Ko-OCR Relationships of Soil

Prévia do material em texto

K,-/OCR RELATIONSHIPS IN SOIL 
By Paul W. Mayne," A. M. ASCE and Fred H. Kulhawy,) M. ASCE 
Assmacr: The relationships between K, and OCR are investigated for pri- 
mary loading-unloadinp-reloading conditions. The study reviews laboratory 
data from over 170 different soils and presents an approach common to clays, 
silts and sands. Simple empirical methods for predicting K, for norimally con- 
solidated and overconsolidated soils are evaluated. The validity of the methods 
is supported by statistical analyses. On the basis of the findings, only the 
effective stress friction angle (4) and prior stress history (OCR. and OCR 4.) 
are nceded to predict approximate values of K,. 
INntTRODUCTION 
The prediction of the in-situ state of stress in soil is of major importance in 
a wide variety of peotechnical problems. Numerous investigators have addressed 
this problem and have achieved varying degrees of success. Although a sub- 
stantial data base has been developed, it is still not possible to predict exactly 
the in-situ state of stress in most natural soil deposits because they have under- 
gone a complex stress history of loading and unloading which is difficult to 
reconstruct preciscly. 
The geostatic vertical stress can be estimated from a profile of effective ov- 
erburden stress with depth. The in-situ horizontal stress, however, is highly de- 
pendent on the geologic history of the soil. It is common to represent the ratio 
of horizontal to vertical effective stress by the at-rest cocfficient: 
Kd aerea ea (1) 
' 
v 
Consider the simplified stress history depicted in Fig. 1 for a homogencous 
soil deposit with horizontal ground surface. Stréss path OA represents virgin 
loading of the soil deposit, associated with sedimentation and normally-consol- 
idated conditions. As represented by Fig. 1, the at-rest cocficient remains con- 
stant during virgin compression (K,,c). Any reduction-jn the effective pyesburden 
stress results in overconsolidation of the soil, represented by path ABC. Mech- 
anisms causing an overconsolidated effect include erosion, excavation, rise of 
'Geotechnical Enpr., Law Engrg. Testing Co., Washington, D.C. 22101. 
*Prof., School of Civ. and Environmental Engrg., Comell Univ., Ithaca, N.Y. 14853. 
Note. -—Discussion open until November |, 1982. To extend the closing date one month, 
a wrilten request must be filed with the Manager of Technical and Professional Publi- 
cations, ASCE. Manuscript was submitted for review for possible publication on April 
21, 1981. This paper is part of the Joumal of the Geotechnical Engincering Division, 
Proceedings of the American Society of Civi! Engincers, OASCE, Vol. 102, No. GT6, 
June, 1982. ISSN 0093-6405/82/0006-0851/$01.00, 
ça act
32 JUNE 1382 STE 
 
 
 
tm ceisadina 
arg inasing 
 
a
 
FG 1 —Sinegilfiad Strass History 0! Soil under X, Conditons 
fe govadwxer table, removal of surcharge lnads, etc. Loring unioading, the 
avrerconsnfadatioa ratio o R = T, has a pronounced effect on the value 
SK, 3 Ioadm z is respplied after simple rebound, the reload relationship sub- 
sequentiy will follow 3 parh similar to CD in Fig. 1. Subsequent unigading and 
reioadirz, fox example by seasonal water table fluctuations, 13 likely to cause 
siress paths to occur within the Ioop ABCDA 
To evaluate the behavior of horizontal stresses during vertical load-unicad- 
reload conditicas, available laboratory K, data were collected from various 
sousces published in the geotechnical Isterature. This study includes data com- 
piled from over 170 different soils tested and reported by many researchers. 
Tables | and 2 contain a somenary of the virgin ioad-unigad data for cohesive 
and cohestonless soils, respectively, with relevant index properties. 
The soils includeá in this study come from a wide variety of sources. Many 
factors exist which coulá not be evaluated quantitatively, including: (1) K, test 
method: (2) different equipment and research personnel, (3; sampling disturbance 
effects; (4) time and aging effects, (5) inherent lateral anisotropy, etc., and (6) 
errors and differences associated with other relevant soil properties (6', D,, etc). 
The problems associated with laboratory K, testing have been considered in 
(Refs. 5, 6, 16, 33, 66, 75, and 76). Difficulties in field measurements of K, 
ae described by others (37,44,45,72,73,77). 
The objective of this study is to delineate the behavior of K, during simple 
loading -unioading-reloading, corresponding to the virgin compression of nor- 
malhy -consolidated soils, subsequent rebound or swzlling associated with over- 
consolidated soils, and recompression under conditions of no lateral yield. A 
“> wealth of data has been accumalated for simple load-unload conditions. Only 
“atew soils reported in the literature also have been tested under reload conditions. 
Normaily-Consolidated Soil. —Several theoretical and empirical relationships 
for K,. have been postulated for normally-consolidated clays and sands (6, 
12,14,24,37,63) Probably the simplest and most widely known is the approx- 
imation to the theoretical formula by Jáky (28) for primary loading: 
 
