簡(jiǎn)諧SH波作用下管樁的振動(dòng)特性

劉林超，肖琪聃，閆啟方，劉滕

(信陽(yáng)師范學(xué)院 土木工程學(xué)院，河南 信陽(yáng) 464000)

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簡(jiǎn)諧SH波作用下管樁的振動(dòng)特性

劉林超，肖琪聃，閆啟方，劉滕

(信陽(yáng)師范學(xué)院 土木工程學(xué)院，河南 信陽(yáng) 464000)

管樁；SH波；振動(dòng)特性；動(dòng)力放大因子

樁基作為一種重要的基礎(chǔ)形式通常要承受地震激勵(lì)、海洋荷載、動(dòng)力機(jī)器荷載等動(dòng)態(tài)激勵(lì)的作用，有關(guān)樁基振動(dòng)特性的研究近幾十年來(lái)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(shí)芯樁的振動(dòng)特性。管樁作為近年來(lái)才出現(xiàn)的一種樁基形式，由于具有抗彎抗拉性能好、強(qiáng)度和承載力高、耐久性好且造價(jià)較低等諸多優(yōu)點(diǎn)而被廣泛應(yīng)用到眾多工程領(lǐng)域。為了給樁基設(shè)計(jì)、施工、檢測(cè)等提供理論依據(jù)，近幾年來(lái)，針對(duì)管樁的振動(dòng)特性的研究越來(lái)越受到關(guān)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(shí)域解析解，鄭長(zhǎng)杰等[9-10]針對(duì)粘彈性地基中現(xiàn)澆大直徑管樁的縱向振動(dòng)及扭轉(zhuǎn)振動(dòng)進(jìn)行了研究，吳文兵等[11]考慮土塞效應(yīng)運(yùn)用附加質(zhì)量法對(duì)成層地基中管樁的縱向振動(dòng)進(jìn)行了研究，劉林超等[12]針對(duì)飽和土中管樁的水平振動(dòng)運(yùn)用多孔介質(zhì)理論進(jìn)行了研究。

1 簡(jiǎn)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(jiǎn)諧水平剪切波(SH波)作用下的振動(dòng)問(wèn)題，且簡(jiǎn)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(shè)式(6)和式(8)的解分別為

(10)

(11)

(12)

(13)

進(jìn)而可以得到簡(jiǎn)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(jiǎn)諧荷載作用下樁周土和樁芯土振動(dòng)求解

樁周土

(ωOzeiωt)+

(16)

(17)

樁芯土

(ωIzeiωt)+

(18)

(19)

令

(20)

對(duì)式(16)～(19)進(jìn)行無(wú)量綱運(yùn)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(jiǎn)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(jiǎn)諧SH波和水平集中荷載作用下管樁振動(dòng)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(wú)量綱化的徑向應(yīng)力和環(huán)向應(yīng)力σOr、τOrθ、σIr、τIrθ，進(jìn)而可以得到樁周土和樁芯土對(duì)管樁的水平作用力。單位厚度樁周土對(duì)管樁的無(wú)量綱化水平作用力幅值為

θ=

(38)

單位厚度樁芯土對(duì)管樁的無(wú)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(duì)管樁的共同作用力為

(40)

由于管樁同樣作簡(jiǎn)諧振動(dòng)，以單位樁長(zhǎng)為研究對(duì)象，考慮式(40)可以建立無(wú)量綱化的管樁的水平振動(dòng)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(wú)量綱化的樁頂簡(jiǎn)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(duì)式(46)兩端運(yùn)用三角函數(shù)的正交性可得

(47)

式(47)中

(48)

由此可得SH簡(jiǎn)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(jiǎn)諧SH波作用下管樁樁頂?shù)膭?dòng)力放大因子。

4 數(shù)值算例與分析

圖2 動(dòng)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(shí)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(shí)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(shí)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(jié)論

以簡(jiǎn)諧SH波和水平集中荷載作用下管樁的振動(dòng)特性為研究對(duì)象，運(yùn)用波的傳播理論、樁基動(dòng)力學(xué)、數(shù)學(xué)物理方法等得到了管樁樁頂?shù)膭?dòng)力放大因子，以數(shù)值算例的形式通過(guò)分析管樁壁厚、樁土模量比和樁芯土與樁周土模量比對(duì)管樁動(dòng)力放大因子的影響，研究了管樁的振動(dòng)特性。

1)管樁樁頂動(dòng)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(dāng)管樁壁厚過(guò)薄時(shí)動(dòng)力放大因子隨頻率變化曲線將會(huì)出現(xiàn)急劇增大，樁基此時(shí)宜發(fā)生穩(wěn)定性破壞，所以管樁不能過(guò)薄。

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

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(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(guó)家自然科學(xué)基金(U1504505)；河南省科技發(fā)展計(jì)劃(142102210063)；河南省高等學(xué)校重點(diǎn)科研項(xiàng)目(15A560036)；河南省高等學(xué)校青年骨干教師資助計(jì)劃(2013GGJS-121)；信陽(yáng)師范學(xué)院重大課題預(yù)研項(xiàng)目(2013ZDYY19)。

劉林超(1979-)，副教授，博士，主要從事多孔介質(zhì)理論、粘彈性性理論、樁基動(dòng)力學(xué)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.