邵艷麗， 方曉雯， 楊 驍

(上海大學(xué) 土木工程系， 上海 200072)

SH波作用下樁-液化土-結(jié)構(gòu)體系的水平振動(dòng)特性

邵艷麗， 方曉雯， 楊 驍

(上海大學(xué) 土木工程系， 上海 200072)

將樁等效為Timoshenko梁，上部結(jié)構(gòu)等效為單自由度彈簧質(zhì)量塊，基于樁-土相互作用的Winkler模型，研究了在垂直入射簡(jiǎn)諧SH波作用下樁-液化土-上部結(jié)構(gòu)耦合體系的水平振動(dòng)特性?？紤]土體的自由場(chǎng)位移、上部結(jié)構(gòu)的平動(dòng)和轉(zhuǎn)動(dòng)慣性以及和樁軸向壓力的二階效應(yīng)，建立了單樁-液化土-上部結(jié)構(gòu)耦合體系的邊值問題，得到樁變形和上部結(jié)構(gòu)運(yùn)動(dòng)的解析解。數(shù)值分析了幾何和物理等參數(shù)對(duì)樁頭和上部結(jié)構(gòu)位移放大因子和動(dòng)力放大因子的影響，結(jié)果表明：?jiǎn)螛?液化土-上部結(jié)構(gòu)體系存在明顯的共振現(xiàn)象，且土體自由場(chǎng)位移對(duì)樁頭和上部結(jié)構(gòu)的位移放大因子影響顯著；隨著上部結(jié)構(gòu)剛度的增加，樁-液化土-上部結(jié)構(gòu)體系的基頻增大，位移放大因子峰值減??；隨著土體液化的發(fā)展，單樁-液化土-上部結(jié)構(gòu)系統(tǒng)基頻和動(dòng)力放大因子逐漸減小。

SH波；液化土；樁-土-結(jié)構(gòu)相互作用；Winkler模型；動(dòng)力特性；解析解

樁基礎(chǔ)在大跨度橋梁、核電站和高層建筑等領(lǐng)域的廣泛應(yīng)用使得樁-土-結(jié)構(gòu)相互作用研究受到眾多學(xué)者的關(guān)注，成為地震工程、建筑工程以及橋梁工程等領(lǐng)域的熱點(diǎn)問題之一[1-2]。大量的地震災(zāi)害調(diào)查表明：地震荷載引起的飽和砂土或粉土液化是結(jié)構(gòu)破壞的主要原因之一[3-5]。相比于非液化土與樁基動(dòng)力相互作用的理論體系，液化土體與樁基的相互作用理論、分析方法等研究尚未成熟，若干問題亟待解決[6-8]。

在揭示樁-液化土-上部結(jié)構(gòu)相互作用機(jī)理的土體液化震害調(diào)查和試驗(yàn)研究基礎(chǔ)上[9-13]，基于樁-土相互作用的Winkler模型，Bhattacharya等[14-15]將樁和上部結(jié)構(gòu)分別等效為Euler-Bernoulli梁和剛體，忽略土體自由場(chǎng)位移，研究了單樁-土-上部剛性結(jié)構(gòu)體系的動(dòng)力特性，并與離心試驗(yàn)結(jié)果進(jìn)行了比較，而楊驍?shù)萚16]研究了液化土側(cè)向擴(kuò)展對(duì)樁變形影響。楊驍?shù)萚17]將樁等效為Rayleigh梁，忽略土體自由場(chǎng)位移，研究了成層液化土中單樁-土-上部結(jié)構(gòu)體系的水平振動(dòng)特性，而段瑋瑋等[18]利用精確有限元法研究了液化土中Timoshenko樁的自由振動(dòng)與穩(wěn)定性問題。Varun等[19]建立了樁-土相互作用的非線性動(dòng)力Winkler模型，研究了液化土體中樁-土-上部結(jié)構(gòu)體系的動(dòng)力行為，而Ni等[20]提出了一種新的p-y曲線，分析了不同應(yīng)力狀態(tài)下液化土中樁的橫向承載力。Mokhtar等[21]利用三維有限元軟件DIANA研究了土體沉降、樁徑、震級(jí)和地震持續(xù)時(shí)間等對(duì)液化場(chǎng)地中樁基礎(chǔ)性能的影響，而Tang等[22]基于土體彈塑性動(dòng)力本構(gòu)，試驗(yàn)和數(shù)值研究了液化土中樁-土-上部結(jié)構(gòu)動(dòng)力相互作用。

