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The effect of prestressing on the settlement characteristics of geosynthetic-reinforced soil
13 (I994) 531-543 1994 ElsevierScienceLimited Printed in Ireland. 0266-1144/94/$7.00
Geotextiles and Geomembranes
ELSEVIER
The Effect of Prestressing on the Settlement Characteristics of Geosynthetic-Reinforced Soil
Sanjay Kumar Shukla & Sarvesh Chandra Department of Civil Engineering, Indian Institute of Technology, Kanpur 208016, I n d i a (Received 22 December 1993; accepted 4 February 1994)
ABSTRACT In this paper, the effect of prestressing the geosynthetic reinforcement on the settlement behaviour of geosynthetic-reinforeed granular fill-soft soil system is studied. The foundation model element proposed by Madhav and Poorooshasb (Computers & Geotechnics, 6, 277-90, 1988), which has a rough membrane embedded in a granular layer, has been modified to include the prestressing effect in the geosynthetic reinforcement. Parametric studies reveal that the settlement reductions within the loaded region are observed even for low prestress in the reinforcement. It is concluded that prestressing the geosynthetic reinforcement is a significant ground improvement technique to enhance the settlement characteristics of the soft soils where the membrane effect of reinforcement is felt.
NOTATION B
Gb Gb at
Gt
Ht Hb
Half width of strip footing (m) Shear modulus of granular fill below reinforcement (kN/m 2) Nondimensionalised shear parameter of granular fill below reinforcement Shear modulus of granular fill above reinforcement (kN/m 2) Nondimensionalised shear parameter of granular fill above reinforcement Thickness of granular fill above reinforcement (m) Thickness of granular fill below reinforcement (m) 531
532
i ks L q q*
T T*
Tp Tp w
W x
X
0 ]At Pb
Sanjay Kumar Shukla, Sarvesh Chandra
Subscript referring to a nodal point Modulus of subgrade reaction for soft soil (kN/m 3) Half width of reinforced zone (m) Applied load intensity (kN/m 2) Nondimensionalised applied load intensity Mobilised tensile force in the reinforcement (kN/m) Nondimensionalised mobilised tensile force in the reinforcement Prestress in the reinforcement (kN/m) Nondimensionalised prestress in the reinforcement Vertical surface displacement (m) Nondimensionalised vertical surface displacement Distance from the centre of footing along x-axis (m) Nondimensionalised distance from the centre of footing along x-axis Slope of the surface deformation profile (degrees) Interfacial friction coefficient at the top of reinforcement Interfacial friction coefficient at the bottom of reinforcement
INTRODUCTION The use of geosynthetics, mainly geotextiles and geogrids, to reinforce soft soil in order to improve its bearing capacity and settlement characteristics is becoming increasingly popular in present-day geotechnical engineering. It has now been well established that geosynthetics, particularly geotextiles, show their beneficial effects only after relatively large settlements (Andrawes et al., 1982; Milligan & Love, 1984; Guido et al., 1985; Rowe & Soderman, 1987; Madhav & Poorooshasb, 1988; Poorooshasb, 1989) which may not be a desirable feature for shallow footings, paved and unpaved roads, and embankments. Andrawes et al. (1982) reported measured and predicted data from which they concluded that the influence of the geotextile on the loadsettlement behaviour of the strip footing on sand is very limited up to settlements equal to approximately 8% of the footing breadth. This suggests that up to that level of settlement, strains in the soil are insufficient to mobilise significant tensile load in the geotextile. From large-scale laboratory tests, Milligan and Love (1984) showed that there is a marked improvement in load-carrying capacity with a geogrid at high deformation and only nominal beneficial effect at low deformation. Poorooshasb (1989) found that at lower settlement level (less than 2.5 cm) the presence of geogrids had no effect at all. Hence there is a need for a technique which can make geosynthetics more beneficial without the occurrence of large settlements. It was thought that
Prestressing and settlement of geosynthetic-reinforced soil
533