Kat losin6o iii A (2) 
im which 6 = the effective stress friction angle. Fig. 2 shows that this rela- 
tionship is reasonable for the cohesive soils in Table 1. A best fit line (assumed 
imercemt b = 1 comstmicted herween K and <im ds indicat
ed
GTS K OCR RELATIONSHIPS 853 
KeS OBTIDO Cissa (3) 
having a sample correlation coetficient r = 0.854, In other words, 4” accounts 
for 73% (or 1) of the variability observed in Rome Values of normally-consolidated 
clays. Nes x VR 
A similar statistical analysis conducted on As, for cohesionless soils (Fig. 2) 
determined 
Ko = | — 0.998 sin &' 
in which r = 0.625. The data of Sherif, etal. (62) and Al-Hussaini and Townsend 
(5) were weighted so as not to bias the statistical trend toward one or more 
researchers who contributed large amounts of data. These two sets of data cach 
accounted for only 5% of the summation totals (Lx, Lx”, etc.) used in calculating 
linear regressions, although together they comprise approximately 75% of the 
total data base for sands listed in Table 2. 
A review of all available data for both clays and sands (total of 121 points) 
indicated the following best fit line from linear regression analysis (r = 0.802): 
Km = 1 10035ind! e (5) 
Numerous investigators have suggested that K,,. may correlate with liquid 
limit, plasticity index, clay fraction, uniformity coefficient, void ratio, or other 
“index properties of the soil. The data collected during this study did not confirm 
any of these relationships. However, the Jáky formula (Eq. 2) was supported 
by these data. 
Horizontal Stress During Unloading;—Overconsolidation because of re- 
bound results in higher values of K, than the Kome values obtaincd during virgin 
compression. One of the ““classic references"" for an observed K,,-OCR rela- 
tionship was presented by Brooker and Ireland (12), although their conclusions 
are based on the data of only five soils. Another empirical approach was proposed 
by Sherif and Koçh (63). Dayal, et al. (18) recommended a method of curve 
fitting Ko, data, requiring two soil parameters. Wroth (77) derived relationships 
for lightly to hcavily overconsolidated soils. Mitachi and Kitago (47) present an 
analysis which requires determination of the isotropic and one-dimensional an- 
isotropic swelling indices. Pender (54) developed a critical-state model of over- 
consolidated soil which predicts K,, during swelling. 
Alternatively, the variation of K,, with OCR may be expressed simply as a 
function of the effective stress friction angle, &”, as hypothesized by Schmidt 
(61) and Prúska (58). This approach has a distinct advantage since only one soil 
parameter is required for predicting both normally-consolidated and overconsoli- 
dated values of K,, as well as defining soil strength.The simplest relationship 
proposed is that given by Schmidt (61) for K,, during primary unloading: 
E a (6) 
enc vd ; | . nom th) ouvia [is VISA Lyreld 
in which «a = an exponent defined as the at-rest rebound Parameter of the soil. 
This approach has subsequently been used by others (7,21,37,41,45,56,60, 
66,72). The compiled K,,-OCR data are presented in Figs. 3 and 4 for the soils
B5A PIE PESE 
e» 
TABLE 1 —-Smecary sf K, Duta for 
 
 
 
 
 
re a 
; = 
Rigtos- | f 
eat | o Car Es 
mater | Pias comtert. EA 
com | Lado . fcitr 33 5 pm fr 
teme, | Gerir |indes, cetaça for 
E 0,8 7.2 ess as ]e 
açer | ape. 4 08 far o. 
Hum- | cet | come | cemt 
tur ce 
ber Soil name | ago | ago | aço mirors 
| qe 
1) (2) GO | (4 
GS | FE F 
j Spestone Kaolin po — | nn 
| — 24 
2 | Sydney Kaolin |- ls pis | — 57 
3 Hydeune 10 Kaotinite — 62 | 
za * 175 
(floc.) | 
! 
4 | Hydrite 10 Kaolinite — | 64 | B | 
% 69 
(disp.) | | 
S | Hydrite PX Kaolinite LS jp — | — 
— 14 9 
6 | Austsalian Kaolia | | — | 35 ) s no 
(7 | Australian Kaolin 2 — 1. 5% 32 | 
“ mM 
3 KEaolin | — | — — 
— DB 2 
9 | Spestone Kaolin | — | 76 37 
cà 207 
10 | Kaolin | — | | — a 59 
1 | Kaolin — | s| Bm “ 723 
12 | London Clay 2 | Ss | 65 s2 
29 
13 | London Clay | — ss 2 Ea I7.s 
14 London Clay — | — (4 
— — 
15 | Weald Clay — Lo 4a | Ho :5 
| 229 
16 | Weald Clay — 46 24 3 | 255 
17º | Weald Clay — — — — | 262 
18 Weald Clay — — 
== — | — 
19 Bearpaw Shale — 101 7a 
sa Is. 
20 Bearpaw Shale — 82 a so 
21.0 
21 Drammen Clay — — px 
cm — 
2 Drammen Clay 1 52 5 31 — 
317 
23 Drammen Clay 2 32 33 Ui] — 300 
24 | Drammen Clay 41 5s 27 — 207 
25 New York Varved Clay — 65/35 | 39/12 — ms 
26 | Hackensack Valley Varved | 49 | 65/40 | 35/25 — 19.0 
Clay 
27 | Connecticut Valley Varved — — 23 — 
— 
Clay 
28 | South African Clay — — — e 227 
29 | Seattle Clay — s2 26 — 22 8 
3% | Seattle Clay 2-1 27 47 18 s3 — 
31 Seattle Clay 3 23 38 Io -— — 
” Hokkaido Clay 1 — 52 21 — 2 
3 Hokkaido Clay 2 — 52 21 — 3s0 
3 | Hokkaido Clay 3 —— n W — 351 
3 Nebraska Clay | a 
no 4 o o 
GT6 de ci K, OCR RELATIONSHIPS 
tam ar rm, 
Clays durina(Virgin Load-Unioad 5 
 
 
 
