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The bearing-capacity of a strip foundation on geogrid-reinforced sand
Geotextiles and Geomembranes 12 (1993)351-361
The Bearing-Capacity of a Strip Foundation on GeogridReinforced Sand
K. H. Khing~, B. M. Dasb*, V. K. Puff", E. E. C o o k a & S. C. Yen a °Department of Civil Engineeringand Mechanics,bOfficefor AcademicAffairs, Southern IllinoisUniversityat Carbondale, Carbondale, Illinois 62901-6603,USA (Received 8 December1991:accepted 12 May 1992)
ABSTRACT Laboratory-model test results for the bearing capacity of a strip foundation supported by a sand layer reinforced with layers of geogrid are presented. Based on the present model test results, the bearing-capacity ratio with respect to the ultimate bearing capacity, and at levels of limited settlement of the foundation, has been determined. For practical design purposes, it appears that the bearing-capacity ratio at limited levels of settlement is about 67- 7096 of the bearing-capacity ratio calculated on the basis of the ultimate bearing capacity.
INTRODUCTION Several laboratory-model test results that are currently available in the literature relate to the improvement in the load-bearing capacity of shallow foundations supported by sand reinforced with various materials such as metal strips (Binquet & Lee, 1975; Fragaszy & Lawton, 1984; Huang & Tatsuoka, 1990), metal bars (Huang & Tatsuoka, 1990), rope fibers (Akinmusuru & Akinbolande, 1981), geotextiles (Guido etal., 1985), and geogrid (Guido et al., 1986) as shown in Fig. 1. Some of these tests were conducted with model square foundations (Akinmusuru & Akinbolande, 1981; Guido et al., 1985, 1986) and the others with strip *To whom correspondenceshould be addressed. 351 Geotextiles and Geomembranes 0266-1144/93/$06.00© 1993 ElsevierSciencePublishers Ltd, England. Printed in Great Britain
K. H. Khing, B. M. Das, V. K. Puri, E. E. Cook, S. C. Yen
352
foundations (Binquet & Lee, 1975; Fragaszy & Lawton, 1984; Huang & Tatsuoka, 1988, 1990). These tests were primarily aimed at evaluating the following parameters in a non-dimensional form, from which the most beneficial effect from the reinforcement can be derived (Fig. 1): (a) the location of the top layer of the reinforcement measured from the bottom of the foundation, u; (b) the depth of reinforcement, d, = u + ( N - 1)h; (c) the number of reinforcement layers, N; (d) the width of each reinforcement layer, b. More recently, the use of geogrid for soil reinforcement has increased greatly. For that reason, it appears necessary to evaluate the load-bearing capacity of strip foundations supported by geogrid-reinforced soil. Similar studies by Guido et al. (1986) were conducted by using model square foundations. This paper presents the results of some recent laboratory-model tests on a strip foundation supported by a sand layer reinforced with layers of geogrid. BEARING-CAPACITY RATIO Most of the existing studies cited above (Guido et al., 1985, 1986), where geotextile and geogrid were employed as reinforcing material used a non-dimensional parameter called the bearing-capacity ratio to determine the increase in the ultimate bearing capacity with reinforcement as opposed to that without reinforcement. The bearing-capacity ratio with respect to the ultimate load can be defined as: BCRu
=
(1)
qutR)/qu
~
.
d
'
.
"
Reinforcement
•
1" N
.
N
t~'
N-1 b
r- ' I
Fig. 1. Geometric parameters for a foundation supported by reinforced soil.
Bearing capacity of strip foundation
353
where qu(R) = ultimate bearing capacity with reinforcement, and qu = ultimate bearing capacity without reinforcement. The present model tests with strip foundations on sand reinforced with layers of geogfid show that, in general, when N > 3 and u/B < 1 (B = width of footing), the load-displacement curves are of the type shown in Fig. 2. For these cases, qu(R) is greater than qu. However, the foundation settlement s at ultimate load with reinforced soil may be twice as much as that obtained with the unreinforced soil. In practice, most shallow foundations are designed for limited settlement. Hence it is essential to determine the bearing-capacity ratio at various levels of settlement (s < Su; see Fig. 2). Referring to Fig. 2, the bearing-capacity ratio at a settlement level s < So can be defined as: B C R s = qR/q
(2)
where qR, q = load per unit area of foundation on reinforced and unreinforced soil, respectively, at a settlement level s. On the basis of the results of the present model tests described below, the variations of BCRu and BCP~ with u/B, Nand b/B will be presented and compared.
q q~
qa
qa(R)
Load per unit area, q
Su
S~(g)
Geogridreinforced soil
Settlement, s Fig. 2. General nature of the load-displacement curves for unreinforced sand and
geogrid-reinforced sand supporting a strip foundation.