prestressing the geosynthetics might have improved the settlement characteristics significantly. The idea of prestressing has been recognised in the recent past. Aboshi (1984) and Watary (1984) described a method to stabilise very soft clay, developed in Japan called 'Rope sheet method' in which the ropes are preloaded to 0-5-0.6 kN in order to increase their effectiveness. For stabilisation of very soft clay using geotextile, Broms (1987) has suggested that the geotextile should be stretched as much as possible before the stabilising berms are placed along the perimeter of the geotextile sheet in order to limit the penetration required to develop the necessary tension in the geotextile. Koerner (1990) expressed the view that a method of prestressing the geotextile would be a significant step forward in ground improvement. Hausmann (1990), while developing construction guidelines for geotextile applications in various geotechnical constructions, pointed out that simple procedures such as pretensioning the geotextile might enhance the reinforcement function in some applications. From the available literature, it can be observed that very little study has been carried out on the prestressing of geosynthetics and its effect on settlement characteristics. Most of the earlier workers have realised the importance of prestressing the geotextile but analytical work is scarce. In this paper the effect of prestressing has been included in the existing foundation model element, the rough membrane proposed by Madhav and Poorooshasb (1988), to represent the response of a prestressed geosynthetic. Using this foundation model element, a model for prestressed geosynthetic-reinforced soil is proposed. The parametric studies were carried out to determine the effect of prestressing on settlement characteristics over a wide range of parameters. MODELS FOR G E O S Y N T H E T I C - R E I N F O R C E D SOIL There are several physical models e.g. Winkler, Filonenko-Borodich, Pasternak, etc. (see Kerr (1964), Selvadurai (1979) and Horvath (in press)) available to represent the behaviour of soils as subgrades. Kerr (1964), Selvadurai (1979) and Horvath (in press) present excellent surveys of the existing foundation models for soils but very few physical foundation models are available for the geosynthetic-reinforced soils. One of the widely used models is that proposed by Madhav and Poorooshasb (1988) for a geosynthetic-granular fill-soft soil system (Fig. 1). The response function of the model is dZw
ks w - (Gt Ht h- Tcos0 + Gb Hb) ~X~X 2=
q(x)
(1)
Sanjay Kumar Shukla, Sarvesh Chandra
534
Parternak
c
Fig. 1. Definition
Shear
Rough Membrane
sketch - foundation model for geosynthetic-granular system. (From Madhav & Poorooshasb, 1988.)
fill-soft
soil
where q is the applied load intensity; G, Ht and GbHb are respectively shear parameters for the soil above and below the membrane; k, is modulus of subgrade reaction for the soft soil; T is the tensile force per unit length mobilised in the membrane; 0 is the slope of the surface deformation profile with respect to the x-axis; and w is the vertical surface displacement. The expression for the variation of the mobilised tension in the membrane with its length measured from the centre of footing is dT - = - (pLtset 0 + sin 0) dx
- (p,, set 0 - sin 0) >
where ,&qand PU,are respectively the interfacial top and bottom of the membrane.
A M6DEL
(2)
friction
coefficients
at the
FOR PRESTRESSED GEOSYNTHETICREINFORCED SOIL
The membrane used in the model proposed by Madhav and Poorooshasb (1988) is a rough elastic one while, the Filonenko-Borodich model uses a thin smooth elastic membrane under a constant tension in all horizontal directions to achieve the continuity between the individual springs in the Winkler model. In the present paper these two foundation model elements have been combined into one as a stretched rough elustic membrane to idealise the behaviour of a prestressed geosynthetic. Further stretching of the membrane may occur because of the tension mobilised
Prestressing and settlement of geosynthetic-reinforced soil
~
q
14
~
2B
=1
/
[ Ht T IIILIIIIIlllllll'rlll
T
~ S t (. • <~ ~> ~.~
r e • <~ ~
t < <~ ~.~
c < <~ ~,
r/F~r~/[
~ <" ~_~
T Ht
I ~ B .-hi I"-1"T'I-1 q It • • • •
Tp I
h e d Rough ..t2 <~ Etastic Membrane <. (Prestressed Geosynthetic ~_~ Layer} I
~ ~ ~ ~ ~
( <" ~, ,~
~ - Pasternak Shear Layer (Granul.ar Fitt) T
<" < ' ~ W i n k t o r Springs ~.~_ (Soft Soi[)
r[ / / I t / / ~ [ r r
(a)
///
i I [
x ~
535
Prestressed
/Geosynthetic Layer
TopGranulorLayer(Gtl/(pt,Pb,Tp) o,,o
o....