Earth Sampls 
pressure correla- 
Maxi- coeffi- Rebound tion 
mum cient, exponent, cosffi- 
OCR K sua a cient, r Fleference 
(8) (3) (10) (11) (12) 
2.6 0.64 0.66 0.994 Parry and Madarajabs (51) 
8.0 0.48 0.47 0.9N Poulos (56) 
17.5 0.75 0.30 0.926 Abdelhamid and Krizek (5) 
17.5 0.69 0.25 0.975 Abdelhamid and Krizek (E) 
15.4 0.65 0.19 0.990 Edil and Dhowian (19) 
— 0.56 — — Moore and Cole (42) 
— 0.44 — — Moore and Cole (42) 
5.z 0.54 0.38 0.591 Parry and Wroth (52) 
4.0 0.66 : 0,29 0.929 Sketchley and Bransby (TO) 
7.8 0.69 0.28 0.994 Burland (14) 
49.0 0.51] 0.30 0.998 Singh (66) 
44.0 0.65 0.46 0.959 Skempton (69) 
32.0 0.66 “0.37 0.999 Brooker and Ireland (52) 
— — 0.46 0.960 Som (71) 
32.0 0.54 0.49 0.995 Brooker and Ireland (12) 
7.8 0.60 0.39 0.996 Henkel and Soma (25) 
2.6 0.52 0.33 0.992 Skempton and Soma (69) 
2.5 0.63 040 0.995 Parry and Amerzasinghe 
(5h) 
32.0 0.10 0.27 0.995 Brooker and Ireland (12) 
35.7 0.55 041 0.992 Singh (57) 
—- 0.50 — -— Prevost (57) 
camas 0.49 =. -— Besre and Bjerruen (8) 
e 049 - e Berro and Bjesrum (2) 
50.0 949 045 0.993 Brown (13) 
29.9 0.67 0.34 9.993 Leathers and Lada (41) 
41 0.65 0.36 — Sazena (14)) 
15.9 0.67 040 Lis Garens (60) 
em 048 039 0.946 | Knight and Bligia (37) 
84 (1.55 9.3 09% Serif amd Serazes (64 
46 0961 043 9.906 Sheril und Koch (63) 
14,7 0.52 045 97 Sheçil ad Pr 163) 
157 045 953 0.915 Muschi sud Eiago (47; 
83 043 44 0% Mitachi nad Kisgo (47) 
19,3 9.41 8.52% 9.981 Muschi amd Kisago (47) 
a 44 ama Chemaechnical Engrs (21) 
Aimee o ia sa cm 
0.59 
sem seara serias e cdr ger
 
B56 JUNE 1982 GT6 
TABLE 1. 
(1) (2) (3) (4) (5) (6) (7) 
36 | Nebraska Clay 2 o 61 
37 | Nebraska Clay 3 H7 
38 | Nebraska Clay 4 102 
39 | Portsmouth Clay 50 35 15 32.0 
40 | Beaumont Clay 26 61 41 24.0 
41 Boston Blue Clay 41 21 26.8 
42 Boston Blue Y 15 30 26,5 
43 | Chicago Clay 26 10 36 26.3 
44 | Goose Lake Flour 32 16 31 27.5 
45 | Albuquerque Clay-Sand 25 H 18 30.5 
46 | Backebol Clay 95 90 60 30.0 
47 | Bombay Clay -— 15 70 48 24.0 
48 | Portogruaro Silt 28 36 13 27 = 
49 | Ponto Talle Clay 2 44 21 20 e— 
50 | Tarquinia Silty Clay 28 43 24 39 - 
51 Tarquinia Clay 22 58 44 55 - 
52 | Catania Clay 3 78 54 15 
53 Pisa Clay 24 57 36 44 - 
54 | Chiani Clay 61 92 62 70 
55 Parana Clay 32 55 33 69 
56 Triesta Clay 47 70 48 32 
57 Leda Clay -— 24 - 
58 | Khor-Al-Zubair Clay 42 55 35 am 27.3 
59 Fao Clay — 39 20 — 36.9 
60 Jarva Krop Clay, 58 50 22 —- 
61 Ska-Edeby Clay 70 55 30 — 
62 Ursvik Clay 55 45 25 — 
63 | Kalix Clay 120 160 105 - 
64 Norwegian Clay 37 26 8 -— 10.0 
65 Saint-Alban Clay 65 45 22 60 27.0 
66 Moose River Muskeg 390 -— mão — 47.7 
67 Middleton Peat 510 — — — S7,4 
68 | Portage Peat 600 — —— — 53.8 
69 | Fon du Lac Peat 240 — -— — 50.2 
70 | Kyoto Clay — 88 57 52 32.5 
7 | Lagunillas Clay — 61 3 30 26.8 
72 | Simple Clay -— — — — 23.1 
73 | New England Marine Clay —- — 20 —— 32.0 
74 | Haney Clay — —- = = 30.0 
75 | Loess â1 35 1 18 31.5 
76 | Konnerud Clay 52 61 29 -— =— 
77 | Sundlund Clay 58 52 23 — a 
78 | Sterling Till 6 E) 3 — - 
79 | Gault Clay — 85 55 68 - 
BO | Massachusetts Clay -— -— 23 = 32.7 
81 Newficld Clay — H 13 2 286 
 
GT6 —- K5OCR RELATIONSHIPS 
 
 
 
 
 
