Soil Mechanics Fifth Edition Salutions Manual Soil Mechanics Fifth Edition Solutions Manual R.F. Craig Department of Civil Engineering University of Dundee, UIC SPRINGER-SCIENCE+BUSINESS MEDIA. B.V. First edition 1992 © 1992 R.F. Craig Originally published by Chapman & Hall in I992 Typeset in 10/12 pt Times by Pure Tech Corporation, India ISBN 978-0-412-47230-5 ISBN 978-1-4899-3772-8 (eBook) DOI 10.1007/978-1-4899-3772-8 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the UK Copyright Designs and Patents Act, 1988, this publication may not be reproduced, stored, or transmitted, in any form or by any means, without the prior permission in writing of the pub lishers, or in the case of reprographic reproduction only in accordance with the terms of the licences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms of licences issued by the appropriate Re production Rights Organization outside the UK. Enquiries concerning repro duction outside the terms stated here should be sent to the publishers at the London address printed on this page. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication data available Contents 1 Basic Characteristics of Soils 1 2 Seepage 7 3 Effective Stress 15 4 Shear Strength 23 5 Stresses and Displacements 29 6 Lateral Earth Pressure 35 7 Consolidation Theory 49 8 Bearing Capacity 59 9 Stability of Slopes 71 Author's note In order not to short-circuit the learning process it is vital that the reader should attempt the problems before referring to the solutions in this manual. Basic Characteristics of 1 Soils 1.1 British system Soil E consists of 98% coarse material (31% gravel size; 67% sand size) and 2% fines. It is classified as SW: well-graded gravelly SAND or, in greater detail, weil graded slightly silty very gravelly SAND. Soil F consists of 63% coarse material (2% gravel size; 61% sand size) and 37% non-plastic fines (i.e. between 35% and 65% fines), therefore the soil is classified as MS: sandy SILT. Soil G consists of 73% fine material (i.e. between 65% and I 00% fines) and 27% sand size. The liquid Iimit is 32 and the plasticity index is 8 (i.e. 32-24), plotting marginally below the A-line in the ML zone on the plasticity chart. Thus the classification is ML: SILT (M-SOIL) of low plasticity. (The plasticity chart is given in Fig. 1.6.) BSSieves ~E:1 CCE:\\J1i 0~E: 1 CEE\J (cEE'D) ~EE ~EE 00 v V V 90 / / 80 H '/ I 70 I 60 I I 50 G F E 40 V 30 t. ... Y 20 V V [/ 10 V 0 !--"' CLAY FINE MEDSIIULTM COARSE FINE MESDAINUDM I COARSE FINE MGERDAIUVMEL COARSE COBBLES 0.001 0.01 0.1 10 100 Particle size (mm) Fig Ql.l ~-2--~~ ~~ ___________s _o_I_L_M_E_c__a_ru_m_ c_ s_:_S_O_LU_T_I_O_N_S__M_A_N_U A_ L_ ________~ Soil H consists of 99% fine material (58% clay size; 47% silt size). The liquid limit is 78 and the plasticity index is 4 7 (i.e. 78-31), plotting above the A-line in the CV zone on the plasticity chart. Thus the classification is CV: CLAY of very high plasticity. Unified system Soil Eis classified as SW, a well-graded gravelly sand. More than 50% of the soil is of sand size and the fine-grained fraction is less than 5%. The following values are obtained from the particle size distribution curve: D =0.16mm; D o=0.53mm; D = 1.40mm 10 3 60 c = 1.40 = 8.8 (equation 1.1) u 0.16 Cz = 0.532 = 1.25 (equation 1.2) 1.40x0.16 i.e.Cu>6 and l<Cz<3 Soil F is classified as SM, a silty sand. The