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OEVELOPMENTS IN GEOTECHNICAL ENGINEERING 4 7
THEORETICAL FOUNDATION ENGINEERING
BRAJA M . DAS, Ph.D.
Department of Civil Engineering & Mechanics, Southern Illinois University of Carbondale, Carbonda/e, IL, U.S.A.
ELSEVIER Amsterdam- Oxford- New York- Tokyo 1987
CONT ENTS
Prefacc
CHAPTER l LATERAL EARTH PRESSURE 1.1
1.2
1.3
1.4
Introduction At - Res~ Earth Pressurc
At - Res~ Force and Resultnnt Rankine ~ctlve Prcssurc (~otation about
Bottom of llall)
1 . 5 Activc Pressure 1dth ll'al l Friction--
Coulomb ' s Actlve Pressure lhcory 1 . 6 Graphical Solut lons for Coulomh ' s Active
Force
1.7 Graphical Procedure for Coulomh's Active
Fo rc e for a c - <b So i l Had.fi Il 1 . 8 Activc Earth Pressure for BacLfiJl hith
Ver~ical Drain
1 . 9 Ka11 Rotation ~equircd for ~ctive Earth
Pressure Condition 1 . 10 Active Force on Kall hith Rotntion ahout
Top
1.10 . 1 Dubrova ' s So lu tion
1.10 . 2 Terz:.~ghi's Genera! licuge Theory
1 . 10 . 3 Empirica] Prcssure Diagrams for
Des i gn or Braccd Cuts
1.11 Active Earth Pressure for l.atet·at Translation of llall
1 . 12 ~ankine Passive Pressurc (~otation ahout the Bottom of thc 1\"all)
IX
di
l
l
3
ì
13
23
29
33
35
38
40
43
49
50
Su
1. 1 3 l'a s :; 1 \ ' l' l' r c~ s u1· c '' i t h Il n l l l r i<.: t i o n (Coul omb ' s l'ass i\'c Pr cssurc)
1.1 ·1 l'a ssiu.' l' n .•ssu r c by Using Cu r vcù lailurc
Su rfacc 1 . 15 Othcr So lutions fo 1· l'assi\·c 1'1 cs s urc
( Ro tat ion about the Bottom)
l . 1h lluiHO\U' S ~letho d f o r C:Jlculati o n or
Passive Prc-ssure Distribution
1.17 Expcrimenta l Results for Passive Pressurc 1 . 18 11' ;~1 1 Rotation Required for Pass i1·e Earth
Pressure Condition
1 . 19 St abilit y or Slurry Trcnch Cuts in
Saturated Cl ay
1 . 20 Stabil ity or Unsupportcù Axlsymmetric
rxcavati ons in Saturated Clay 1 . 21 Latcr::~l Earth Prcssurc on Linings or
Circular Sharts in Sand
1 . 22 Latera! Earth Pressure on Linings or
Circular Sharts in Saturated Clay Re re 1·e nccs
CHAPTER 2 SHEET PILE WALLS 2 . L
2 . 2 2 . 3
2 . 4
2 . 5
2 . 6
2 . 7
2 . 8
lntroùuction
1ypcs of Shce t Pile Wa ll s Anchors in Shect Pile ~all Design
Construction Ncthods ror Shcct Pile ~a1ls Latera! Carth Prcssurc -- Gcnc r al Consiùerations
Canti l evc-r Shcet Pile Kalls Pcnctrating into Sand
Cantllevcr Shce t Pile Kalls Pene trating into Clay Laye r
Anchorcù Shcct Pile Wa l l Penetra ting into Sand--Free Ea rth Support Ncthod
2 . 9 Latera] Eorth P1·essure Due to Strip Loaù Neo r u Woll
2 . 10 Rowe ' s Nomcnt Reduction Ncthod 2 .11 Anchorcd Shcc t Pile Wall with Sl opi ng
Drcdge Linc
2 . 12 Computat i o nDlPressurc Diag r am Ncthod
b3
ò5
"()
78
80
81
84
86
96 100
103
103 104
108 109
111
114
126
131
133
135
140
141
2 . 13 Anc ho r ed Shcc t Pile lla l l Pcnct r u t ing
in t o Cl oy - -Frec Earth Support ~l e t hod
2 . 1~ I ixcd Ear t h Suppor t ~c t hoù for ~nchored
Shec t Pile Ka ll s
2 .1 5 Oth e r Observat ions on ~nc hored Shcct
Pile Kall Desi gn
Rcrere nc e s
CHAPTER 3 HOLDING CAPACITY OF ANCHOR SLABS AND HELICAL ANCHORS 3 .l
- ? ..) , _
3 . 3
3 . 4
3.5
3 . 6
lntroduction Ultimate Hold ing Ca pacity of Shallow
Yertical Anchor Slabs in Sand