Continued as Hr, 4 A
 5 pa TS 
(8) ipod go jo ud qo 2
) 
— 0.78 it; 0,33 lj [é hoo) | Geotechnic
al, Engrs. ani as Hz 
cce ph 0.78 | d 0.35 HI ditado |
! Geotechnical Engrs! (21) 5º 
fem 0.80 (| 1 0.47 A po im vô e Geotechnical En
grs: E | 
80, 047 4]; 0,46 | “0.998 | Simon, etal. (65) “ + 
Fi. 
5.0 0.55 “| 1 0.36 1 | 0.932 Mahar and 
Ingram (43) Ep 
- BO 0.54 “| 4 040 4 0.997 Kinner and La
dd (30) 4; 44 
320 048 4] 1 045 | 0.999 | Ladd (35) 
32.0 0.46 41: 0,53 4 0.994 Brooker a
nd Ireland (12) 
32.0 0.50 049 + » 0.994 Broo
ker and Ireland (12) 
8.0 0.56 0.37, 0.990 Calhou
n and Triandafilidis 
: (15) 
— 0.49 —— — Massa
rsch and Broms (44) 
24.4 0.63 0.39 0.994 Kulka
rni (33) 
64.0 0.41 0.39 0.980 Be
llotti, et al. (7) 
64.0 0.53 0.41 : 0.990 
Bellotti, et al. (7) 
64.0 0.58 0.43 - 0,985 
Bellotti, et al. (7) 
64.0 0.65 0.49 0.985 
Bellotti, et al. (7) 
64.0 0.70 0.43 0.990 
Bellotti, et al. (7) 
64.0 0.44 0.58 0.995 
Bellotti, et al. (7) 
64.0 0.62 0.46 0.920 
Bellotti, et al. (7) 
64.0 0.65 0.49 0.995 
Bellotti, et al. (7) 
64.0 0.55 0,52 
0.995 Bellotti, et al. (7). 
= md 0.38 0.950 Kelly (29) 
5.0 0.49 0.40 0.994. 
Hanzawa (22) 
— 0.44 — —
 Hanzawa (23) 
ada, 0.41 im — Mass
arsch, et al. (45) 
— 0.52 — — 
Massarsch, et al. (45) 
sa 0.47 — — Massar
sch, et al. (45) 
E 0.52 — — Mass
arsch, et al. (45) 
— 0.75 — — 
Bjerrum (10) 
8.9 0.70 0.47 
1.000 Tavenas, et al. (73) 
13.6 0.30 0.22 
- 0.901" Adams (2) 
B.0 0.31 0.18 - 
0.998 Edil and Dhowian (19) 
16.0 0.30 0.09 0.
998. Edil and Dhowian (19) 
8.0 0.53 0.18 0
.998 Edil and Dhowian (19) 
Ls 0.45 — — Akai and Adachi (3) 
Ls 0.53 — O — 
Lambe (38,40) 
24.0 0.61 0.32 
0.997 Ladd (34) 
16.0 0.50 0.41 
0.995 Ladd (36) 
16.3 0.55 0.41 0.998 
Campanella and Vaid (16) 
6.3 0.36 0.54 0.983, 
Huergo (27) 
1.5 0.49 0.51 — Bjerr
um and Andersen (11) 
A) 0.49 0.59 — Bjerrum an
d Andersen (11) 
24.4 0.41 0.46 0.995 Murphy,
 et al. (49) 
4.0 0.75 0.27 0.989 Thompson (74) 
mm 0.48 0.45 — Ladd (39) 
20.0 0.50 0.28 0.996 Singh (66) 
 
JUNE 1982 GT6 
TABLE 2. Summary of K, Data for 
 
 
 
 
Ini- Relative | Do | Unifor- | Effective 
tial density, in mity friction 
void | D, asa | milli- | coeffi- angle, 
Num- ratio, | percent- | me- cient, din 
ber Soil name e age ters C, degrees 
1) (2) (3) (4) (5) (6) (7) 
8 Decomposed Granite — — — — — 
8 Brasted Sand — 40 — — aim 
Es Medium Sand — 16 — — — 
Es Minnesota Sand 0.62 34 — — 36.9 
86 | Reid-Bedford Sand 0.59 100 0.24 I.5 34.0 
&7Reid-Bedford Sand 0.68 72 0.24 1.5 32.6 
ES Reid-Bedford Sand 0.82 25 0.24 1.5 28.5 
ES Monterey No. 20 Sand | 055 93 — -— 40.0 
90 Monterey No. 20 Sand | 0.73 32 o — — 
gi Eastern Silca Sand 0.52 93 — — 36.5 
2 Eastern Silca Sand 0.68 33 — — — 
23 | Ripley Send 0.67 — = — a 
4 Glass Bzllotni 0.56 100 01 — 36.5 
95 Filter Sand 0.52 — 0.82 1.8 492 
96 Filter Sand 0.61 — 0.82 1.8 45.2 
s7 Filter Sand 0.80 — 0.82 1.8 35.8 
S& Russian Sand — — — — — 
99 | Crechoslovakian Sand — — — — — 
100 | German Sand — — — — — 
101 | German Standard Sand | 0.67 — LO LO 35.0 
I02 | Kilyos Sand 0.64 47 0.15 1.25 28.0 
103 Ayvalik Sand 0.63 86 0.59 1.3 36.5 
104 Awvalik Sand 0.75 47 0.59 1.3 33.5 
105 | Avvalik Sand 0.80 33 0.59 1.3 29.5 
106 | Falgu Sandy Gravel 1 0.72 88 1.9 1.5 36.5 
107 Falg= Sandy Gravel 1 0.91 4 3.6 1.4 33.0 
108 Falgu Sandy Gravel UI 0.68 87 6.0 I.s 41.0 
108 Sangamon Sand — — — — 37.6 
10 | Sangamon Sand — — — — 32.5 
m Sangamon Sand — — — — — 
112 Wabash Sand — — — — 38.6 
113 | Wabash Sand no — — — 34.6 
114 Wabash Sand — — — — — 
115 | Chatahoochee Sand — — — -— 40.5 
116 | Chatahoochee Sand — — — — 37.2 
117 || Chataboochee Sand — — — — 33.5 
118 | Chzahoochee Sand — — — — 323 
IS | Brasted Sand — — — -— 39.0 
im | Brasted Sand — — — — n9 
121 | Sand — — = == 38.2 
In | Sand — — — — 37.0 
123 | Sasd — — — — 35.4 
IM | Sand — — — — 32.9 
125 | Beigrem Sand — — a am 433 
GT6 
 