coarse-grained fraction is 63% and the fine-grained fraction 37%. Virtually all the coarse-grained fraction is of sand size. The fine-grained fraction is non-plastic. Soil G is classified as ML, an inorganic silt with slight plasticity. The coarse-grained fraction is 27% and the fine-grained fraction 73% (60% silt size; 13% clay size). The liquid Iimit is 32 and the plasticity index is 8 (i.e. 32-24), plotting marginally below the A-line in the ML zone on the plasticity chart (Fig. 1.7). Soil H is classified as CH, an inorganic clay of high plasticity. Virtually all the soil is fine-grained, 58% being of clay size and 41% of silt size. The liquid Iimit is 78 and the plasticity index is 4 7 (i.e. 78-31 ), plotting above the A-line in the CH zone on the plasticity chart (Fig. 1.7.) 1.2 From equation 1.17: I+ e =G5(l + w) Ppw = 2.70x 1.095 X 1l.O.9O1 = 1.55 :. e = 0.55 Using equation 1.13: S = wGs = 0.095 X 2.70 = 0.466 (46.6%) r e 0.55 Using equation 1.19: Psat = TGs+ +e e Pw = 31..2555 X 1.00 = 2.10 Mg/m1 I ~------------B_A_s_Ic_ _c_ H_A_R_A_ c_ T_ER_I_s_TI_c_s_o__r _s_ o_IL_s_ ___________~ l 3 From equation 1.14: w = ~ = 0·55 = 0.204 (20.4%) Gs 2.70 1.3 Equations similar to 1.17 to 1.20 apply in the case of unit weights, thus: Gs 2.72 Yct=1--+Ye w=1. 7-0x9.8= 15.7kN/m-1 Gs+e 3.42 1 Ysar=----.--:teYw= 1.70x9.8= 19.7kN/m- U sing equation 1.21 , Gs-1 1.72 Y = ----.--:te Yw = 1.70 X 9.8 = 9.9 kN/m-1 Using equation 1.18a with Sr=0.75: Gs + Sre 3.245 y= 1 +e Yw= 1.70 x9.8= 18.7kN/m-1 Using equation 1.13: w=Sre =0.75x0.70=0.193 (19.3%) Gs 2.72 1.4 i Volume of specimen = x 382 x 76 = 86 200 mm3 Bulk denst.t y: (p) = Mass = 168.0 = 1. 95 Mg I m1 Volume 86 200x w--1 Water content: (w) = 168·0- 130·5 = 0.287 (28.7%) 130.5 From equation 1.17: PPw 1.00 I+ e = Gs(1 + w) = 2.73 X 1.287 X 1.95 = 1.80 :. e = 0.80 Using equation l.l3: S = wGs = 0.287x 2.73 =0.98 (98%) r e 0.80 ___________ ~-4--~1 ~~ s_o_a_ _M _E_ c ___~_ c _s_:_s_o__Lu_n_ o_ N_S_ M _A_N_U_ A _L_ ________ ~ 1.5 Using equation 1.24: p 2.I5 3 Pd=--=-= 1.92Mg/m I+w 1.12 From equation l.I7: pPw 1.00 I+ e = G.(I + w) = 2.65 x 1.12x 2.I5 = 1.38 :. e = 0.38 Using equation 1.13: S = wG. = 0.I2 x 2.65 = 0.837 (83.7%) r e 0.38 Using equation 1.15: A = e-wG. = 0.38-0.318 = 0.045 (4.5%) I+ e 1.38 The zero air voids dry density is given by equation 1.25: ~ 2ß ' Pd= I+ wG. =I+ (0.135 x 2.65) x l.OO= 1.95 Mg/rn· i.e. a dry density of 2.00 Mg/m3 would not be possible. 1.6 Mass p w Pd Pdo Pd, Pdw (g) (Mg/m3) (Mg/m3) (Mg/m3) <Mg/m3> (Mg/m3) 2010 2.010 0.128 1.782 1.990 1.890 1.791 2092 2.092 0.145 1.827 1.925 1.829 1.733 2114 2.114 0.156 1.829 1.884 1.790 1.696 2100 2.100 0.168 1.798 1.843 1.751 1.658 2055 2.055 0.192 1.724 1.765 1.676 1.588 In each case the bulk density ( p) is equal to the mass of compacted soil divided by the volume of the mould. The corresponding value of dry density (Pd) is obtained from equation 1.24. The dry density/water content curve is plotted, from which: Wopt = I5% and Pdm., = 1.83 Mg/m3 Equation 1.26, with A equal, in turn, to 0, 0.05 and 0.10, is used to calculate values of dry density ( Pdo• Pd,, Pd respectivel~ for use in plotting the air 10 content curves. The experimental values of w have been used in these calcu lations; however, any series of w values within the relevant range could be used. By inspection, the value of air content at maximum dry density is 3.5%.