The University of Iowa Dept. of Civil & Environmental Engineering 53:030 SOIL MECHANICS Midterm Exam #2, Fall Semester 2005

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1 5:00 Sil Mehanis Midterm Exam # Fall 005 Semester The Uniersity f Iwa Dept. f Ciil & Enirnmental Engineering 5:00 SOIL MECHANICS Midterm Exam #, Fall Semester 005 Questin #: (0 pints) A sand with a minimum id rati f 0.45 and a maximum id rati f 0.97 has a relatie density D r 40 %. The aerage speifi graity f the minerals in the sil is.68, and w 9.8 kn m - a. Cmpute dry and sat fr the sand in its present state with D r 40%. b. Under ibratry lading, the sand is densified t D r 75%. Hw muh will a m thik stratum f this sand settle under this densifiatin? Questin #: (40 pints) Figure a shws a hmgeneus, saturated sandy sil depsit with a hrizntal grund surfae. Befre the strip lad is applied, the stresses at pint A are as fllws: ertial stress 00 kpa; hrizntal stress h 75kPa; pre water pressure p w 50kPa. a. Cmpute the maximum shear stress at pint A befre the surfae pressure is applied. b. Using the infrmatin prided in Figure, estimate (mpute) the maximum shear stress at pint A after the unifrm strip lad is applied.. Estimate (mpute) the intensity f the strip surfae pressure q required t ause shear failure in the sil at pint A. Assume that the sand features a drained behair, suh that any exess pre pressures due t the applied lad are dissipated quikly. d. What are the rientatins f the failure planes at pint A when shear failure is reahed by inreasing the surfae pressure? 0 m A saturated sand sat 0kN m - 0; φº q4kpa 5m Fig. a. Fig. b. /

2 5:00 Sil Mehanis Midterm Exam # Fall 005 Semester Questin #: (40 pints) A wastewater treatment aeratin tank f diameter 40m and grss weight 86.5 MN is t be nstruted n the site shwn belw in Figure a. T nstrut the tank, 6m f the tp dense sand layer will be exaated, and the tank will be built as shwn in Figure b. Fr the alues prided in Figure : a. Cmpute the inreased aerage ertial stress in the silty lay layer diretly beneath the enter f the tank. b. Calulate the ultimate nslidatin settlements that will ur at the enter f the tank due t mpressin f the silty lay layer.. Hw lng will it take fr 90% f this nslidatin settlement t ur? (Use ne dimensinal nslidatin thery t answer this questin.) The nndimensinal time nstant fr 90% nslidatin is T dense sand, d 9kN m - 0m nrmally nslidated lay; C s 0.05; C 0.45; e sat 0kN m - ; m yr - dense sand 0m 5m Nte: The ertial stress inrease diretly beneath the enter f a irular, unifrmly laded area is gien by the fllwing relatin in whih q is the magnitude f the unifrm lad; R is the radius f the irular area; and z is the depth f interest beneath the laded area: Δ q / ( ) z + [ ] Figure. Bnus Questin (0 pints!!) Explain in detail hw ne an g abut estimating the permeability f a fine-grained sil frm a -dimensinal nslidatin test. /

3 5:00 Sil Mehanis Exam Slutin Fall 005 Slutin f 5:00 Sil Mehanis Midterm Exam #, Fall Semester, 005. Questin #: (0 pints) a) 0 pints emax e Dr 00% * e emax Dr * ( emax emin ) e e max min Fr D r 0.40, e *(.97.45) d Gs w + e.7 *9.8kN m kN m sat w ( G + e) 9.8kN m *( ) s + e kN m b) 0 pints Fr D r 0.75, e *(.97.45) The resulting settlement f the m thik sand layer is: Δ H H + e m Δe * ( ) 0.m Questin #: (40 pints) a) 0 pints ' ' 00kPa 50kPa 50kPa ' h ' 75kPa 50kPa 5kPa The resulting effetie stress Mhr s Cirle has a enter at ( 50 5) kPa r ' '. 5 τ r.5kpa., and a radius f ( ) kpa max b) 0 pints Frm the hart, at the pint 5m diretly beneath the enter f the strip lad, the inrease f majr prinipal stress is: Δ 0.8 * q while the minr prinipal stress inrease is: Δ 0.8* q. Sine the sil behair is said t be fully drained, these hanges in stress are due t hanges in effetie stress rather than hanges in the pre water pressure. Thus: /4