354
K. H. Khing, B. M. Das, V. K. Purl E. E. Cook, S. C Yen
LABORATORY-MODEL TEST ARRANGEMENT Laboratory-model tests were c o n d u c t e d in a steel box m e a s u r i n g 1.1 m (length) x 304.8 m m (width) X 914 m m (depth). The sides of the box were braced with stiffeners to avoid lateral yielding d u r i n g soil p l a c e m e n t a n d loading o f the model foundation. T h e model f o u n d a t i o n used for the tests was m a d e out of h a r d w o o d a n d m e a s u r e d 304.8 m m (length) X 101.6 m m (width) × 25.4 m m (thickness). Since the inside width of the box was equal to the length o f the m o d e l foundation, a plane-strain condition was generally maintained. A rough-base condition was achieved by c e m e n t i n g a thin layer of sand onto the base of the model f o u n d a t i o n with epoxy glue. A 6-35-mm-thick steel plate, having the same plan d i m e n s i o n s as the m o d e l f o u n d a t i o n a n d with a groove at the center, was m o u n t e d on the model foundation. The groove was m a d e to ensure that the applied load during the tests would be centric a n d vertical. The ends of the model f o u n d a t i o n a n d the sides of the model test box were m a d e as s m o o t h as possible to reduce friction during tests. A u n i f o r m fine r o u n d e d silica sand was used for the present model tests. The dry unit weight a n d the specific gravity of the sand reported in Table 1 were d e t e r m i n e d according to A S T M test designations D-4253 a n d D-854, respectively. The angle of internal friction of the sand was d e t e r m i n e d from direct-shear tests. Biaxial geogrid was used as the reinforcing material. The physical properties of this geogrid are given in Table 2. For c o n d u c t i n g the model tests, s a n d was p o u r e d into the test box in 25-4-mm-thick layers by using a raining technique. The accuracy of sand p l a c e m e n t a n d consistency o f the p l a c e m e n t density were checked during raining by placing small cans with k n o w n volumes at different Table 1
Properties of the Sand Used in the Laboratory-Model Tests Parameter
Uniformity coefficient, Cu Coefficient of gradation, C z Unified soil classification Effective size, Dl0 (mm) Minimum dry unit weight (kN/m3) Maximum dry unit weight (kN/m3) Average dry unit weight during model tests (kN/m3) Average relative density Dr during model tests (%) Average angle of internal friction of sand, ¢~, from direct-shear tests (deg)
Quantity
1.53 1.10 SP 0.34 14.07 18.94 17.14 70-0 40-3
Bearing capacity
o f strip f o u n d a t i o n
355
Table 2 Physical Properties of the Geogrid Parameter
Quantity
Structure Polymer Junction method Aperture size ( M D / X M D ) Rib thickness Junction thickness
Punctured sheet drawn P P / H D P E co-polymer Unitized 25.4 mm/33.02 m m 0.762 m m 2.286 m m
locations in the box. Geogrid layers were placed in the sand at desired values ofu/B and h/B. The model foundation was placed on the surface of the sand bed, and load on the model foundation was applied by a hydraulic jack. The load and the corresponding foundation settlement were measured by a proving ring and two dial gauges placed on each side of the center line of the foundation. Three series of tests were conducted, the details of which are given in Table 3.
MODEL TEST RESULTS
Variation of bearing capacity with u/B (Test Series A) The variations of the load per unit area with foundation settlement for various values of u/B obtained from the present laboratory model tests are shown in Fig. 3. For the tests, N, h/B, and b/B were kept constant at 6, 0-375, and 10-75, respectively. Also shown in this figure is the loadsettlement plot for the model foundation supported by unreinforced Table 3 Details of Model Tests Test series
Variable parameter
A
u/B
B
N (i.e. d/B)
C
b/B
aD r = relative density of sand.
Constant parameters
h / B = 0 . 3 7 5 , b / B = 10-75,N = 6,D~r = 70% u / B = 0.375, h / B = 0 . 3 7 5 , b / B = 10.75,Dg~ = 70% u / B ffi 0 . 3 7 5 , h / B = 0.375,N = 6,D~ = 70%
