由此可得SH簡諧地震波和樁基水平集中荷載作用下管樁的水平位移為

(49)

up(1)=SgUg

(50)

式(50)中，

λp+cosλp-tghλpsinhλp+

(51)

這里，Sg即為簡諧SH波作用下管樁樁頂?shù)膭恿Ψ糯笠蜃印?/p>

4 數(shù)值算例與分析

圖2 動力放大因子隨頻率變化曲線Fig. 2 Curves of dynamic amplification factor versus frequency

圖3 管樁壁厚不同時放大因子隨頻率變化曲線Fig. 3 Curves of dynamic amplification factor versus frequency for different pipe pile wall thickness

圖4 樁土模量比不同時放大因子隨頻率變化曲線Fig. 4 Curves of dynamic amplification factor versus frequency for different pile-soil modulus ratio

圖5 樁芯土和樁周土模量比不同時放大因子隨頻率變化曲線Fig. 5 Curves of dynamic amplification factor versus frequency for different modulus ratio of

5 結論

以簡諧SH波和水平集中荷載作用下管樁的振動特性為研究對象，運用波的傳播理論、樁基動力學、數(shù)學物理方法等得到了管樁樁頂?shù)膭恿Ψ糯笠蜃樱詳?shù)值算例的形式通過分析管樁壁厚、樁土模量比和樁芯土與樁周土模量比對管樁動力放大因子的影響，研究了管樁的振動特性。

1)管樁樁頂動力放大因子隨頻率變化曲線存在較明顯的峰值，系統(tǒng)存在有共振現(xiàn)象。

2)當管樁壁厚過薄時動力放大因子隨頻率變化曲線將會出現(xiàn)急劇增大，樁基此時宜發(fā)生穩(wěn)定性破壞，所以管樁不能過薄。

3)由于樁基在施工中通常會造成樁周土剛度的弱化，所以采用管樁的抗震性能有時要比實芯樁好。

[1] NOVAK M. Dynamic stiffness and damping of piles [J]. Canadian Geotechnical Journal, 1974, 11(4): 574-598.

[2] NOGAMI T,KONAGAI K. Time domain axial response of dynamically loaded single piles [J]. Journal of Engineering Mechanics, 1986,12(11):1241-1252.

[3] MAESO O， JUAN J, GARCIA A F. Dynamic impedances of piles and groups of piles in saturated soils [J]. Computer & Structurees,2005, 83:769-782.

[4] 高洪波,劉林超,閆啟方.分數(shù)導數(shù)微分算子描述的粘彈性土層中群樁的水平振動研究[J].工程力學,2012,29(6): 160-168. GAO H B, LIU L C,YAN Q F. Lateral vibration of pile groups in visocelastic soil layer described by fractional derivative operator[J].Engineering Mechanics, 2012, 29(6): 160-168. (in Chinese)

[5] 李強,鄭輝,王奎華.飽和土中摩擦樁豎向振動解析解及應用[J].工程力學,2011,28(1):157-170. LI Q,ZHENG H,WANG K H. Analytical solution and its application of vertical vibration of a fraction pile in saturated soil [J].Engineering Mechanics, 2011,28(1): 157-170.

[6] 王奎華,王寧,劉凱,等.三維軸對稱條件下基于虛土樁法的單樁縱向振動分析[J].巖土工程學報,2012,34(5): 885-892. WANG K H,WANG N,LIU K,et al. Longitudinal vibration of piles in 3D axisymmetric soil based on fictitious soil pile method [J]. Chinese Journal of Geotechnical Engineering,2012,34(5): 885-892. (in Chinese)

[7] 崔春義,張石平,楊剛,等.考慮樁底土層波動效應的飽和黏彈性半空間中摩擦樁豎向振動[J].巖土工程學報,2015,37(5): 878-892. CUI C Y,ZHANG S P, YANG G,et al. Vertical vibration of floating piles in saturated viscoelastic half-space considering wave effect of subsoil under pile bottom[J]. Chinese Journal of Geotechnical Engineering, 2015,37(5): 878-892. (in Chinese)

[8] 丁選明,劉漢龍. 大直徑管樁在瞬態(tài)集中荷載作用下的振動響應時域解析解[J].巖土工程學報,2013,35(6): 1010-1017. DING X M,LIU H L. Time-domain analytical solution of the vibration response of a large-diameter pipe pile subjected to transient concentrated load [J]. Chinese Journal of Geotechnical Engineering,2013,35(6):1010- 1017. (in Chinese)

[9] 鄭長杰,丁選明,黃旭,等.滯回阻尼土中大直徑管樁縱向振動響應解析解 [J]. 巖石力學與工程學報,2014, 33(Sup1): 3284-3290. ZHENG C J, DING X M,HUNG X,et al. Analytical solution of vertical vibration response of large diameter pipe pile in hysteretic damping soil [J]. Chinese Journal of Rock Mechanics and Engineering, 2014, 33(Sup1): 3284-3290. (in Chinese)