 
 
— K,/OCR RELATIONSHIPS 859 
Sands during Virgin Load-Unload * 
Earth Sample 
pressuro correla- 
Maxi. | - coeffi- Rebound tion 
mum clent, expo- coeffi- 
OCR Kane nent, a cient, r Referenca 
(8) (9) (10) (11) (12) 
19.5 0.41 0.64 0.999 Pells (53) 
74.1 0.43 0.27 0.983 Bishop (9) 
— 0.50 0.50 0,975 Bellotti, et al, (7) 
24.0 0.41 0,40 0.997 Hendron (24) 
5.5 0.42 0.53 0.999 Al-Hussaini and Townsend (4,5) 
— 0.45 — — Al-Hussaini and Townsend (4,5) 
5.2 0.56 0,33 0.995 Al-Hussaini and Townsend (4,5) 
32.0 0.35 0,55 0.998 Wright (76) ' 
32.0 0.40 0.46 0.998 ' | Wright (76) 
16.0 0.38 0.50 0.996 Wright (76) 
16.0 0.42 0.41 0.986 Wright (76 
9.8 0.47 0.51 0.997 Menzies, ct al. (46) 
62.5 0.38 0.26 0.997 Andrawes and El-Sohby (6) 
7.9 0.36 0.70 0.996 Weiler and Kulhawy (75) 
38.1 0.39 0,52 0.998 Weiler and Kulhawy (75) 
11.2 0.44 0.48 0.998 Weiler and Kulhawy (75) 
6.0 0.40 0.47 0.979 Ejodorov and Malychev (20) 
11.3 0,41 0.49 0.995 Plelm (55) 
4.7 0.39 0,71 0.998 Mach (42) 
42.9 0.53 0,44 0.983 Kjellman (31) 
— 0.52 0.39 — Saplamer (59) 
18.7 0.42 0.43 0.999 Saglamer (59) 
18.9 0.47 0.45 -— Saglamer (59) 
18.9 0.51 0.40 0.925 Saglamer (59) 
3.7 0.39 0.72 0.999 Dayal, ct al. (18) 
4.6 0,37 0.69 0.997 Dayal, et al. (1B) 
6.3 0,25 0.78 0.999 Dayal, etal. (18) 
e. 0.40 Ga me Al-Hussaini and Townsend (5) 
-— 0.44 — — Al-Hussaini and Townsend (5) 
— — 0.43 0.990 Holden (26) 
— 0.39 — — Al-Hussaini and Townsend (5) 
— 0.42 — — Al-Hussaini and Townsend (5) 
— —— 0.41 0.980 Holden (26) 
amem 0.44 pre — Al-Hussaini and Townsend (5) 
u- 0.44 —— me Al-Hussaini and Townsend (5) 
ne 0.49 — =—— Al-Hussaini and Townsend (5) 
ue 0.49 ps mms Al-Hussaini and Townsend (5) 
ra 0.36 — -— Al-Hussaini and Townsend (5) 
em 0.46 — — Al-Hussaini and Townsend (5) 
-— 037 me = Al-Hussaini and Townsend (5) 
e 0.42 e -— Al-Hussaini and Townsend (5) 
ee 0 48 mimo m- Al-Hussaini and Townsend (5) 
vma 0.54 ans em Al-Hussaini and Townsend (5) 
a 0,40 o Ab-Hussaini and Townsend (5)
bi cr 4 seg 
 
 
 
— -— — — — —-— — — -— e il Rail Dil 
JUNE 1982 TT Tr 
TABLE 2 — 
(2) (3) (4) (5) (6) (7) 
Relgium Sand — — — — 40.2 
Belgium Sand — — -— — 35.3 
Retgium Sand — — — = 342 
Minnesota Sand — — — = 37.5 
Minmexota Sand uma cem — — 28.0 
Pennsylvania Sand am — — — 35.8 
Pensavivania Sand — — — — 31.0 
Penniyvania Sand uma — — -— — 
Úawma Sand Ss? 73 04 21 42.7 
Quana Sand vos 42 04 241 34.4 
Mtawa Sand Qs 4 0.42 21 28.0 
Oriawa Sand ——. — — — — 
Atawa Sand 20-30 0ss — 0.75 1.2 34 6 
Útawa Sand 20-30 Us? — 0Is 12 332 
Ouawna Sand D0-%0 os —— 075 12 0.4 
Del Monte Sand Us so DIS 241 40.9 
Del Monte Sand RES 41 Dis 2» 34.3 
Del Monte Sand ui) t DIS 21 26.2 
Mitture Sand 0so sa 04 3º 40.6 
Axture Sara 0ss e 0a 39 30 
Minture Sand 0s9 SA RER 2º 3.1 
Mivivre Sand “mn 7 04 29 257 
Highway £20 Sand to &o 0 19 454 
Highway SD0 Sand VIR os 0a 19 0 8 
Haghuay SM Sand os 7 om 19 30.0 
Golden Ganteos Sand 0.os 7? eso 18 4.s 
Golden Gardeos Sand Q.7s So eso L& 37.8 
Golden Gardens Sand oi 2? os Ls ERR 
Seward Prá Sand 05 “2 O Só 19 478 
Sewand Park Sand RR 78 0 86 19 443 
Seward Pri Sand os 28 O So 1º 3º 
Savers Pu Saod 0e 7 do 28 as a 
Savers Pu Sumé e? s4 2 o 23 as” 
Savers Pu Sand 07 I8 0. 22 3 7 
Museus Besch Sand os é! 0% 1º 447 
| Masdews Bench Sand Q se 4 O 39 38) 
| Madews Beach Sand Qm s 2 19 Na 
AM: Beach Sand “e | 8 0 14 48 
| Als Beach Sand an S2 0 14 3 
Adã: Besch Samé om 2 om 14 22 
Pes Ed Sund eo | o 0 sa 24 Va 
à Prer B% Sand os | 62 Qua 24 33 
| Pres 8% Sand 0% | À 04 | 24 wo 
| Ram Rrver Sand en) o — 0as - o 
| Ras River Sand es | meme as - no 
Fig Som -L-|-|[- 10
Continued 
 