356
K H. Khing B. M. Das, V K. Puri, E. E. Cook, S. C Yen
0
I00
Load per unit area (kN/m 2 200 300
400
500
0
O.(M
0.08
s/B 0.12
0.16
0.20
0.24 Fig. 3. Variation ofs/B versus load per unit area for various values of u/B--Test Series A.
sand. It can be seen from the plots that, for tests conducted on unreinforced sand and reinforced sand with u/B > 1, the magnitude ofsu is approximately equal to sutm. However, for u/B < 1 (although the magnitude of the ultimate load increased sharply), the foundation settlement at the ultimate load was about twice as much as that obtained from the test with unreinforced soil. On the basis ofthe experimental plots shown in Fig. 3, the magnitudes of BCR~ for various values of u/B were calculated and are shown in Fig. 4. From the average plot of BCRu versus u/B, it appears that, at u/B = 1, the failure mechanism in the soil at ultimate load changes. The topmost geogrid layer acts somewhat like a rigid rough base. The remaining geogrid layers act as stiffeners in the soil. If the average plot of BCR~ is extrapolated to u/B "~ 2.5, one obtains a value of BCRu ~ 1. Experimental studies for a shallow strip foundation supported by a sand layer with a rigid rough base located at a shallow depth were published by Pfeifle and Das (1979). In that study, for a similar soil-friction angle, the ultimate bearing capacity was essentially unaffected when the rigid rough base was located at a depth of about 2.5 B or greater. This adds more validity to the present findings.
357
Bearing capacity of strip foundation
4.5
I
4.0
i
BC R, o s/s= = 25% zx s/s= = 51)% o sis.....2 ~ - 75....~%
\ -\
3.5
i
\ X
• BCRu
~
BCR~
BCR
2"5 (average ; i ; t )
~NN~ " ~ .
(ulB)o,, \
0
- ~
1.5 1.0
0
I
I
t
0.5
1.0 u/B
1.5
2.0
Fig. 4. Variation of BCR u and BCR~ with u/B--Test Series A.
Figure 4 also shows the plots of BCR~ with u/B calculated at foundation settlement levels ofs = 0.25 su, 0.5 su, and 0-75 s~. In practice, a foundation would be designed for a given value of settlement. Hence comparison of BCR~ at various values of s/s~ has little practical meaning. However, it does give a general indication of the comparative stiffness of the soil. Despite some scatter, a single average curve for the variation of BCR~, versus u/B can be plotted. This is also shown in Fig. 4. It is important to note that, for u/B < 0.75, the average plot of BCR~ falls below the plot of BCP~. On the basis of the average plots shown in Fig. 4, the ratio BCRJBCP~ for various values of u/B was calculated and is plotted in Fig. 5. For most reinforced-earth foundation works, the magnitude of u/B is kept between 0.25 and 0.4; hence, for all practical cases of design: BCP~ ~, (0.67-0.7) BCRu
(3)
Variation of bearing capacity with d/B (Test Series B) For the tests in this series, b/B was equal to 10-75 and u/B = h/B was ff 375. On the basis of the load-settlement curves, the variations of BCP~ and BCR~ with N are shown in Fig. 6. As in Fig. 4, the magnitudes of BCR~ for various values of N were calculated at settlement levels of
358
K.H. Khing B. M. Das, V. K. Purl, E. E. Cook, S. C Yen 1.5
1.0 A v
0.5
0
J 0.5
i 1.0
i 1.5
2.0
u/B
Fig. 5. Variation of BCRu/BCP~ with u/B--Test Series A.
s = 0-25 su, 0.5 s,,, and 0.75 su. The average curve of BCR~ versus N s h o w s a similar trend to that obtained from the plot of BCRu versus N. The magnitudes of BCRu and BCR, increase with N and appear to become practically constant a t N ~ 6, which is located at a depth o f 2.25 B. Thus it can be concluded that reinforcement layers located beyond d/B ~ 2-25 4.5
I
I
I
I
i
I
BCR, s/s. = 25% 4.0
~ s/su = 50% 2 sls_.._.~=75____%.%/
7
• BCRu /
3.5
A 0 / X"BCR.
3.0
A
/
8cn
2.5
/
/
o
.'~"'-
;z~/ ~/~.o
2.0
o __=_
°
,-BCR, ('average plot)
/
1.0
0
I
I
I
I
1
i
1
2
3
4
5
6
N Fig. 6. Variation of BCR~ and BCR~ with N--Test Series B.
Beating capacity of stripfoundation
359
will not contribute to the increase in the bearing-capacity ratio. It is interesting to note that, for similar tests conducted by Guido et al. (1986) with a square footing, the maximum value of d/B was determined to be about 1.25. If Boussinesq's solution (see Das, 1990) is used to determine the pressure increase in soil due to a distributed load on a flexible foundation, the following results are obtained: for square foundation: Ap ~ 0.25 q (at d/B ~ 1.25 below the center of the foundation) and for strip foundation: Ap ~ 0.25 q (at d/B ~ 2.5 below the center of the foundation) where Ap = increase in pressure, and q = load per unit area of the foundation. Hence it appears that the optimum depth of reinforcement is approximately equal to the depth at which A p / q ,~ 0-25. Based on the average plots shown in Fig. 6, the variation of BCRu/BCP-~ with N is shown in Fig. 7. For all values of N, it appears that BCP-~ ~ 0-67 BCRu.