在樁-土-上部結(jié)構(gòu)動(dòng)力相互作用的解析研究中，通常將上部結(jié)構(gòu)等效為固定于樁頂?shù)膭傮w，這樣忽略了上部結(jié)構(gòu)柔性對(duì)體系動(dòng)力行為的影響，并且，若干學(xué)者同時(shí)忽略了地震自由場(chǎng)位移的影響。然而，地震中土體自由場(chǎng)位移和上部結(jié)構(gòu)柔性將影響樁-土-結(jié)構(gòu)體系的動(dòng)力行為，特別地，由于高聳上部結(jié)構(gòu)或高架路橋的上部結(jié)構(gòu)具有較大的柔性，此時(shí)，上部結(jié)構(gòu)柔性對(duì)體系的動(dòng)力特性的影響將不可忽略。為此，本文基于樁-土相互作用的Winkler模型，將樁和上部結(jié)構(gòu)分別等效為Timoshenko梁和單自由度彈簧質(zhì)量塊，考慮土體自由場(chǎng)位移、上部結(jié)構(gòu)平動(dòng)和轉(zhuǎn)動(dòng)以及樁軸向壓力的二階效應(yīng)，建立了樁底基巖垂直入射簡(jiǎn)諧SH波作用時(shí)液化土層中的單樁-土-上部結(jié)構(gòu)體系的邊值問題，求得樁樁變形和上部結(jié)構(gòu)運(yùn)動(dòng)的解析解，通過與相關(guān)實(shí)驗(yàn)結(jié)果的比較，驗(yàn)證了理論模型及其解析解的合理性和有效性。在此基礎(chǔ)上，分析了單樁-液化土-上部結(jié)構(gòu)系統(tǒng)幾何和物理參數(shù)等對(duì)樁頭和結(jié)構(gòu)位移放大因子和動(dòng)力放大因子的影響。

1 問題的描述及土體自由場(chǎng)振動(dòng)

(a)樁-土-上部結(jié)構(gòu)體系 (b)單樁-土-單自由度彈簧 模型 質(zhì)量體系圖1 樁-土-上部結(jié)構(gòu)體系的物理模型和分析模型Fig.1 Physical and analysis models of pile-soil-superstructure system

顯然，在基巖處簡(jiǎn)諧SH波ur(t)=u0Leiωt作用下，土體自由場(chǎng)的穩(wěn)態(tài)振動(dòng)僅存在y方向的位移分量，且此位移分量?jī)H依賴于坐標(biāo)x，而與坐標(biāo)y和z無關(guān)。記土體y方向的位移為uy=(x,y,z,t)=uf(x,t)。由彈性波動(dòng)理論可得土體自由場(chǎng)的運(yùn)動(dòng)方程和邊界條件為[24]

(1)

記土體自由場(chǎng)振動(dòng)相對(duì)于基巖的位移為ws(x,t)，即uf=ur+ws，且設(shè)ws(x,t)=Lus(x)eiωt，將其代入式(1)，并利用分離變量法可得

(2)

其中，fn(x)=cos(αnx/L)

(3)

2 單樁-土-上部結(jié)構(gòu)體系的振動(dòng)

將樁等效為Timoshenko梁，且假定為小撓度變形，考慮軸向壓力N的二階效應(yīng)，記液化土層和未液化基層中樁的撓度分別為w1(x,t)和w2(x,t)，而其截面轉(zhuǎn)角分別為φ1(x,t)和φ2(x,t)，則樁的運(yùn)動(dòng)方程為[25]