 
 
 
(8) (9) (10) (11) (12) 
— 0.40 — — Al-Hussaini and Townsend (5) 
— 0.50 — — Al-Hussaini and Townsend (5) 
— 0.50 — — Al-Hussaini and Townsend (5) 
— 0.33 — — Al-Hussaini and Townsend (5) 
— 0.38 — — Al-Hussaini and Townsend (5) 
— 0.40 — — Al-Hussaini and Townsend (5) 
— 0.51 — — Al-Hussaini and Townsend (5) 
— — 0.42 0.980 Holden (26) 
30.0 0.49 0.69 0.990 Shenf, et al. (62) 
30.0 0.38 0.62 0.981 Shenf, et al. (62) 
30.0 0.58 0.53 0.979 Shenf, et al. (62) 
— — 0.51 0.990 Holden (26) 
— 0.41 — — Edil and Dhowian (19) 
— 0.44 — — Edil and Dhowian (19) 
— 0.50 — — Edil and Dhowian (19) 
30.0 0.32 0.78 0.997 - | Shenif, et al. (62) 
30.0 0.36 0.76 0.998 Sherif, et al. (62) 
30.0 0.38 0.62 0.994 Sherif, et al, (62) 
30.0 0.35 0.78 0.999 Sherif, et al. (62) 
30.0 0.37 0.73 0.996 Shenf, et al. (62) 
30.0 0.41 0.69 0.997 Sherif, et al. (62) 
30.0 0.42 0.66 0.996 Sherif, et al. (62) 
30.0 0.31 0.75 0.998 Sherif, et al. (62) 
30.0 0.33 0.72 0.999 Sherif, et al. (62) 
30.0 0:36 0.62 0.996 Sherif, et al. (62) 
30.0 0.32 0.84 0.997 Shenif, et al. (62) 
30.0 0.38 0.82 0.999 Shenf, et al. (62) 
30.0 0.38 - 0.73 0.997 Shenf, et al. (62) 
30.0 0.37 0.71 0.988 Shenf, et al. (62) 
30.0 0.40 0.67 0.995 Shenf, et al. (62) 
30.0 0.43 0.50 0.989 Shenf, et al. (62) 
30.0 0.36 0.64 0.990 Shenif, et al. (62) 
30.0 0.37 0.54 0.96] Shenf, et al. (62) 
30.0 0.37 0.54 0.986 Sherif, et al. (62) 
30.0 0.35 0.74 0.997 Shenf, et al. (62) 
30.0 0.37 0.73 0.999 Shenif, et al. (62) 
30.0 0.38 0.68 - 0.999 Shenf, et al. (62) 
30.0 0.33 0.69 0.993 | Sherif, etal. (62) | 
30.0 0.38 0.57 0.986 Shenif, et al. (62) 
30.0 0.35 — — Shenif, et al. (62) 
30.0 0.34 0.81 0.999 Shenf, et al. (62) 
30.0 0.37 0.83 0.999 Shenif, et al. (62) 
30.0 0.38 0.60 0.995 Shenif, et al. (62) 
3.5 0.53 0.19 0.996 Daramola (17) 
5.9 0.39 0.58 0.988 Daramola (17) 
— — 0.34 0.970 Holden (26) 
 
 
 
WWW <<< ===" 
Ube JUNE Iutd 
úla 
 
 
 
 
 