Variation of bearing capacity with b/B (Test Series C) For these tests, b/B was varied with N = 6 and u/B = h/B = 0.375. The widths of the geogrid layers were varied as 2B, 4B, 6B, 8B, and 10-75B. Based on these test results, the average plots for the variations of BCRu and BCRs with b/B have been developed in Fig. 8. From this figure, it can
1.75
|
|
I
I
|
l
~- 1.50
1.25
1.00
0
I
I
t
I
I
1
2
3 N
4
5
Fig. 7. Variation of BCI~/BCR~ with N~Test Series B.
360
I~ H. Khing B. M. Das, V. K. Purl, E. E. Cook, S. C Yen 4.5
I
I
I
I
i
4.0
B
3.5
3.0 BCR
2.5
I
/~
~
x.. BCRs (average plot)
/
2.0
l
/
_
1.5
BcR.
0 slsu = 75% • BCRu
1.0
I
I
i
I
l
2
4
6
8
10
O/B Fig. 8. Variation of BCR~ and BCP~ with b / B - - T e s t Series C.
be seen that the magnitudes of BCRu and BCP-~ remain practically constant for b/B > 6. For square foundations, Guido et al. (1986) have reported that the maximum value of BCR~ is obtained at b/B > 2 to 3. Figure 9 shows the plot of BCP-~/BCP-~ (based on the average plots shown in Fig. 8) with b/B. For all values of b/B, BCR~ ~ 0.7BCRu. 1.75
I
~" 1.50
I
A
I
I
i
i
~
~" 1.25
1.00
0
t
I
i
J
i
2
4
6
8
10
b/B
Fig. 9. Variation of BCRu/BCP~ with b/B--Test Series C.
°
Bearing capacity of stripfoundation
361
CONCLUSIONS The results of a number of laboratory-model tests conducted to determine the bearing capacity of a shallow strip foundation supported by sand reinforced by geogrid layers have been presented. On the basis of the model-test results, the following conclusions can be drawn. (1) The maximum benefit of geogrid reinforcement in increasing the bearing capacity was obtained when the ratio of the depth of the first reinforcing layer to the foundation width was less than unity. (2) For the case of the strip foundation, a reinforcement placed below the foundation at a depth of more than 2.25 times the foundation width did not contribute to any increase in bearing capacity. (3) For maximum benefit, the minimum width of the geogrid layers should be about six times the foundation width. (4) The bearing-capacity ratio calculated on the basis of the ultimate bearing capacity may be somewhat misleading for the actual foundation design, since most foundations are constructed on the basis of limited settlement. The bearing-capacity ratio calculated on the basis of limited settlement appears to be about 67-70% of the ultimate bearing-capacity ratio. REFERENCES Akinmusuru, J. O. • Akinbolande, J. A. (1981). Stability of loaded footings on reinforced soil. J. Geotech. Engng Div., ASCE, 107, 819-27. Binquet, J. & Lee, K. L. (1975). Bearing capacity analysis of reinforced earth slabs. J. Geotech. Engng Div., ASCE, 101, 1257-76. Das, B. M. (1990). Principles of Geotechnical Engineering, 2nd edition, PWS-Kent Publishing, Boston, MA, USA. Fragaszy, R. J. & Lawton, E. C. (1984). Bearing capacity of reinforced sand subgrades. J. Geotech. Engng Div., ASCE, 110, 1500-7. Guido, V. A., Biesiadecki, G. L. & Sullivan, M. J. (1985). Bearing capacity of a geotextile reinforced foundation. In Proceecfings of llth International Conference on Soil Mechanics and Foundation Engineering, Vol.3, A. A. Balkema, The Netherlands, pp. 1777-80. Guido, V. A., Chang, D. K. & Sweeney,M. A. (1986). Comparison of geogrid and geotextile reinforced slabs. Canad, Geotech. J, 23, 435--40. Huang, C. C. & Tatsuoka, F. (1988). Prediction of bearing capacity in level sandy ground reinforced with strip reinforcement. In Proceedingsof the International Geotechnical Symposium on Theory and Practice of Earth Reinforcement, Fukuoka, Kyushu, Japan, ed. T. Yamanouchi, N. Miura and H. Ochiai. A. A. Balkema, The Netherlands, pp. 191-6. Huang, C. C. & Tatsuoka, F. (1990). Bearing capacity of reinforced horizontal sandy ground. Geotext. & Geomemb., 9, 51-82. Pfeifle, T. W. & Das, B. M. (1979). Model tests for bearing capacity in sand. J. Geotech. Engng Div., ASCE, 105, 1112-116.
