Question

Consider the following concrete retaining wall: 1.5ft La = 12° Sand: y = 115pcf 16ft d' = 32° c'=0 d' = (2/3) Concrete: y = 150pcf TAVI- N 3ft 5ft '1.5ft 6.5ft y = 120pcf ' = 22°C' = 200psf Clay Use Rankine active earth pressure with: cosa - Ka = cosa- cosa + cosa - cos2 cos2a - cos20 a. Calculate Rankine active and passive lateral forces and show their location onthe diagram. b. Calculate the factor of safety against overturning include active and passive forces). Present your calculations in a table format. c. Calculate maximum and minimum bearing pressures and sketch the pressure distribution at the bottom of the wall. d. Calculate factor of safety against sliding. Assume c, = (2/3)c' and 8' = (2/3) e. Calculate the Coulomb active lateral force and show its location (redraw the above sketch to avoid clutter). Make sure you calculate and clearly show the angle of the Coulomb force. Assume K Coulomb = 0.488.

Answer 1

part Send Har 115 pcf a 2 C-o 5st 11565st Clayes 120 pcf ; qf=22°; c= poopsf BC = H Ja 12 1 ton lao = H' 6.5 fosil H = 1:3816f H = (3+.16 +1.3816) = 20.381694 @ Rankine earth lateral forces (i) active force (pa) - da kariye üni) paste force (Pp) Kyrie

TAM ka - (050.00 sd - J costa - caste cosa + J costa-cose 0 =B1 = 39" = cos(13) Cos(11) - 1 (03160) - cos (39) cas(19) +cosciale cose 293 = cos(ia) x0.4907 11465 = 0.3973 3) Kp = cosec. cosa + J costa - Costa I cosoc - Josfa- cosso = (0842) Cosus) +5 ooskus)-co$139) Coola) - J 10$) - cogies) = costq) x 15465. 004907 = 4.92;

I achive force (fa) - to xx, x H²xka = x115x(20:3816.) 0397 3 7810.74 pounds (ft 9 pessive force (pp) = 5x115 x [ 201381989192 = 69747.27 lb lift ; -Po & Pp some point acts but different mognite des.... - Postosa H = 20:3816 = 6.793 ~ 6-793ft. ar) متاح) Pa = 7810.74 lblist Po=69747.27 eblift -6.793.44 6.793 ft teo=12° sections & 0 ③ are ve 224 kN/m3 0 Y = 1151 - 24x 6493 pes I = 154.159 pelo

! Section Pe=154,159 PCF 8591 2115 pcffor 059 Area(A) W=rxai al fom me = wl se) (ebist) lol point (1h-ft) 4705 7392.92 9x5 3:33; 94383 Vc 154.13 pof 9815 4393.332 5+1,5 - 5,75; 95961.66 61.75 9518.886 $9598.74 5+1:57625 .=8667; 61675 7101.45 5+15+2x6:5 76906-53 = 10.83;. 13816 4.49 516:35 54548x545 5599.07 - 10-83 6.5 EV'= 98859-038 lble Emo = 314672

Eva Ev' + Pa Sind sackve Evp = Ev' + P p sind + Passive a=120 na pe cosa tra coso G = 6-793 vertical components of active con pcessive earth forces are added ; # EX= 18859.038 + 781074 Sin (12") = 30475.98 lblft ; I 2 E Vp = 28852.038 + sin (19°) 69747.97 =.43353.37 Ibisto + Overtlerning momento o Horizontal load ca ases it; (i) (mola = (Pa Cosa) j = Pelosa ý. = 7810.74 43 42 ) x6-793 = 51898.9 lb-ft (M) Q = 51898.9 laft

cii) (m.) p = pp cosa xý = 69747-47 COSL12) X6-793 = 463439.6368 lb-ft-; Active case (Fs) overturning = EMR (mola - 914672 51898.9 = 4.13 > Q ; safe possive case 7 () overtuering = Emr. Mop =214672 46343906868 = 0.463 22; unsese!

Posive - Resultant force B-1360 K B=13ft Imer = PEP (1+) 9 min = (-60) | ă= {MR-(Molp Evp = 914679 -463439668 43353.31 =-5.738 m; A e = 1 - 2 - Emmet Ellola = {MR - (Mola Elva) 214679-51898.9 30475.98 a = 5:34ft e = B- - - 5:34 a l'16 m), : +19 45738 g. =12978 =0762 m;

Imea o amin is for active case only fearable: B = 13 ft 2 mex, min = het in dit ) = 30475.98 + 6x1.16 13U 19 = 9344.306 + 1855-105 Imed = 3600 lb ist? the arly taken) → Emin = 1089.201 lb/ft ~ 1090 e blet? ke 116ift: 360 | 11 tog og bly

d a chove (Fs) Sliding = (Eve) tanes) + CQB+pé Pa cosa Øg = Bottom Soil 3300 =190; 8 - = 48 499 = 14.67% Cal = R x C = X 200 = 133:33 p4 B = 1345 )=367 Ppl= A 2 kpx YaxD* + 2 cajke ke - ltsinde - Itsing 2. = 8.197 - singa T-sing2 JHp = 42:197 = 1.4823 app = $x 2-197x 120 x(3)? + 2x200 7:197 = 1779.18 Ablft TPP = 1779 18 Iblst I (ES) Sliding = 30475198 tan 14.67)+

possive conditions: sliding = 30475.98 ten [14:67) +13X13933+ 1379:18 7810.74 (8512 = 115 315 Sale for passive conditions CEE) sliding - Evp tan s'+8 ce + Pin - Pp (Oslo = 43353.3) Jan 11467) + 13x133193+ 1774. ME 69747.97 (OSL120) = 0.9178 < 105 constfe