3 . 2 . 1 Te ng ' s Procedu re fo r Sha llOh
.\ncho rs 3 . 2 . 2 Ovesen and Stromann's Procedure
[or Shallow Anchors
3 . 2 . 3 Analysis or Shallow Anchors by Bi arez , Boucraut , and Negre
3 . 2 . 4 Ne ycrhor•s Thcory
3 . 2 . 5 Nceley , Stuart , anù Graham's
~lethod
3 . 2 . 6 Load-Displacmcnt Relationship fo r Shal l ow Yertical Anchors in Sand
3 . 2 . 7 Deep Yertical Anchors in Sand
3 . 2 . 8 Soil Friction Anglc for Estimation of the Ultimate Anchor Capacity
Yertical Anchor Slabs in Clay
Uplift Capaclt y of Horlzontal Anchors
in Sand
Upl ift Capacity of Horizontal Group Anchors
Uplift Capaclty of llorizontal Gr oup Anchors in Clay
3 . 7 Upl ift Capacity or llelica1 Anchors Rcrcrenccs
CHAPTER 4 ULT IMATE BEAR ING CAPACITY OF SHALLOW FOUNDATIONS
Xl
146
150
1 56
158
160
160
160
162
164
1 70 171
1 72
174
177
1 79
180
183
192
194
200 205
206
XII
4 . 1
.t. Z
4 . 3
4 . 4
4 . 5 4 . ()
4 . 7
4 . 8
4 . 9
4 . 10
4.11
4 .12
lntrou uction
Types of Bearing Capaci t y ~ai1ure
Tc r=aghi ' s Beari ng Ca pa ci t y Theory
Some Obscrvations on 1crzoghi's Bea r ing
Capacity Theory
Neyerhof ' s Bearing Ca pacity Theor y
Ge ne rai Bearing Capaci t y Equa t ion Ot her So luti ons for Bearing Cnpoc ity
Factors
Effec t of Water Tabl e Beari ng Capaci t y of Fountlations on
Anisotropie So il Extending to a Great
Depth Ultimate Bearing Capacity Due to Vertica l
Ecccntric Load Foundations Supported by a Soi l with a Rigid Rough Base at a Limited Depth Bearing Capaci t y o( Foundations on S1opes
4 . 13 Bearing Capacity of Foundations on Layered Sol l
4 . 14 Co ntinuous Foundation on Weak C1ay with
a Granular Trench 4 . 15 Sha1low Foundation Above Voids
4 . 16 Interfe r ence o( Shallow Con tinuous
Foundation in Granular Soi l 4.17 Fo undati on Se ttlement
Re(erences
CHAPTER 5 SLOPE STABILITY 5 .1
5 . 2
5 . 3
5 . 4
5 . 5
5 . 6
5 . 7
Introduc tion
Factor of Safe t y--Defi ni tion
Stability of Finite Slopes (c- ~ Soil)- Plane Failurc Surface
Stability of Clay S1opes (~=O Condition )
Clay Slopes with Aniostropic Strength Prope rties (~=O Condition) S t ability of Slopes in Cl ay (~=O
Condition) with e u lncreasing with Depth Stability of Finite Slopes with c- ~
So ils --Nass Proced ure
20()
:!06 210
224
241 248
249
260
277
283
286
317 322
325
330
339
342
342
34 4
346
350
356
361
365
5. 8
5 . 9
5. 10
5 . j' . l
5 . 7 . z l<~ylor's l i·iction l' irclc \lelhtHI
Cousins' St;Jhility \nalysis
(u - t C.,oil)
,\lethod of Sl ices
5 . 8 . 1
5 . 8 . 2
5 . 8 . 3
5 . 8 . 4
5 . 8 . 5
Ordinary Ncthou of Sl iccs Bi shop ' s Simplificd Nc thou of
Slices Bishop anu ~lorgcnstc rn ' s ~lethod
of Sl ices Norgcnstern's Nethou of Slices
[or Rapicl llrD\\UOI"n Cond iti on Spenccr's Ncthocl of Sli ces
Limit Analysis So lut ions fo r Sl opes
Es timation or Ditch Safcty by Us i ng a
Cycloiclal Fa ilurc Surface
5 . 10 . 1 Ca l culat i on of thc Side Sl opes for Ditch wlth Dceper Cu t s
Rcfercnces
APPENDIX A THE POLE METHOD FOR FINDING STRESSES FROM MOHR ' S CIRCLE
APPENDIX B PROPERTI ES OF LOGARI THMIC SP IRALS AND LOGARITHr.IC SPIRAL SECTORS
APPENDIX C HELICAL ANCHORS
INDEX
XIII
385
380
390
39 1
398 399
413
416
422
4 :!4
426
429
434
436
424
(5 . 129) .