The Bearing-Capacity of a Strip Foundation on GeogridReinforced Sand
K. H. Khing~, B. M. Dasb*, V. K. Puff", E. E. C o o k a & S. C. Yen a °Department of Civil Engineeringand Mechanics,bOfficefor AcademicAffairs, Southern IllinoisUniversityat Carbondale, Carbondale, Illinois 62901-6603,USA (Received 8 December1991:accepted 12 May 1992)
ABSTRACT Laboratory-model test results for the bearing capacity of a strip foundation supported by a sand layer reinforced with layers of geogrid are presented. Based on the present model test results, the bearing-capacity ratio with respect to the ultimate bearing capacity, and at levels of limited settlement of the foundation, has been determined. For practical design purposes, it appears that the bearing-capacity ratio at limited levels of settlement is about 67- 7096 of the bearing-capacity ratio calculated on the basis of the ultimate bearing capacity.
INTRODUCTION Several laboratory-model test results that are currently available in the literature relate to the improvement in the load-bearing capacity of shallow foundations supported by sand reinforced with various materials such as metal strips (Binquet & Lee, 1975; Fragaszy & Lawton, 1984; Huang & Tatsuoka, 1990), metal bars (Huang & Tatsuoka, 1990), rope fibers (Akinmusuru & Akinbolande, 1981), geotextiles (Guido etal., 1985), and geogrid (Guido et al., 1986) as shown in Fig. 1. Some of these tests were conducted with model square foundations (Akinmusuru & Akinbolande, 1981; Guido et al., 1985, 1986) and the others with strip *To whom correspondenceshould be addressed. 351 Geotextiles and Geomembranes 0266-1144/93/$06.00© 1993 ElsevierSciencePublishers Ltd, England. Printed in Great Britain
K. H. Khing, B. M. Das, V. K. Puri, E. E. Cook, S. C. Yen
352
foundations (Binquet & Lee, 1975; Fragaszy & Lawton, 1984; Huang & Tatsuoka, 1988, 1990). These tests were primarily aimed at evaluating the following parameters in a non-dimensional form, from which the most beneficial effect from the reinforcement can be derived (Fig. 1): (a) the location of the top layer of the reinforcement measured from the bottom of the foundation, u; (b) the depth of reinforcement, d, = u + ( N - 1)h; (c) the number of reinforcement layers, N; (d) the width of each reinforcement layer, b. More recently, the use of geogrid for soil reinforcement has increased greatly. For that reason, it appears necessary to evaluate the load-bearing capacity of strip foundations supported by geogrid-reinforced soil. Similar studies by Guido et al. (1986) were conducted by using model square foundations. This paper presents the results of some recent laboratory-model tests on a strip foundation supported by a sand layer reinforced with layers of geogrid. BEARING-CAPACITY RATIO Most of the existing studies cited above (Guido et al., 1985, 1986), where geotextile and geogrid were employed as reinforcing material used a non-dimensional parameter called the bearing-capacity ratio to determine the increase in the ultimate bearing capacity with reinforcement as opposed to that without reinforcement. The bearing-capacity ratio with respect to the ultimate load can be defined as: BCRu
=
(1)
qutR)/qu
~
.
d
'
.
"
Reinforcement
•
1" N
.
N
t~'
N-1 b
r- ' I
Fig. 1. Geometric parameters for a foundation supported by reinforced soil.
Bearing capacity of strip foundation
353
where qu(R) = ultimate bearing capacity with reinforcement, and qu = ultimate bearing capacity without reinforcement. The present model tests with strip foundations on sand reinforced with layers of geogfid show that, in general, when N > 3 and u/B < 1 (B = width of footing), the load-displacement curves are of the type shown in Fig. 2. For these cases, qu(R) is greater than qu. However, the foundation settlement s at ultimate load with reinforced soil may be twice as much as that obtained with the unreinforced soil. In practice, most shallow foundations are designed for limited settlement. Hence it is essential to determine the bearing-capacity ratio at various levels of settlement (s < Su; see Fig. 2). Referring to Fig. 2, the bearing-capacity ratio at a settlement level s < So can be defined as: B C R s = qR/q
(2)
where qR, q = load per unit area of foundation on reinforced and unreinforced soil, respectively, at a settlement level s. On the basis of the results of the present model tests described below, the variations of BCRu and BCP~ with u/B, Nand b/B will be presented and compared.
q q~
qa
qa(R)
Load per unit area, q
Su
S~(g)
Geogridreinforced soil
Settlement, s Fig. 2. General nature of the load-displacement curves for unreinforced sand and
geogrid-reinforced sand supporting a strip foundation.
