土力学及基础工程复习题及参考答案508

第第#页共6页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基底平均应力p=ZN/F=EN/(AXB)=588/(3.5X3.0)=56kPa基底应力的最大值pma=EN/F(1+6e/B)=56(1+6X0.44/3.5)=98.24kPa基底应力的最小值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地基承载力设计值f=fak2+nby(B3)ny0(D0.5)=230+0.3X19X(3.03)+1.6X19X(2.30.5)=284.72kPa因为p=56kPa<f=284.72kPa,pma=98.24kPa<1.2f=341.66kPa,pm>0因此持力层强度满足要求。 " "(2)软弱下卧层强度的检算：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软弱下卧层的容许承载力3f=fak3+ny0(D'0.5)=78+1.1X19X(5.80.5)=188.77kPa软弱下卧层顶面处的自重应力为：a=19X1.5+19X0.8+19X3.5=110.2kPa软弱下卧层顶面处的附加应力为：(以基底附加应力按23°扩散至下卧层顶面处)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因此下卧层强度满足要求。.答：(1)持力层承载力验算：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(满足)1.2f=1.2X269.6=323.5kN/m2>pma=316.8kN/m2(满足)(2)软弱下卧层承载力验算："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自重压力：a=19X1.8+10X2.5=52.9kN/m2附加压力：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(满足).答：(1)持力层强度的检算：持力层的容许承载力[a]=a0+k1y1(B2)+k/2(h3)因为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基底平均应力a=N/F=N/(AXB)=4224.64/(7.8X7.2)=75.23kPa<[a]=270kPa基底应力的最大值a=(N/)(1+6/B)max=75.23(1+6X0.189/7.2)=87.08kPa<1.2[a]=324kPa因此持力层强度满足要求。(2)软弱下卧层强度的检算：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软弱下卧层的容许承载力[a]=a0+k2Y2’(h3)=90+1.5X13.93X(5.8-3)=148.51kPa软弱下卧层顶面处的自重应力为：a=16X0.8+19.8X1.9+(19.8-10)X(5.8-0.8-1.9)=80.8kPacz软弱下卧层顶面处的附加应力为：(以基底附加应力按22°扩散至下卧层顶面处)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(下卧层强度满足要求)czz.答：若A点竖向有效应力a'W0,则A点将隆起，基坑将失稳。以A点的a,=0为基坑开挖的极限状态。A点总应力、孔隙水压力分别为：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由于是大面积连续均布荷载可以认为土中附加应力沿深度均匀分布即a=1且aZ=p=120kN/2m最终沉降量s=a-aZ-H/(1+0)=3.0X10X120X10/(1+1.0)=0.18m=18m固结系数为：=k(1+0)/(a・Y)=0.018X(1+1.0)/(3.0X10-4X10)=12m2/a单面排水时：时间因数=•t/H2=12X1/102=0.12VVTOC\o"1-5"\h\z由a=1和=0.12查图可得： =0.4Vt则加荷1年的沉降量为：S=•S=0.4X18=7.2m(l分)双面排水时：时间因数=•t/(H/2)2tt VV=12X1/(10/2)2=0.48由a=1和=0.48查图可得： =0.75Vt则加荷1年的沉降量为：St=t・S=0.75X18=13.5m⑵求沉降量达14.41所需的时间：固结度为：t=St/S=14.4/18=0.8由a=1和=0.8查图可得：=0.57tV单面排水时：t=・史/=0.57X102/12=4.75年VV双面排水时：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土压力强度分布图为：(2)=蚊45°+中/2)=3=Xq=3X15=45kPa:X(yh+q)=3X(19X5+15)=330kPa=(+)/2Xh=(45+330)/2X5=93.5k/m土压力强度分布图为：.答：⑴依题意：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饱和重度Y=(W+Y・V)/V=(162+1X48)/108=1.94g/cm3干重度Y=W/V=16