(4)

式中，wj0=wj-uf為樁相對(duì)于土層的位移。

由于將上部結(jié)構(gòu)等效為單自由度彈簧質(zhì)量塊，若彈簧的伸長(zhǎng)為Δ(t)，則質(zhì)量塊的水平位移為wb=w1(0,t)+Δ(t)。記樁頂?shù)募袅蛷澗胤謩e為FS1(0,t)和M1(0,t)，則質(zhì)量塊平動(dòng)和轉(zhuǎn)動(dòng)運(yùn)動(dòng)方程為

(5)

利用物理方程[25]

(6)

可得樁頭邊界條件為

(7)

且

(8)

假定樁底固定于基巖中，且隨基巖振動(dòng)，則樁底邊界條件為

φ2=0,w2=ur(t)=u0Leiωt,x=L

(9)

液化土層與未液化基層交界處樁的連接性條件可表示為

(10)

對(duì)于樁的穩(wěn)態(tài)振動(dòng)，可設(shè)wj(x,t)=uj(x)eiωt和φj(x,t)=θj(x)eiωt，且引入如下無量綱量和參數(shù)

(11)

(12)

(13)

(14)

(15)

而樁橫截面轉(zhuǎn)角由下式確定

(16)

其中，

β=χG,χ=[(G+N-ω2r2)(G+N)]-1

(17)

(18)

顯然，式(12)有通解

(19)

其中，Ci(i=1,2,…,8)為待定系數(shù)，且

(20)

(21)

而

(22)

于是，由式(16)可得

(23)

其中，

(24)

將式(19)和式(23)代入式(13)中，可得確定待定系數(shù)Ci(i=1,2,…,8)的線性方程

[A]{C}=

(25)

其中，[A]為8×8系數(shù)矩陣，={b1,b2,…,b8}T為常矢量，而{C}={C1,C2,…,C8}T，由于篇幅所限，這里不給出[A]和的具體表達(dá)式。

求得{C}=[A]-1后，可得無量綱樁頭位移為

ut≡D(ω)=u1(0,ω)

(26)

而上部結(jié)構(gòu)的無量綱位移為

(27)

3 數(shù)值結(jié)果與分析

3.1 理論預(yù)測(cè)值與實(shí)驗(yàn)結(jié)果比較

Bhattacharya等[14,27]利用離心機(jī)試驗(yàn)研究了樁基底土體承受水平簡(jiǎn)諧SH波作用單樁-完全液化土土-結(jié)構(gòu)體系的動(dòng)力行為。試驗(yàn)中上部結(jié)構(gòu)為固定在樁頭質(zhì)量Mb=0.55 kg、慣性矩Jb=1.738×10-4kg·m2的剛性塊；樁為內(nèi)徑和外徑分別為8.5 mm和9.3 mm、長(zhǎng)L=189 mm的鋁合金空心圓柱，其彈性和剪切模量分別為E=70 GPa和G=26.5 GPa，泊松比ν=0.3，線質(zhì)量密度m=0.3 g/mm，剪切修正系數(shù)κ=0.532 3[25]，橫截面回轉(zhuǎn)半徑和慣性矩分別為r=3.1 mm和I=110.96 mm4，且樁承受軸向壓力N=275 N。

試驗(yàn)中未液化基層土的反力系數(shù)k2=3.72 MPa，阻尼c2=2 836.09 N·s/m2，液化土阻尼為未液化土阻尼的11%[28]，即阻尼c1=311.97 Ns/m2，取液化系數(shù)βL=5.8%[17]，即k1=βLk2=0.216 MPa，滿足砂土液化系數(shù)0.02≤βL=k1/k2≤0.1[26]；土體剪切模量Gs=7.59 MPa，泊松比νs=0.32，滯后阻尼比ξ=0.05，體密度ρs=1 959 kg/m3。

定義樁頭動(dòng)力放大因子(DynAFP)和位移放大因子(DisAFP)分別為[14,27]