4 5:00 Sil Mehanis Exam Slutin Fall 005 ' ' 50kPa + 0.8* q 69.68kPa ' ' 5kPa + 0.8* q 9.kPa τ max ) 0 pints h r ( ' ') ( ) kpa 0.8kPa At shear failure, the effetie stress Mhr s Cirle is tangent t the failure enelpe. Ardingly, the peratie relatinship between the majr and minr effetie prinipal stresses is: (realling that the hesin anishes) φ ( 45 + ) ' tan ( 6 ).5 ' ' ' tan Nting that ' 50kPa 0.8 * q and that ' 5kPa 0.8* q it fllws that + '.5 ' 50kPa + 0.8* q.5* * ( 5kPa q) + Sling fr q gies: q kpa d) 0 pints ' 59kPa A ' 48.9kPa 90+φ Orientatin f the planes n whih shear failure urs at A: φ θ ± 45 + ± 6 wrt the hrizntal φ φ P θ θ 90+φ Questin # (40 pints) a) 4 pints Just beneath the tank, the riginal ertial stress was 6m*9kN/m 4kPa. /4

5 5:00 Sil Mehanis Exam Slutin Fall 005 After the tank is built and filled, the ertial stress at the same leel is q W 86.5MN 8kPa A π ( 0m) The net bearing stress, is the final stress just beneath the tank minus the riginal ertial stress at this leel. The net bearing stress gies rise t stress inreases in the sft lay layer beneath. S, q q 6m( ) 8 4 4kPa. net d sand At the tp f the lay layer, z 4m. The ertial stress inrease due t the tank: ( ) [( ) ] Δ qnet * 4kPa*. kpa tp / / 0 z + [( 4 ) + ] At the middle, z9m. ( ) [( ) ] Δ qnet * 4kPa * 06. kpa mid / / z + 0 [( ) ] 9 + And at the bttm, z4m. ( ) [( ) ] Δ qnet * 4kPa * 9. 5kPa bt / / z + 0 [( ) ] 4 + Taking the weighted aerage f these stress inreases ( Δ ) + 4( Δ ) + ( Δ ) tp mid bt.+ 4(06.) ( Δ ) ae kPa b) pints Sine the sil is nrmally nslidated, ( ) ' f ( ) ' H H S Δ lg e C + e + e At the enter f the lay layer, ' 0m d + 5m b 0 *9 + 5* (0 9.8) 4 ( ) ( ) ( ) kpa sand lay ( ) ' ( ) ' + ( Δ ) 4kPa + 05kPa kpa f f 46 ae S: 0m 46 S *0.45lg 0. 6m ) pints /4

6 5:00 Sil Mehanis Exam Slutin Fall 005. T t.848 * 0.848* ( H ) 0.848* ( 5m) 90 dr 90 0 t90 ( H ) m yr dr Bnus Questin (0 pints) Hw t measure the permeability frm the -D nslidatin test? This an be dne fllwing the same predure used in pressing f the Lab 9 experimental data:.yr ) Frm the displaement ersus time ure, nte the time t 50 required fr 50% nslidatin t ur. ) Using the knwn drainage distane, estimate the effiient f nslidatin er the interal as: 0.96( H dr ) t ) Frm nslidatin thery, 50 k( + e ), s re-arranging gies an expressin fr the wa sil permeability k. The sil mpressibility effiient a er the interal needs t be estimated as a Δe / Δ '. 4/4