354
K. H. Khing, B. M. Das, V. K. Purl E. E. Cook, S. C Yen
LABORATORY-MODEL TEST ARRANGEMENT Laboratory-model tests were c o n d u c t e d in a steel box m e a s u r i n g 1.1 m (length) x 304.8 m m (width) X 914 m m (depth). The sides of the box were braced with stiffeners to avoid lateral yielding d u r i n g soil p l a c e m e n t a n d loading o f the model foundation. T h e model f o u n d a t i o n used for the tests was m a d e out of h a r d w o o d a n d m e a s u r e d 304.8 m m (length) X 101.6 m m (width) × 25.4 m m (thickness). Since the inside width of the box was equal to the length o f the m o d e l foundation, a plane-strain condition was generally maintained. A rough-base condition was achieved by c e m e n t i n g a thin layer of sand onto the base of the model f o u n d a t i o n with epoxy glue. A 6-35-mm-thick steel plate, having the same plan d i m e n s i o n s as the m o d e l f o u n d a t i o n a n d with a groove at the center, was m o u n t e d on the model foundation. The groove was m a d e to ensure that the applied load during the tests would be centric a n d vertical. The ends of the model f o u n d a t i o n a n d the sides of the model test box were m a d e as s m o o t h as possible to reduce friction during tests. A u n i f o r m fine r o u n d e d silica sand was used for the present model tests. The dry unit weight a n d the specific gravity of the sand reported in Table 1 were d e t e r m i n e d according to A S T M test designations D-4253 a n d D-854, respectively. The angle of internal friction of the sand was d e t e r m i n e d from direct-shear tests. Biaxial geogrid was used as the reinforcing material. The physical properties of this geogrid are given in Table 2. For c o n d u c t i n g the model tests, s a n d was p o u r e d into the test box in 25-4-mm-thick layers by using a raining technique. The accuracy of sand p l a c e m e n t a n d consistency o f the p l a c e m e n t density were checked during raining by placing small cans with k n o w n volumes at different Table 1
Properties of the Sand Used in the Laboratory-Model Tests Parameter
Uniformity coefficient, Cu Coefficient of gradation, C z Unified soil classification Effective size, Dl0 (mm) Minimum dry unit weight (kN/m3) Maximum dry unit weight (kN/m3) Average dry unit weight during model tests (kN/m3) Average relative density Dr during model tests (%) Average angle of internal friction of sand, ¢~, from direct-shear tests (deg)
Quantity
1.53 1.10 SP 0.34 14.07 18.94 17.14 70-0 40-3
Bearing capacity
o f strip f o u n d a t i o n
355
Table 2 Physical Properties of the Geogrid Parameter
Quantity
Structure Polymer Junction method Aperture size ( M D / X M D ) Rib thickness Junction thickness
Punctured sheet drawn P P / H D P E co-polymer Unitized 25.4 mm/33.02 m m 0.762 m m 2.286 m m
locations in the box. Geogrid layers were placed in the sand at desired values ofu/B and h/B. The model foundation was placed on the surface of the sand bed, and load on the model foundation was applied by a hydraulic jack. The load and the corresponding foundation settlement were measured by a proving ring and two dial gauges placed on each side of the center line of the foundation. Three series of tests were conducted, the details of which are given in Table 3.
MODEL TEST RESULTS
Variation of bearing capacity with u/B (Test Series A) The variations of the load per unit area with foundation settlement for various values of u/B obtained from the present laboratory model tests are shown in Fig. 3. For the tests, N, h/B, and b/B were kept constant at 6, 0-375, and 10-75, respectively. Also shown in this figure is the loadsettlement plot for the model foundation supported by unreinforced Table 3 Details of Model Tests Test series
Variable parameter
A
u/B
B
N (i.e. d/B)
C
b/B
aD r = relative density of sand.
Constant parameters
h / B = 0 . 3 7 5 , b / B = 10-75,N = 6,D~r = 70% u / B = 0.375, h / B = 0 . 3 7 5 , b / B = 10.75,Dg~ = 70% u / B ffi 0 . 3 7 5 , h / B = 0.375,N = 6,D~ = 70%