[10] 鄭長杰,丁選明,劉漢龍,等.黏彈性地基中PCC樁扭轉振動響應解析方法研究[J].巖土力學,2013,34(7): 1943-1950. ZHENG C J,DING X M,LIU H H L,et al. Analytic method of torsional vibration response of cast-in-place concrete large-diameter pipe pile in viscoelastic soil [J].Rock and Soil Mechanics, 2013, 34(7):1943-1950. (in Chinese)

[11] 吳文兵,蔣國盛,王奎華,等.土塞效應對管樁縱向動力特性的影響研究[J].巖土工程學報,2014,36(6): 1129-1141. WU W B, JIANG G S,WANG K H, et al. Influence of soil plug effect on vertical dynamic response of pipe piles [J]. Chinese Journal of Geotechnical Engineering, 2014,36(6): 1129-1141. (in Chinese)

[12] 劉林超,閆啟方. 飽和土中管樁的水平動阻抗研究[J].巖土力學,2014,35(5):1348-1356. LIU L C, YAN Q F. Study of lateral dynamic impedance of pipe pile in saturated soil [J].Rock and Soil Mechanics, 2014,35(5):1348-1356. (in Chinese)

[13] KAYNIA A M, NOVAK M. Response of pile foundations to Rayleigh waves and obliquely body wave [J]. Earthquake Engineering and Structural Dynamics,1992, 21(4):303-3l8.

[14] MAKRIS N. Soil-pile interaction during the passage of Rayleigh waves: an analytical solution[J]. Earthquake Engineering and Structural Dynamics,1994,23(2):153- 167.

[15] 王海東,尚守平.瑞利波作用下考慮樁土相互作用的單樁豎向動力響應計算研究[J].工程力學,2006,23(8):74- 78. WANG H D, SHANG S P. Computation research on vertical dynamic response of single-pile considering pile-soil interaction during passage of Raleigh waves[J].Engineering Mechanics,2006,23(8): 74 -78. (in Chinese)

[16] 馮永正,王立忠,陳云敏.瑞利波作用下雙層地基中群樁橫向動力響應[J].振動工程學報,2001,14(3):264-291. FENG Y Z,WANG L Z, CHEN Y M. Lateral dynamic response of pile group in double-layered soils during the passage of Rayleigh waves[J].Journal of Vibration Engineering,2001,14(3): 264-291. (in Chinese)

[17] GAZETAS G, DOBRY R. Simple radiation damping model for piles and footings [J].Journal of Engineering Mechanics, 1984, 110(6):937-956.

[18] 胡安峰,謝康和,肖志榮.水平荷載下單樁動力反應分析[J].浙江大學學報,2003,37(4):420-425. HU A F, XIE K H, XIAO Z R. Dynamic response analysis for single pile subjected to lateral loading [J]. Journal of Zhejiang University, 2003,37(4): 420-425. (in Chinese)

(編輯 胡玲)

Dynamic properties of pipe pile under harmonic SH waves

LiuLinchao，XiaoQidan，YanQifang，LiuTeng

(School of Civil Engineering, Xinyang Normal University, Xinyang, 464000 Henan, P.R.China)

The displacements of soil around pile and pile core soil under harmonic SH waves are obtained based on one-dimensional wave motion model. Under the three-dimensional axial symmetry case, the vibrations of soil around pile and pile core soil caused by horizontal harmonic concentrated load and SH waves are solved by potential functions and variable separation method, and the radial and ring displacements of soil around pile and pile core soil are also obtained. The vibration of pipe pile under harmonic concentrated load and SH waves is investigated by considering pipe pile-soil dynamic interaction and continuous conditions. And the dynamic magnification factor at pipe pile has got. The results of numeral example indicate that pipe pile has resonance phenomenon under harmonic SH waves, the pipe pilecould lead to instability if the pipe pile wall too thin, and seismic performance of pipe pile is better than solid core pile under the same outside diameter.

pipe pile; SH waves; dynamic properties; dynamic magnification factor

2016-03-09

國家自然科學基金(U1504505)；河南省科技發(fā)展計劃(142102210063)；河南省高等學校重點科研項目(15A560036)；河南省高等學校青年骨干教師資助計劃(2013GGJS-121)；信陽師范學院重大課題預研項目(2013ZDYY19)。

劉林超(1979-)，副教授，博士，主要從事多孔介質理論、粘彈性性理論、樁基動力學的研究，(E-mail)llc109@126.com。

Foundation item：National Natural Science Foundation of China (No.U1504505); Development of Science and Technology Plan Project of Henan Province(No.142102210063); Key Scientific Research Project of Henan Province(No.15A560036); Youth Backbone Teacher Plan Project of Colleges and Universities in Henan Province(No.2013GGJS-121); Major Beforehand Research Project of Xinyang Normal University(No.2013ZDYY19).

10.11835/j.issn.1674-4764.2016.06.006

TU435

A

1674-4764(2016)06-0038-08

Received:2016-03-09

Author brief：Liu Linchao(1979-),associate professor,PhD, main research interests: theory of porous medium,viscoelastic theory and pile dynamics, (E-mail) llc109@126.com.