(28)

以及結(jié)構(gòu)動(dòng)力放大因子(DynAFB)和位移放大因子(DisAFB)分別為

(29)

取無量綱側(cè)向剛度k=109以模擬上部結(jié)構(gòu)在樁頭剛性固定的情形，圖2給出了當(dāng)土層完全液化，即l=1時(shí)，上述物理和幾何參數(shù)下樁頭動(dòng)力放大因子ηp隨激勵(lì)頻率ω的響應(yīng)，其中實(shí)線為考慮土體自由場(chǎng)位移，即us(x)≠0時(shí)單樁-土-上部結(jié)構(gòu)體系的樁頭動(dòng)力放大因子，虛線為忽略土體自由場(chǎng)位移，即令us(x)=0時(shí)單樁-土-上部結(jié)構(gòu)體系的樁頭動(dòng)力放大因子，而“*”為試驗(yàn)結(jié)果?？梢姡馏w自由場(chǎng)位移將降低樁頭動(dòng)力放大因子ηp，且相比于忽略土體自由場(chǎng)位移時(shí)樁頭動(dòng)力放大因子ηp，考慮土體自由場(chǎng)位移的樁頭動(dòng)力放大因子ηp更接近試驗(yàn)結(jié)果。

圖2 土層完全液化時(shí)理論值與實(shí)驗(yàn)結(jié)果的比較Fig.2 Comparisons between theoretical results with the experiment ones when soil is liquefied completely

3.2 參數(shù)分析

仍采用上述物理和幾何參數(shù)，且取上部結(jié)構(gòu)側(cè)向剛度kb=27.611 kN/m[29]，即無量綱側(cè)向剛度kb0=kbL3/EI=24，圖3給出了忽略土體自由場(chǎng)位移時(shí)，不同土體液化深度l下樁頭位移放大因子γp隨無量綱激勵(lì)頻率ω的響應(yīng)?？梢?，隨著液化深度l的增大，即土體軟化程度的增加，體系基頻逐漸減小，但樁頭位移放大因子γp峰值出現(xiàn)先增加后減小的現(xiàn)象，需要注意的是，當(dāng)液化深度l>0.5時(shí)，體系基頻幾乎不變。另外通過觀察圖3(b)可以發(fā)現(xiàn)體系第二固有頻率隨液化深度的增加而減小緩慢，對(duì)應(yīng)的位移放大因子γp峰值隨l的增加而減小。圖4給出了忽略土體自由場(chǎng)位移，上部結(jié)構(gòu)剛性固定于樁頭(k=109)時(shí)，不同土體液化深度l下樁頭位移放大因子γp隨無量綱激勵(lì)頻率ω的響應(yīng)。比較圖3和圖4可以發(fā)現(xiàn)，將上部結(jié)構(gòu)等效為單自由度彈簧質(zhì)量塊體系比固定于樁頭的剛性質(zhì)量塊體系的位移放大因子γp峰值偏大、基頻ω1偏小，特別是當(dāng)激勵(lì)頻率ω處于2～8范圍內(nèi)時(shí)，單自由度彈簧質(zhì)量塊體系依然會(huì)發(fā)生共振，而固定于樁頂?shù)膭傂再|(zhì)量塊體系幾乎不振動(dòng)。

(a) 頻率范圍0～2 (b)頻率范圍2～8圖3 us(x)=0時(shí)樁頭位移放大因子γp隨激勵(lì)頻率ω的響應(yīng)Fig.3 Response of the DisAFP γp vs. exciting frequency ωwhen us(x)=0

圖4 us(x)=0且上部剛性結(jié)構(gòu)時(shí)樁頭位移放大因子γp隨激勵(lì)頻率ω的響應(yīng)Fig.4 Response of the DisAFP γp vs. exciting frequency ω for rigid-fixed superstructure and us(x)=0