356
K H. Khing B. M. Das, V K. Puri, E. E. Cook, S. C Yen
0
I00
Load per unit area (kN/m 2 200 300
400
500
0
O.(M
0.08
s/B 0.12
0.16
0.20
0.24 Fig. 3. Variation ofs/B versus load per unit area for various values of u/B--Test Series A.
sand. It can be seen from the plots that, for tests conducted on unreinforced sand and reinforced sand with u/B > 1, the magnitude ofsu is approximately equal to sutm. However, for u/B < 1 (although the magnitude of the ultimate load increased sharply), the foundation settlement at the ultimate load was about twice as much as that obtained from the test with unreinforced soil. On the basis ofthe experimental plots shown in Fig. 3, the magnitudes of BCR~ for various values of u/B were calculated and are shown in Fig. 4. From the average plot of BCRu versus u/B, it appears that, at u/B = 1, the failure mechanism in the soil at ultimate load changes. The topmost geogrid layer acts somewhat like a rigid rough base. The remaining geogrid layers act as stiffeners in the soil. If the average plot of BCR~ is extrapolated to u/B "~ 2.5, one obtains a value of BCRu ~ 1. Experimental studies for a shallow strip foundation supported by a sand layer with a rigid rough base located at a shallow depth were published by Pfeifle and Das (1979). In that study, for a similar soil-friction angle, the ultimate bearing capacity was essentially unaffected when the rigid rough base was located at a depth of about 2.5 B or greater. This adds more validity to the present findings.
357
Bearing capacity of strip foundation
4.5
I
4.0
i
BC R, o s/s= = 25% zx s/s= = 51)% o sis.....2 ~ - 75....~%
\ -\
3.5
i
\ X
• BCRu
~
BCR~
BCR
2"5 (average ; i ; t )
~NN~ " ~ .
(ulB)o,, \
0
- ~
1.5 1.0
0
I
I
t
0.5
1.0 u/B
1.5
2.0
Fig. 4. Variation of BCR u and BCR~ with u/B--Test Series A.
Figure 4 also shows the plots of BCR~ with u/B calculated at foundation settlement levels ofs = 0.25 su, 0.5 su, and 0-75 s~. In practice, a foundation would be designed for a given value of settlement. Hence comparison of BCR~ at various values of s/s~ has little practical meaning. However, it does give a general indication of the comparative stiffness of the soil. Despite some scatter, a single average curve for the variation of BCR~, versus u/B can be plotted. This is also shown in Fig. 4. It is important to note that, for u/B < 0.75, the average plot of BCR~ falls below the plot of BCP~. On the basis of the average plots shown in Fig. 4, the ratio BCRJBCP~ for various values of u/B was calculated and is plotted in Fig. 5. For most reinforced-earth foundation works, the magnitude of u/B is kept between 0.25 and 0.4; hence, for all practical cases of design: BCP~ ~, (0.67-0.7) BCRu
(3)
Variation of bearing capacity with d/B (Test Series B) For the tests in this series, b/B was equal to 10-75 and u/B = h/B was ff 375. On the basis of the load-settlement curves, the variations of BCP~ and BCR~ with N are shown in Fig. 6. As in Fig. 4, the magnitudes of BCR~ for various values of N were calculated at settlement levels of
358
K.H. Khing B. M. Das, V. K. Purl, E. E. Cook, S. C Yen 1.5
1.0 A v
0.5
0
J 0.5
i 1.0
i 1.5
2.0
u/B
Fig. 5. Variation of BCRu/BCP~ with u/B--Test Series A.
s = 0-25 su, 0.5 s,,, and 0.75 su. The average curve of BCR~ versus N s h o w s a similar trend to that obtained from the plot of BCRu versus N. The magnitudes of BCRu and BCR, increase with N and appear to become practically constant a t N ~ 6, which is located at a depth o f 2.25 B. Thus it can be concluded that reinforcement layers located beyond d/B ~ 2-25 4.5
I
I
I
I
i
I
BCR, s/s. = 25% 4.0
~ s/su = 50% 2 sls_.._.~=75____%.%/
7
• BCRu /
3.5
A 0 / X"BCR.
3.0
A
/
8cn
2.5
/
/
o
.'~"'-
;z~/ ~/~.o
2.0
o __=_
°
,-BCR, ('average plot)
/
1.0
0
I
I
I
I
1
i
1
2
3
4
5
6
N Fig. 6. Variation of BCR~ and BCR~ with N--Test Series B.
Beating capacity of stripfoundation
359
will not contribute to the increase in the bearing-capacity ratio. It is interesting to note that, for similar tests conducted by Guido et al. (1986) with a square footing, the maximum value of d/B was determined to be about 1.25. If Boussinesq's solution (see Das, 1990) is used to determine the pressure increase in soil due to a distributed load on a flexible foundation, the following results are obtained: for square foundation: Ap ~ 0.25 q (at d/B ~ 1.25 below the center of the foundation) and for strip foundation: Ap ~ 0.25 q (at d/B ~ 2.5 below the center of the foundation) where Ap = increase in pressure, and q = load per unit area of the foundation. Hence it appears that the optimum depth of reinforcement is approximately equal to the depth at which A p / q ,~ 0-25. Based on the average plots shown in Fig. 6, the variation of BCRu/BCP-~ with N is shown in Fig. 7. For all values of N, it appears that BCP-~ ~ 0-67 BCRu.