1a v ' 1 * ' ' 4 , 
ta ent nhanbatt Mai 
a mit 
. Matta 
mM e Gina Quim 
“ 
ue 
“ 
. 
ma 4 
a“ 
Nes 
tabenioa Rel N, 
ua . x 
a a uu N 
“em 
+ AMmbncos Untliva Brum 
vu N 
N 
o > ' , + , 1 ' ' 1 N 
“ “a aa ue ne e 
a é 
FIG. 2. Observed Relationship between A, and sin p' for Cohaslve and Cohe
slonians 
Solls 
extrapolated using dashed lines. Then, by definition 
log (Au) — TOR (Mano) (7) 
CEO og (OCR) O Vo apuensod log (€ Mo des M 
for a range of values of OCR. The atrest rebound parameter, eo) ds also the slope 
of the relationship between log (A) and lop (OCR) The mean values of a in 
Tables 1 and 2 have been determined from linear regression analyses for the 
solls considered, generally for values of OCR «15, The sample correlation 
coefficients, r, are seen to be quite high, indicating thate appenes to be constant 
with OCR. 
Tavenas (72) has suggested that, as areasonable upper limit; as | This 
seems intultivgly correct since It cannot be expected to pet more energy out of 
a soil than |s put into it, Considering both clays and sands/a has a mean value 
of 0,509 with a standard deviation of 0.134, vd 
Several investigators have suggested that the parameter a Is related to the index 
properties of the soil, However, only vague trends were observed between a und 
plasticity index, clay fraction, liquid limit, or activity, 
Schmidt (61) proposed that the parametena is uniquely related to the effective 
stress Íriction angle, 4”, of the soil, This approach appears to be substantiated 
by the general trend between a and sin 4", as shown in Fig. 5. The hypothesis 
taken is that 
a sind (8) | Eve ar red Ciro de tired a 
which places theoretical upper and lower bounds on the YA) an) pa ameter 
such that Os as 1 A statistical study of the data in Tables | and 2 revealed 
Urat 
a» 0018 + 0974 sind, (82 points) 
= 099 -08872A (9a) (107 points) (9h)
 
 
GT6 K, OCR RELATIONSHIPS 
eo v T i T 
NOTE: Numerols refer to cohssive 4 ': 
soils listed in Toble |. to . ç. 
o 
10H 1 A 
a E 
o o 
| 
sr a 
” 
Elo 
D| E 
8/8 
| o 
a2|2 
E SA a x x 
I 4 4 
OCR 
 
 
 
co) T T T 
NOTE: Numerals refers to cohesioniess 
soils listed In Table 2. 
A IoH l J 
o 
e a Ss e e ale s A É o| o 
- 
Xi : 
s 
n 
elo 
v| c 
o 
S/c 
O 
Sl= à | 
—|.o 
eix 
bd 
| 1 1 1 
' 2 5 10 co 
OCR 
FIG. 4. —Trend between K, and OCR for Cohesionless Solis during Unloading 
which have sample correlation coefficients bf 0.671 and 0.720, respectively. 
Since Egs. 8 and 9a are approximately equal, the data suggest that K, during 
loading-unloading simply may be related to 4" and OCR by 
K.=(1-sin&b) ocR sb MN
voa JUNE 1987 0 TT] 
ppm 
 
 
 ao. “ + ee eo do me ah ide q os “4 “e. o. o 
ne a 
Fa, 5 —Nelatlonship between At-Hest Rebound Parameter, a, and sin 4' for Clays and 
Sends 
The application of Eg, 10 to four clays is shown in Fig. 6 and to four sands in 
Fig. 7, 
Passive Fallure.—The coefficient of passive earth pressure, K,, may be as- 
sumed to be the upper Jimit on the value of Ku: This defines a limiting value 
of OCR above which atrest conditions do not apply and passive pressure is 
mobilized, For simplicity, a Rankine passive pressure coefficient can be adopted 
such that 
k 1 + sing (1) 
sing otite crer erre tenen care cirscereeenanaaneaios 
When K,, = K, in Eg. 10, the limiting value of OCR for at-rest conditions is 
determined to be as Boo PO 8: 0,437 
 
 
 
 
 
 
Ro mta tes Send Fig Semest E ” 
s- «oo o Sao 
EO Drdá 
) A ca te 
é A 
E A 
+ 
, q 
teia. mes Depei. ot el 10) 
x 4 tqrett Sewé Driges Send 
zoo esmo o 
2.1 a 
nd a s7 
. 27 
d Pd ea 
po” Ar 4 es! e 
Toque TS 1 tm Da 
SS &SL—+T&——sS 
oca oca 
FIG. 6 —Messured and Predicted K, of FIG. 7. —Messured and Predicted K, of 
Four Clays during Loading Uniosding Four Sands during Loading-Unioading
Gts 
OCR. = (em 
Ad mt | sind 
By seconstructing a peological history at Bradwell, 
Siempios (65) deduced 
a likely profile cf K, wi depés for Londom Clay. v
abucs of K, were reported 
o increase vp 19 29 OCR of abeut 25 and tem decrease 
for higher valnes of 
OCR, soggesting passíve failure Usibg as cficctve frict
iom amgle. O = 25, 
for the Eocene clay, 25 determined by Stempios, Es. 12 p
redicis that OCR 
=277. 121,30) 
Horizontal Stress During Reloading —Tne lxie publish
ed data avaiizbic om 
the bekavior cf K, for soils during reloading are given in Tabic 3. Based om te 
trends observed with these 15 sois, as empórical approach ma
y be formulntod. 
Wroth (77) suggested that a linear relationship between o; und 9, may
 de as 
sumed, coresponding to the path CD in Fig 1, such coa 
EAR AR A (Pa PA RD nre
reccereenano (13) 
isasse sanada Aa A MA A
 A 
 
ja which m, = a constant termed the reload coefficiems and 0, andou, refer 
to point Cin Fig. 1. lí a new stress history parameser is defincé 
as 
Then the value of K, during reload, K,. cam be expressed as 
TABLE 3 Summary of X, Data during Reicad 
 
 
 