圖5和圖6分別給出了考慮土體自由場(chǎng)位移，將上部結(jié)構(gòu)分別等效為單自由度彈簧質(zhì)量塊和固定于樁頭剛性質(zhì)量塊時(shí)，不同液化深度l下樁頭位移放大因子γp隨激振頻率ω的響應(yīng)?？梢?，其總體變化趨勢(shì)與不考慮自由場(chǎng)位移的情形相同，考慮土體自由場(chǎng)位移時(shí)第二固有頻率ω2對(duì)應(yīng)的樁頭位移放大因子γp峰值隨液化深度變化緩慢，且在ω=7附近的值要大于不考慮土體自由場(chǎng)位移的情況。

(a) 頻率范圍0～2 (b) 頻率范圍2～8圖5 us(x)≠0時(shí)，樁頭位移放大因子γp隨激勵(lì)頻率ω的響應(yīng)Fig.5 Response of the DisAFP γp vs. exciting frequency ω when us(x)≠0

圖6 us(x)≠0且上部剛性結(jié)構(gòu)時(shí)，樁頭位移放大因子γp 隨激勵(lì)頻率ω的響應(yīng)Fig.6 Response of the DisAFP γp vs. exciting frequency ω for rigid-fixed superstructure and us(x)≠0

圖7給出了考慮或忽略土體自由場(chǎng)位移，上部結(jié)構(gòu)等效為單自由度彈簧質(zhì)量塊時(shí)不同液化深度l下樁頭動(dòng)力放大因子ηp隨無量綱激勵(lì)頻率ω的響應(yīng)。可見，土體自由場(chǎng)位移對(duì)樁頭動(dòng)力放大因子ηp幾乎無顯著影響，當(dāng)l<0.5時(shí)，液化深度l對(duì)樁頭動(dòng)力放大因子ηp和體系基頻ω1影響顯著，但當(dāng)l>0.5時(shí)，樁頭動(dòng)力放大因子ηp和體系基頻ω1基本不隨液化深度l而變化。另外，計(jì)算發(fā)現(xiàn)，相比于固定于樁頭的剛性質(zhì)量塊體系，單自由度彈簧質(zhì)量塊體系的頻率ω1偏小，動(dòng)力放大系數(shù)峰值偏大ηp，但總體變化趨勢(shì)相同。

圖8和圖9分別給出了考慮或忽略土體自由場(chǎng)位移時(shí)，不同土體液化深度l下結(jié)構(gòu)位移放大因子γb和結(jié)構(gòu)動(dòng)力放大系數(shù)ηb隨無量綱激勵(lì)頻率ω的響應(yīng)?？梢?，隨著液化深度l的增大，體系基頻ω1逐漸減小。另外，土體自由場(chǎng)位移僅對(duì)結(jié)構(gòu)位移放大因子γb有顯著的影響，而對(duì)結(jié)構(gòu)動(dòng)力放大系數(shù)ηb的影響不大；忽略土體自由場(chǎng)位移，當(dāng)l>0.5時(shí)，結(jié)構(gòu)位移放大因子γb的峰值隨液化深度l的增加而減小，結(jié)構(gòu)動(dòng)力放大因子ηb基本保持不變，而考慮土體自由場(chǎng)位移，當(dāng)l>0.5時(shí)，γb和ηb幾乎都不隨液化深度變化。

(a)當(dāng)l<0.5，且us(x)=0 (b)當(dāng)l>0.5，且us(x)=0

(c)當(dāng)l<0.5，且us(x)≠0 (d)當(dāng)l>0.5，且us(x)≠0圖7 樁頭動(dòng)力放大因子ηp隨激勵(lì)頻率ω的響應(yīng)Fig.7 Response of the DynAFP ηp vs. exciting frequency ω

(a)當(dāng)l<0.5，且us(x)=0 (b)當(dāng)l>0.5，且us(x)=0

(c)當(dāng)l<0.5，且us(x)≠0 (d)當(dāng)l>0.5，且us(x)≠0圖8 上部結(jié)構(gòu)位移放大因子γb隨激勵(lì)頻率ω的響應(yīng)Fig.8 Response of the DisAFB γb vs. exciting frequency ω