Variation of bearing capacity with b/B (Test Series C) For these tests, b/B was varied with N = 6 and u/B = h/B = 0.375. The widths of the geogrid layers were varied as 2B, 4B, 6B, 8B, and 10-75B. Based on these test results, the average plots for the variations of BCRu and BCRs with b/B have been developed in Fig. 8. From this figure, it can
1.75
|
|
I
I
|
l
~- 1.50
1.25
1.00
0
I
I
t
I
I
1
2
3 N
4
5
Fig. 7. Variation of BCI~/BCR~ with N~Test Series B.
360
I~ H. Khing B. M. Das, V. K. Purl, E. E. Cook, S. C Yen 4.5
I
I
I
I
i
4.0
B
3.5
3.0 BCR
2.5
I
/~
~
x.. BCRs (average plot)
/
2.0
l
/
_
1.5
BcR.
0 slsu = 75% • BCRu
1.0
I
I
i
I
l
2
4
6
8
10
O/B Fig. 8. Variation of BCR~ and BCP~ with b / B - - T e s t Series C.
be seen that the magnitudes of BCRu and BCP-~ remain practically constant for b/B > 6. For square foundations, Guido et al. (1986) have reported that the maximum value of BCR~ is obtained at b/B > 2 to 3. Figure 9 shows the plot of BCP-~/BCP-~ (based on the average plots shown in Fig. 8) with b/B. For all values of b/B, BCR~ ~ 0.7BCRu. 1.75
I
~" 1.50
I
A
I
I
i
i
~
~" 1.25
1.00
0
t
I
i
J
i
2
4
6
8
10
b/B
Fig. 9. Variation of BCRu/BCP~ with b/B--Test Series C.
°
Bearing capacity of stripfoundation
361
CONCLUSIONS The results of a number of laboratory-model tests conducted to determine the bearing capacity of a shallow strip foundation supported by sand reinforced by geogrid layers have been presented. On the basis of the model-test results, the following conclusions can be drawn. (1) The maximum benefit of geogrid reinforcement in increasing the bearing capacity was obtained when the ratio of the depth of the first reinforcing layer to the foundation width was less than unity. (2) For the case of the strip foundation, a reinforcement placed below the foundation at a depth of more than 2.25 times the foundation width did not contribute to any increase in bearing capacity. (3) For maximum benefit, the minimum width of the geogrid layers should be about six times the foundation width. (4) The bearing-capacity ratio calculated on the basis of the ultimate bearing capacity may be somewhat misleading for the actual foundation design, since most foundations are constructed on the basis of limited settlement. The bearing-capacity ratio calculated on the basis of limited settlement appears to be about 67-70% of the ultimate bearing-capacity ratio. REFERENCES Akinmusuru, J. O. • Akinbolande, J. A. (1981). Stability of loaded footings on reinforced soil. J. Geotech. Engng Div., ASCE, 107, 819-27. Binquet, J. & Lee, K. L. (1975). Bearing capacity analysis of reinforced earth slabs. J. Geotech. Engng Div., ASCE, 101, 1257-76. Das, B. M. (1990). Principles of Geotechnical Engineering, 2nd edition, PWS-Kent Publishing, Boston, MA, USA. Fragaszy, R. J. & Lawton, E. C. (1984). Bearing capacity of reinforced sand subgrades. J. Geotech. Engng Div., ASCE, 110, 1500-7. Guido, V. A., Biesiadecki, G. L. & Sullivan, M. J. (1985). Bearing capacity of a geotextile reinforced foundation. In Proceecfings of llth International Conference on Soil Mechanics and Foundation Engineering, Vol.3, A. A. Balkema, The Netherlands, pp. 1777-80. Guido, V. A., Chang, D. K. & Sweeney,M. A. (1986). Comparison of geogrid and geotextile reinforced slabs. Canad, Geotech. J, 23, 435--40. Huang, C. C. & Tatsuoka, F. (1988). Prediction of bearing capacity in level sandy ground reinforced with strip reinforcement. In Proceedingsof the International Geotechnical Symposium on Theory and Practice of Earth Reinforcement, Fukuoka, Kyushu, Japan, ed. T. Yamanouchi, N. Miura and H. Ochiai. A. A. Balkema, The Netherlands, pp. 191-6. Huang, C. C. & Tatsuoka, F. (1990). Bearing capacity of reinforced horizontal sandy ground. Geotext. & Geomemb., 9, 51-82. Pfeifle, T. W. & Das, B. M. (1979). Model tests for bearing capacity in sand. J. Geotech. Engng Div., ASCE, 105, 1112-116.