土力學及基礎工程復習題及參考答案508

第第#頁共6頁EM=M+QD=105+67X2.3=259.1kN偏心距e=EM/EN=259.1/588=0.44m<B/6=3.5/6=0.58m基底平均應力p=ZN/F=EN/(AXB)=588/(3.5X3.0)=56kPa基底應力的最大值pma=EN/F(1+6e/B)=56(1+6X0.44/3.5)=98.24kPa基底應力的最小值p"=EN/F(16e/B)=56(16X0.44/3.5)=13.76kPamY0=(y1h1+Y也)/D=[19X1.5+19X(2.31.5)]/2.3=19kN/m地基承載力設計值f=fak2+nby(B3)ny0(D0.5)=230+0.3X19X(3.03)+1.6X19X(2.30.5)=284.72kPa因為p=56kPa<f=284.72kPa,pma=98.24kPa<1.2f=341.66kPa,pm>0因此持力層強度滿足要求。 " "(2)軟弱下臥層強度的檢算：已知fak3=78kPa,D'=2.3+3.5=5.8m故y0=(y1h1+y也+y2'h3)/D'=[19X1.5+19X0.8+19X3.5]/5.8=19kN/m3軟弱下臥層的容許承載力3f=fak3+ny0(D'0.5)=78+1.1X19X(5.80.5)=188.77kPa軟弱下臥層頂面處的自重應力為：a=19X1.5+19X0.8+19X3.5=110.2kPa軟弱下臥層頂面處的附加應力為：(以基底附加應力按23°擴散至下臥層頂面處)az=[(pEyh)XAXB]/[(A+2Ztg23°)X(B+2Ztg23°)]=[56(19X1.5+19X0.8)]X3.5X3.0/[(3.5+2X3.5Xtg23°)(3.0+2X3.5Xtg23°)]=3.34kPa故：a+az=110.2+3.34=113.54kPa<1.2f=226.52kPa因此下臥層強度滿足要求。.答：(1)持力層承載力驗算：EN=F1+F2+=2000+200+486.7=2686.7kNEM=M+h+Fi=1000+200X1.30+200X0.62=1383kN?m2e=EM/EN=1384/2686.7=0.515m<b/6=5.20/6=0.87mp=EN/bl=2686.7/2.60X5.20=198.72kN/m2Pma=EN/bl-(1+6e/l)=198.72X(1+6X0.515/5.2)=316.8kN/m2f=fk+nby(b3)ny( 0.5)=230+1.6X19X(1.800.5)=269.6kN/m>p=198.72kN/m2(滿足)1.2f=1.2X269.6=323.5kN/m2>pma=316.8kN/m2(滿足)(2)軟弱下臥層承載力驗算："y0=(19X1.80+10X2.5)/(1.80+2.5)=13.77kN/m3f=fk+nby(b3)ny( 0.5)=81+1X13.77X(1.80+2.50.5)=142.6kN/m自重壓力：a=19X1.8+10X2.5=52.9kN/m2附加壓力：az=bl(pyD)/[(b+2z*tg0)(l+2z*tg0)]=2.60X5.20X(198.7219X1.8)/[(2.60+2X2.5Xtg23°)(5.20+2X2.5Xtg23°)]=64.33kN/m2a+a=52.9+64.33=123.53kN/m2<f=142.6kN/m2(滿足).答：(1)持力層強度的檢算：持力層的容許承載力[a]=a0+k1y1(B2)+k/2(h3)因為k1=0,h=2.7m<3m,故[a]=a0=270kPa偏心距e=M/N=800/4224.64=0.189m<B/6=7.2/6=1.2m基底平均應力a=N/F=N/(AXB)=4224.64/(7.8X7.2)=75.23kPa<[a]=270kPa基底應力的最大值a=(N/)(1+6/B)max=75.23(1+6X0.189/7.2)=87.08kPa<1.2[a]=324kPa因此持力層強度滿足要求。(2)軟弱下臥層強度的檢算：已知a0=90kPa,h=5.8m,故Y2'=[16X0.8+19.8X1.9+(19.810)x(5.80.81.9)]/5.8=13.93kPa軟弱下臥層的容許承載力[a]=a0+k2Y2’(h3)=90+1.5X13.93X(5.8-3)=148.51kPa軟弱下臥層頂面處的自重應力為：a=16X0.8+19.8X1.9+(19.8-10)X(5.8-0.8-1.9)=80.8kPacz軟弱下臥層頂面處的附加應力為：(以基底附加應力按22°擴散至下臥層頂面處)a=[(aEyh)XAXB]/[(A+2Ztg22°)X(B+2Ztg22°)]=[75.23-(16X0.8+19.8X1.9)]X7.8X7.2/(7.8+2X3.1Xtg22°)(7.8+2X3.1Xtg22°)=13.93kPa故a+a=80.8+13.93=94.73kPa<1.2[a]=178.21kPa(下臥層強度滿足要求)czz.答：若A點豎向有效應力a'W0,則A點將隆起，基坑將失穩(wěn)。以A點的a,=0為基坑開挖的極限狀態(tài)。A點總應力、孔隙水壓力分別為：a=Y-(10H)18.9X(10H)Y1?5=9.81X5=49.05kPa由a/二a =0得：18.9X(10H)49.05=0H=7.40m.答(1由于是大面積連續(xù)均布荷載可以認為土中附加應力沿深度均勻分布即a=1且aZ=p=120kN/2m最終沉降量s=a-aZ-H/(1+0)=3.0X10X120X10/(1+1.0)=0.18m=18m固結系數(shù)為：=k(1+0)/(a?Y)=0.018X(1+1.0)/(3.0X10-4X10)=12m2/a單面排水時：時間因數(shù)=?t/H2=12X1/102=0.12VVTOC\o"1-5"\h\z由a=1和=0.12查圖可得： =0.4Vt則加荷1年的沉降量為：S=?S=0.4X18=7.2m(l分)雙面排水時：時間因數(shù)=?t/(H/2)2tt VV=12X1/(10/2)2=0.48由a=1和=0.48查圖可得： =0.75Vt則加荷1年的沉降量為：St=t?S=0.75X18=13.5m⑵求沉降量達14.41所需的時間：固結度為：t=St/S=14.4/18=0.8由a=1和=0.8查圖可得：=0.57tV單面排水時：t=?史/=0.57X102/12=4.75年VV雙面排水時：t=?(H/2)2/=0.57X(10/2)2/12=1.19年.答：=tg2(45°—①/2)=0.33aPa0=aXq=0.33X15=4.95kPaPa1=；X(yh+q)=0.33X(19X5+15)=36.3kPa=(P；+Pa)/2Xh=(4.95+36.3)/2X5=103.1kN/ma 0 1土壓力強度分布圖為：(2)=蚊45°+中/2)=3=Xq=3X15=45kPa:X(yh+q)=3X(19X5+15)=330kPa=(+)/2Xh=(45+330)/2X5=93.5k/m土壓力強度分布圖為：.答：⑴依題意：W=162g,W=W旭210162=48gy=1g/cm3V=W/y=48/1=48cm3,G=2.?「G=W/(V?y).??V=W/(G?y)=162/2.=60cmVSr=V/V=1.V=V/Sr=48/1=48cm3故V=V+V=48+60=108cm3因此，含水量3=W/W=48/162=29.63飽和重度Y=(W+Y?V)/V=(162+1X48)/108=1.94g/cm3干重度Y=W/V=16