 
Number Sod name m ! r 
(1) (2) Ro tu 
H" Kacim 043 Eos 
s8 Khor Al-Zubasr os 
2 200 
14 Haney Clay qa! E] 
82 Decomposed Granito 23 
2 ves 
Eó Reid Bedford Sand 
22 | o 
85 Reid-Bedford Sand 043 q 996 
so Monterey Sand 725 
0995 
95 Fiker Sand 02 
2 208 
96 Filter Sand 
en 2 095 
97 Fiter Sand o3s 2 o98 
103 Ayraiik Sand o» | NA 
104 Ayvaiik Sand 2 | 
NUA 
os Ayvalik Sand 242 Ny A 
o = =" ww 
 
gt) JUNE 1982 Gts 
k 4 ( OCR |, f OCR | o cet looais) em 2E) o 00 
The coefficient m, was found 19 be à function of 4"; or alternatively as à 
function of K,.,, às shown in Fig. 3. The small data base suggests that 
| (au in &' (2 K (17) 
m, q sin 6”) 4) ME decvcrsisrocccncio- dd d- cegas 
By including the relationships given previously, one equation can be con- 
structed to represent K, as a function of stress history 
 
OCR 3 OCR | K=(lL-sinos' [e fi e (18 
o =( in) (a) z 1 | z) 
Eq. 18 can be used to determine K, anywhere along the stress paths shown 
in Fig. 1, and to determine the probable bounds of K, in soil with more complex 
5. 
 
sb 
 
 
 
| 
emma Ed 
os 2. “ | 
es 
. . ) 
9 s1 o cs . ” 
 
Foo mag) 
FIG. 8-—Trend between Reload Parameter m, and k.orsin é 
 
 
Ta Somd 
IUeiior qd 
- Eisor, 01H 
- 
8 
r 
< 
( ve SA 
9 a k Da ” 1 
- cc” 
am 0,4 
« TT 4 . A «a ” 
x A A te £ > = cas 
Mm dá 1 taty 
* . To ua 
* “ . Te rumutag 
:4 A eis 10 miss 
ss .-as 1» matas 
A 4 4 A 
s - o Naa = rss
GT6 Ko OCR RELATIONSHIPS 807 
 
 
 
“ r e put pt 
Kou / 
"” A. as fo) 
/ elas 
/ tol 7º 
/ 
A 
T) MM 
Pá Reid. Dedisid Son 
UML Munsalal nd dá M Tentond, toi Sa) 
” 
.” Cree Dema 
2 Ma quim") 
04 eras 
. 1 rs 
. , A] 
o a , nos 
0 tem Aa AA 
' , 19 20 
oca 
FIG. 10.—Obsorvod K,-OCN Rolatlonship of Rold-Bodford Sand (5) for Thros Lond-Un- 
load Cyclos 
unload-reload historics. The approach requires thaton)y the stress history (OCR 
and OCR) and 4! for a particular soil be known, For normally-consolidated 
soils, OCR,,, = OCR = 1 and Eq. 18 reduces to Eg. 2. For overconsolidated 
soils during, swelling or rebounding, OCR, = OCR, and Eq. 1B is identical 
to Eq. 10. An application of Eq. 18 is shown in Fip. 9. 
For natural soils, the current value of OCR may be determined from conven- 
tional consolidation tests or other methods. Al present, however, there appears 
to be no known technique of determining OCR for a specific soil deposit other 
than a good knowledge of local peolopy and stress history of the soil deposit. 
Additional Constderntions—Some interpretation of available data by the 
writers was necessary to compile information as complete as possible. Generally, 
the soil data included in this study reflect soil parameters as reported by the 
respective authors. The effective stress friction angles cited are lincar approxi- 
mations to the failure envelopes over specific stress ranges, The actual failure 
envelopes are best represented by curved surfaces. In this study, no distinction 
has been made between 4” values determined from triaxial, direct shear, or sim- 
ple shcar devices. 
One major problem in comparing the data is a consistent definition of effective 
stress friction angle, The most common alternative definitions used by the peo- 
technical community include: (1) Maximum deviator stress; and (2) maximum 
principal effective stress ratio. Which definition is most appropriate in the study 
of K, still remains to be established, In addition, further rescarch is necded to 
establish K, behavior with regard to cyclic loading, rheological effects, residual 
soil deposits, gravels, and compacted fills. 
Little is known about the effects of load-unload cycles on the value of K,. The 
consequences of applying large numbers of cyclic loads on K, remains to be 
investigated, For only a few cycles of load-unload, Eq. 10 still appears tobe 
valid, as shown by Fig. 10. Within the applied stress ranges, different values 
of 0,4 had no appreciable effect on the K,,-OCR relationship. 
ConcLusions 
i i : Ietarmes mnbto So Ju jane Re reviescine laboratoer data Fera use PIO AEE s
— — — — — dd -— 
868 JUNE 1982 GT6 
that K, behavior during virgin compression, rebound, and reload can be repre- 
sented approximately by simple empirical relationships. Statistical analyses are 
used to support the validity of the methods considered, The conclusions of this 
study are as follow: 
1. The approximate theoretical relationship for K,, Of normally consolidated 
soils introduced by Jáky (28) appears valid for cohesive soils and moderately 
valid for cohesionless soils. 
2. The vanation of K,, with OCR during unloading is approximately depen- 
dent on the effective stress friction angle of the material, b', as suggested by 
Schmidt (61). 
3. Horizontal stresses during reload may be estimated from a knowledge of 
4" and the stress history (OCR and OCR). 
4. The preceding relationships for K, may be represented entirely by Eq. 18. 
ACKNOWLEDGMENTS 
The writers extend appreciation to Donna L. Reese, James P. Stewart, Anne 
V. Bethoun, and W. R. Sawbridge for their aid in completing this study. 
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o o o or o -— o — — e ae e = o om 
K. OCA RELATIONSHIPS Es 
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ta ' 5 ms
 
“q
 MI
 
ta
 
É 
q = t D
R
)
 
ç ' ne a ' ' + 
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q? 
DPG ME mam e - -—- 
Vest qnd Disto 
Tr