Reinforcement Bond Capacity: Jewell, R. A. (1990) - Gcotechnique 40, No. 3,51Q8
Reinforcement Bond Capacity: Jewell, R. A. (1990) - Gcotechnique 40, No. 3,51Q8
Reinforcement Bond Capacity: Jewell, R. A. (1990) - Gcotechnique 40, No. 3,51Q8
3,51%518
TECHNICAL NOTE
R. A. JEWELL*
KEYWORDS: bearing capacity; geotextile; reinforced research confirms this analysis of bond capacity
soil; sands; soil-structure interaction; stress analysis. to be a powerful and practical tool. The research
also indicates two improvements to the theory
which are described below. Palmeira & Milligan
INTRODUCTION (1989) proposed a more significant modification
In their recent paper, Palmeira & Milligan (1989) to the theory based on a new empirical corre-
presented a set of high quality test data on lation. Unfortunately their proposal appears not
pullout tests which show clearly how inapprop- to be fundamental and, as shown below, to lead
riate boundary conditions in pullout tests can to errors in certain cases.
lead directly to unrealistically high values of
pullout resistance (bond capacity) for reinforce-
ment. Their data also cast valuable new light on EXISTING THEORY FOR REINFORCEMENT
the influence of bearing member shape and soil BOND
particle size. The analysis derived by Jewel1 et al. (1984) can
While it is possible to achieve satisfactory be summarized briefly as follows. It is assumed
boundary conditions for pullout testing in a that there are two independent sources of bond
research laboratory-including a stress- capacity
controlled upper boundary, a smooth lubricated
front boundary, adequate sample size and depth (1) skin friction, tan 6, mobilized between the
of burial in the soil-it is unlikely that such con- soil and the plan area of plane reinforcement
ditions will be achieved in more routine labor- surfaces
atory testing, or in field testing. (2) bearing stress o</cr”’ mobilized by soil bearing
Two separate sources, or mechanisms, for on reinforcement bearing surfaces.
reinforcement bond capacity in soil can be identi- It is further assumed that
fied as skin friction and bearing stress. Perhaps it
is fortunate that pullout testing can be avoided (a) the two mechanisms above are independent
for reinforcement materials that depend only on and additive
skin friction for bond capacity, such as the major- (b) an upper limit, or cut-off to the bond capacity
ity of geotextiles, and plane strips. For these for an area of reinforcement is that for a fully
materials simpler modified direct shear tests are rough sheet, tan 6 = tan 4, covering the same
adequate to measure the shearing resistance at plan area.
the soil to reinforcement surface contact. Unfor- A general expression for bond capacity may be
tunately, however, the simpler test does not apply derived in terms of the reinforcement dimensions
where bearing stress is the important bond defined in Fig. 1. The expression for pullout
mechanism, such as for grids, ribbed strips and resistance is
anchored earth reinforcements.
Jewel1 et al. (1984) derived an analysis to P, = 2L, Wran’ fb tan f$ (1)
describe the interaction mechanisms between
wheref, is the bond coefficient, 0,’ is the effective
reinforcement and soil so that the bond capacity
stress in the soil normal to the reinforcement
could be calculated, as an adjunct to pullout
surface, and L, and W, are the length and width
testing, from the fundamental properties of the
of the reinforcement providing bond (i.e. being
reinforcement geometry and the soil angle of fric-
pulled out). The maximum possible pullout resist-
tion. The support and additional insight into the
ance is wheref, = 1.00, the bond coefficient being
interaction mechanisms provided by the new
restricted to the range l@O >fb > 0. The com-
ponent of the pullout resistance due solely to skin
Discussion on this Technical Note closes 4 January friction is
1991; for further details see p. ii.
* University of Oxford. (P,),, = 2a, L, W, 0”’ tan S (2)
513
Géotechnique 1990.40:513-518.
514 JEWELL
Bearing stress
The bearing stress which can be mobilized
against a reinforcement bearing surface is much
more difficult to define. Jewel1 et al. (1984) sug-
gested the following safe or lower estimate for
bearing stress
d=tan(i+t)exp[(t+4)tan$] (6)
0”‘
Géotechnique 1990.40:513-518.
REINFORCEMENT BOND CAPACITY 515
0 *A Present work
V Akinmusuru (1978)
+o Audibert & Nvman (19771
x Dickln & L&g (19i3) ’
0 Dyer (1985)
. Peterson (1980)
0,/o, = e(n’z+@) Ian 0 tan ((n/4) + (9/2)) A Trautmann 8 O’Rourke (1985)
+ Wang & Wu (1980)
1 I 1
20 40 60
9: degrees
Fig. 2. Comparison of measured and predicted bcaring stress, from Fig. 15 of Jewel1 ef ul.
(19ll4) and Fig. 18 of Palmeirn & Milligan (1989)
2.5 . Lelghton Buzzard sand 14/25 If only the bearing stress term in equation (4) is
. q Leighton Buzzard sand 14125 used to define a bond coeffkient due to bearing,
(square section)
then
2 4 A Leighton Buzzard sand 25/52
- Equation (7)
Géotechnique 1990.40:513-518.
516 JEWELL
-- - Possible rounding off Starting from Palmeira & Milligan’s equation (l),
- Theory, equation (10) the existing theory is found to give the following
expression for the degree of interference
DI=l-2
Géotechnique 1990.40:513-518.