Example 5 .11. Referto Examp1e 5 .10 . Other quantitics rcmaining
the samc , if H= 3 m detcrmine Sc r ·
Solution .
So
e
(1-sin<P) ] 2tan 2 (45+~/2 )
cos-1 [ 1- (3)(17.5) 1-sin12° J 16 2tan 2 (45+1 2/2)
cos -1 l1_ (3. 281) (O. 792) ] 3.05 cos- 1 (0 . 148) = 81.49°
However
ec 90 - $ = 90-12 = 68°
So , 6>6c . Now , 6=81.49°=6" . Substituting •=12° and 6 "=81.49° in Eq . (5 . 130) gives
e = tan-1 f (3)(17 . 5) x c r l 16
co,l2 (1- ,inll) ) 2 (1+ s i n 12 ) [ (1; 0 81. 49) -·s in81. 4 9-TT/ L+ ( 1 ~ 0 1 2) +cos12 ° J]
References Bishop, A.W., 1955 . The use of the s1ip circ1e i n the stabi1ity
ana1ysis of s1opes . Geotechnique , 5(1):7-17. Bis hop, A.W . and Morgenstern , N.R ., 1960. St~bi1ity coefficient of
earth s 1opes. Geotechnique , 10(4):129- 150 . Casagrande , A. and Carri11o , N. 1944 . Shear fai1ure of anisotropie
soi1s . J. Boston Soc. Civ. Eng . Contr i bution to Soi1 Mechanics 1941 - 1953.
Chen, W. F., 1970. Discussion . J . Soi1 Mech. Found. Div ., ASCE , 96(SM1):3 24 -326 .
Chen, W.F. and Giger , M. W., 197 1. Limit ana1ysis of stab ili ty of s1opes . J . Soi1 Mech. Found. Div ., ASCE , 97(SM1 ): 19-26 .
Chen, W. F., Giger , M.W ., and Fang , H.Y., 1969. On thc 1imit analys i s of stabi1ity of s 1opes. So il s and Foundations , 9(4):23-32 .
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Cousins , B.F., 1978 . Stabi1ity chart s for simp1e carth slopes . J . Geotech. Eng. Div. , ASCE , 104(GT2) :267-279 .
Cu1mann, K., 1866. Die graphische s tat ik . Meyer and Ze l1er,
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ana1ysis of 1imit design. Q. App1 . Nath. 10:157-165. Ellis , Il . B. , 1973. Use of cyc1oida1 arcs for estima t ing ditch
safety. J . Soi1 ~lech . Found . Div ., ASCE , 99(S~12):1o5-179.
125
Fc11enius , W. , 1927. Erdstatische berechnungen. W. Ernst U. Sohn , Berlin.
Koppu1a, S.O ., 1984 . On stabi1ity of s1opes on c1ays with 1inea r1 y increasing s trength. Canadian Geotech. J. , 21(3):577-581 .
Lo , K. Y. , 1965 . Stabi1ity of s1opes in anisotropie soi1s . J . Soi1 Mech . Found . Div ., ASCE , 91(SM4):85-106.
Morgenstern , N., 1963 . Stabi1ity charts for earth s 1opes during rapid drawdown . Geotechn ique , 13 (2) :1 21- 131.
O' Connor, M.J. and Mitche11 , R. J. , 1977 . An ex t ension of the Bishop and Morgenstern s 1ope stabi1ity c ha rt s . Canadian Geotech. J., 14 (1): 144- 151.
Singh , A. , 1970 . Shear s treng th and stabi1ity of manmade s1opes . J . Soi1 Mech . Found. Div. , ASCE , 96(St-16):1879-1892.
Spcncer , E., 1969. Ci r cu1ar and 1ogarithmic spira1 s1ip surfaces . J. Soi1 Mech. Found. Div. , ASCE , 95(SM1):227-234 .
Spencer, E., 1967 . A method of ana1ysis of the stabi1ity of embankments assuming para11e1 inter-s1ice forces. Geotechnique , 17(1):11-26.
Tay1or , D. W. , 1937 . St abi1i t y of earth s1opes. J . Boston Soc . Civ. Eng ., 24:197-246 .
Terzaghi , K., and Peck , R.B., 1967 . Soi1 mechanics in engineering practice, 2nd ed. John Wi1ey and Sons, New York.
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