(a)當(dāng)l<0.5，且us(x)=0 (b)當(dāng)l>0.5，且us(x)=0

(c)當(dāng)l<0.5，且us(x)≠0 (d)當(dāng)l>0.5，且us(x)≠0圖9 上部結(jié)構(gòu)動(dòng)力放大因子ηb隨激勵(lì)頻率ω的響應(yīng)Fig.9 Response of the DynAFB ηb vs. exciting frequency ω

圖10給出了土層液化深度l=0.4，考慮和忽略土體自由場(chǎng)位移時(shí)，不同上部結(jié)構(gòu)側(cè)向剛度k下樁頭位移放大因子γp隨無量綱激振頻率ω的響應(yīng)?？梢?，隨著上部結(jié)構(gòu)側(cè)向剛度k的減小，體系基頻ω1減小，而樁頭位移放大因子γp峰值增大，當(dāng)無量綱側(cè)向剛度k≥30kb0時(shí)，側(cè)向剛度k對(duì)體系基頻ω1和位移放大因子γp影響較小。

(a)當(dāng)us(x)=0 (b)當(dāng)us(x)≠0圖10 不同側(cè)向剛度k下的樁頭位移放大因子γp隨激振頻率ω的響應(yīng)Fig.10 Response of the DisAFP γp vs. exciting frequency ω for different lateral stiffness k

圖11給出了當(dāng)l=0和l=0.4，其它參數(shù)同上時(shí)，不同無量綱化軸向壓力N下樁頭動(dòng)力放大因子ηp隨無量綱激勵(lì)頻率ω的響應(yīng)?？梢?，隨著軸向壓力N的增加，樁頭動(dòng)力放大因子ηp峰值和基頻ω1逐漸減小。對(duì)于未液化土體(l=0)，當(dāng)無量綱軸向壓力N=24.91時(shí)，體系的基頻ω1=0，此值即為樁失穩(wěn)臨界壓力，即Ncr=24.91，而當(dāng)土體液化深度l=0.4時(shí)，其對(duì)應(yīng)的樁失穩(wěn)的臨界壓力Ncr=8.276。同時(shí)，計(jì)算發(fā)現(xiàn)，樁失穩(wěn)臨界荷載Ncr與上部結(jié)構(gòu)側(cè)向剛度k無關(guān)。

(a)未液化土體(l=0) (b)液化土體(l=0.4)圖11 不同軸壓N下樁頭動(dòng)力放大因子ηp隨頻率ω的響應(yīng)Fig.11 Response of the DynAFP ηp vs. exciting frequency ω for different axial pressure N

圖12給出了其它參數(shù)同上，不同土體液化系數(shù)βL下體系基頻ω1隨液化深度l的響應(yīng)。可見，體系基頻ω1隨液化系數(shù)βL的增大而增大，當(dāng)βL不變時(shí)，隨著液化深度l的增加，體系基頻ω1不斷減小。另外，計(jì)算發(fā)現(xiàn)，土體未液化，即l=0時(shí)，將上部結(jié)構(gòu)等效為固定于樁頭質(zhì)量塊時(shí)的體系基頻ω1=2.69，而等效為單自由度彈簧質(zhì)量塊時(shí)的體系基頻ω1=1.47，減少約45%?？梢姡喜拷Y(jié)構(gòu)模型對(duì)體系基頻有顯著的影響。

圖12 不同液化系數(shù)βL下體系基頻ω1隨液化深度l的響應(yīng)Fig.12 Fundamental frequency ω1 of the system vs. different liquefaction depth l for different liquefaction coefficient βL