REINFORCEMENT BOND CAPACITY 517
friction 4 which is sensitive to small changes in number of bearing members n, and the high-
density or stress level. The mobilized bearing lighted ranges for DI, correspond approximately
stress cri,‘/un’depends critically on 4. with Palmeira & Milligan’s test data (Fig. 5).
The comparison in Fig. 6 suggests that the pro-
posed empiricism is simply a fit to the data for
the grid geometries used in laboratory testing.
Empirical correlation for interference
Numerical investigations then show that the
The results in Fig. 5 show that the existing
empiricism can become erroneous for practical
theory predicts interference well, and suggest that grids with larger numbers of bearing members n,
any error in predicted bond capacity due to
and for more widely spaced bearing members
rounding off (Fig. 4) is small in comparison with
where there is little interference. This is illustrated
other factors, such as the accuracy with which the
as follows : Palmeira & Milligan’s (1989) modified
angle of friction for the soil may be measured.
theory, their equation (3), gives
The existing theory captures the main features of
reinforcement bond capacity in a conceptually
simple and satisfying manner. fbezwing
= (1 - “V(y)(3) & (15)
When viewed in this light, the modification to
the theory with the new empirical correlation for
DI proposed by Palmeira & Milligan (1989) which, following equation (10) can be expressed
appears to be seeking only a marginal improve- as
ment at the expense of the simplicity of the exist- (SlabB)+
ing analytical solution. What is equally significant fbearing = (1 - w (SIa,B) (16)
is that the proposed empiricism is expressed in
terms of a parameter whose value depends on the
number of reinforcement bearing members rr. The The comparison shown in Fig. 7 can now be
parameter is made. The results are for a typical sand
(S/a,B)+ = 20, and the number of grid bearing
members varies from 2 to 50. The DI is taken
directly from the empirical correlation (Fig. 6).
Several features of the modified theory are
For any single value of this parameter, the apparent from Fig. 7. The effect of interference
existing theory indicates that DI depends on both suggested by the modified theory is to reduce sig-
the number of bearing members n (equation (14)) nificantly the pullout resistance of grid reinforce-
and the angle of friction of the soil C$(equations ment below that given by the current theory over
(6) and (9)). This is illustrated in Fig. 6 which most of the practical range (i.e. the modified
compares the value of DI given by the existing theory is more conservative than the existing
theory with Palmeira & Milligan’s empirical theory in this range). However, the modified
correlation. The typical range for sands theory also gives pullout resistances for grids sub-
(S/a,B& = 10-25 has been bracketed, and the stantially higher than those for a fully rough sheet
1.2-
06 -
Fig. 6. Comparison of DI for sand in existing theory aod Fig. 7. Comparison between the existing and the modi-
in empirical relation proposed by Milligan & Palmeira fied tbeory for typical sand where (S/a, Z#),= 20 and for
WW grids with diierent numbers of bearing members
Géotechnique 1990.40:513-518.
518 JEWELL
(fbcaring > 1.0) once the grid geometry (S/a,B) The bearing stress mobilized on rectangular
falls below a certain value which denends on the bearing members, or surfaces, is approx-
number of bearing members n. The bond coefll- imately 1.2 times greater than that for circular
cient then rises rapidly as the grid geometry is bearing members. A factor 1.2 may be applied
reduced further so that fbearing $ 1. There is little, to equation (6) for calculations on reinforce-
if any, data to support such values. ment with rectangular bearing surfaces or
members. This assumes equation (6) to be
applicable to circular members.
CONCLUSIONS
The existing theory for reinforcement bond, The concept of degree of interference, DI dis-
summarized in this Technical Note has been sup- cussed explicitly by Milligan and Palmeira (1989)
ported by Palmeira & Milligan’s (1989) new test is already contained in the existing theory, equa-
data. There are two separate elements to the tion (14). The proposal to modify the existing
theory: theory with an empirical correlation for DI has
been found not to improve the prediction of bond
(a) the prediction of bearing stress, which is sup- capacity, and is therefore not recommended.
ported by the data in Fig. 2 As further data is assembled, it may be possible
(b) the concept of a limit to bond capacity (fb < to show that the rounding off indicated in Fig. 4
1.00) illustrated in Fig. 4 and supported by should be incorporated into a modified analysis.
the data in Fig. 5 For practical purposes, however, such an effect is
Two improvements to the existing theory for likely already to have been allowed for in the
the prediction of bearing stress have been sug- selection of c#/, and in the conservative relation
gested in this Technical Note based on the new for (a;&,) used to determine (S/a, B), .
data. They are as follows.
(a) Particle size can increase significantly the load
transmitted to bearing members in coarse-
REFERENCES
grained soils, B/OS0 < 10. In this range, a pro- Jewel], R. A., Milligan, G. W. E., Sarsby, R. W., and
portional increase in transmitted load by a DuBois, D. (1984). Interaction between soil and
factor grids. Polymer Grid Reinforcement, pp. 18-30,
London: Thomas Telford.
Palmeira, E. M. & Milligan, G. W. E. (1989). Scale and
other factors affecting the results of pull-out tests of
grids buried in sand. Gbotechnique 39, No. 3, 511-
has been suggested (equation (7) and Fig. 3). 524.
Géotechnique 1990.40:513-518.