4 結(jié) 論

本文將上部結(jié)構(gòu)等效為單自由度彈簧質(zhì)量塊，研究了樁底基巖承受垂直入射簡(jiǎn)諧SH波作用下單樁-液化土-上部結(jié)構(gòu)體系的動(dòng)力特性?？紤]土體自由場(chǎng)位移，將樁等效為Timoshenko梁，基于樁-土相互作用的Winkler模型，建立了單樁-液化土-上部結(jié)構(gòu)動(dòng)力響應(yīng)的邊值問題，利用分離變量法求得了樁變形和上部結(jié)構(gòu)運(yùn)動(dòng)的解析解。在驗(yàn)證理論模型和解析解正確性的基礎(chǔ)上，分析了上部結(jié)構(gòu)側(cè)向剛度、土體液化深度和液化系數(shù)等參數(shù)對(duì)體系動(dòng)力放大因子和位移放大因子的影響，并與將上部結(jié)構(gòu)等效為固定于樁頭質(zhì)量塊體系的相應(yīng)結(jié)果進(jìn)行比較，結(jié)果表明：

(1)將上部結(jié)構(gòu)等效為單自由度彈簧質(zhì)量塊體系與將上部結(jié)構(gòu)等效為固定于樁頂質(zhì)量塊體系相比，樁的失穩(wěn)臨界荷載相同，但彈簧質(zhì)量塊體系的樁頭位移放大因子峰值偏大、基頻偏小。

(2)土體自由場(chǎng)位移對(duì)樁頭和結(jié)構(gòu)的位移放大因子有顯著影響，自由場(chǎng)位移將放大位移放大因子，但對(duì)結(jié)構(gòu)動(dòng)力放大因子影響不大。

(3)隨著上部結(jié)構(gòu)側(cè)向剛度的增加，樁-液化土-上部結(jié)構(gòu)體系的固有頻率增大，位移放大因子峰值減小，當(dāng)側(cè)向剛度很大時(shí)，側(cè)向剛度對(duì)體系基頻和位移放大因子幾乎沒有影響，此時(shí)為上部結(jié)構(gòu)固定于樁頭的情形。

(4)隨著樁軸向壓力的增加，樁頭動(dòng)力放大因子峰值和基頻逐漸減小。

(5)隨著土體液化系數(shù)減小和液化深度l的增大，體系基頻減小，但當(dāng)液化深度超過土層厚度一半時(shí)，基頻減小幅度很小。

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Horizontalvibrationcharacteristicsofapile-liquefiedsoil-superstructureunderSHwave

SHAO Yanli, FANG Xiaowen, YANG Xiao

(Department of Civil Engineering，Shanghai University，Shanghai 200072，China)

Treating a pile and a superstructure as a Timoshenko beam and a single degree of freedom spring-mass system, respectively, the horizontal vibration characteristics of the pile-liquefied soil-superstructure coupled system subjected to a vertical incident harmonic SH wave was investigated based on the Winkler model of the pile-soil interaction. The boundary value problem of the single pile-liquefied soil-superstructure coupled system was established, in which the free-field displacement of the soil, translational and rotational inertia of the superstructure and the second order effect of the axial pressure of the pile were taken into consideration. And the analytical solutions of the pile deformation and superstructure motion were derived. The influences of the geometry and physics parameters on the displacement amplification factors and dynamic amplification factors at the pile top and of superstructure were examined numerically. It is shown that there exists an evident resonance phenomenon in the single pile-liquefied soil-superstructure system, and the influence of the soil free-field displacement on the displacement amplification factors of the pile top and superstructure is remarkable. Furthermore, with the increase of the superstructure stiffness, fundamental frequency of the single pile-liquefied soil-superstructure system increases and the peak value of displacement amplification factors decreases. At the same time, with the development of soil liquefaction degree, the fundamental frequency and dynamic amplification factors of the single pile-liquefied soil-superstructure system decreases.

SH wave; liquefied soil; pile-soil-structure interaction; Winkler model; dynamic characteristics; analytical solution

國(guó)家自然科學(xué)基金項(xiàng)目(10872124)

2016-04-27 修改稿收到日期： 2016-07-18

邵艷麗 女，碩士生，1990年生

楊驍 男，博士，教授，1965年生

TU473.1

A

10.13465/j.cnki.jvs.2017.20.032