,or
Soft Soil
(ks)
~///1//////////[/t///]//I
(b)
Fig. 2. Definition sketch, (a) foundation model proposed for prestressed geosyntheticreinforced granular fill-soft soil system, (b) foundation system analysed. by the transference of shear resistance acting at the top and bottom of the geosynthetic reinforcement. Hence the load coming from the structure is distributed on a wider area without causing excessive settlement, resulting in reduction of subgrade stress which also occurs because of sharing the load by the membrane through structural action commonly called membrane effect as explained by Giroud and Noiray (1981). Combining the modified foundation model element with Winkler springs and Pasternak shear layer representing respectively soft soil and granular fill, a foundation model is proposed to represent the response of a granular fill-prestressed geosynthetic-soft soil system (Fig. 2(a)). Considering equilibrium of the fill and reinforcement elements the response function of the model is derived as: k s w - {GtHt + ( T +
d2 W Tp)cOs 0 + GbOb} ~ ----q(x)
(3)
where Tp is the pretension per unit length applied to the geosynthetic reinforcement. For no prestressing the present model reduces to the model proposed by Madhav and Poorooshasb (1988) whereas for a stretched smooth membrane and no shear layer this model reduces to the Filonenko--Borodich model. Pasternak and Winkler models are also particular cases of the present model. The expression for variation of the mobilised tension in the reinforcement remains the same as eqn (2). M E T H O D OF ANALYSIS The basic eqns (2) and (3), governing the response of the present model, are coupled and solved by a nondimensionalised finite difference scheme, iteratively, in a convenient way. Nondimensionalising with
536
Sanjay Kumar Shukla, Sarvesh Chandra
X = x/B, W = w/B, G t = Gt Ht/ks B 2, G b =- Gb Hb/ks B 2,
q* = q/ks B, T* = T/ks B 2 and Tp = Tp/ks B 2,
eqns (2) and (3) become
(q*+G~ d2W d X Z J - (#b sec 0 -- sin 0)
dr*_dX
(Ptsec0+sin0)
(
.d2W )
(4)
W -- G b -d-~
and d 2 W q, W - {G t + ( T * + Tp)COsO+G;} d X 2 --
(5)
Writing eqns (4) and (5) in finite difference terms leads to T 1 =T~+ l + A X/2 {
*
sec 0i + sin 0i) (d2W i
(q~+qi+l)+Gt \~--/
d2W +d-X-2-
i+l
)}+(#bsec0i_sin0i)
(d2W d2W { ( W i + W i + , ) - G ~ , k d X 2 i+~-~-~ i + , ) } ]
(6)
and Wi-{a~+(r;+Tp)COsOi+6~,}"
{
Wi_,
2Wi + Wi+, (AX)2
}
= qi
(7)
Values of sin 0i, cos 0i & sec 0i at each node along x-axis in eqns (6) and (7) are obtained from tan0i = d W / d X l i . In order to minimise the numerical error, average values of q*, W and d 2 W / d X z for each element are taken in eqn (6). Solutions are obtained for a uniformly loaded flexible strip footing. Loading conditions
The loading conditions considered are q~ (X) = q*
for IX[ < 1.0
(8a)
=0-0
for I X I > 1.0
(8b)
Prestressing and settlement of geosynthetie-rein['orced soil
537
Boundary conditions Boundary conditions considered at the centre and at the edge of the reinforcement/shear layer are
dW/dX = 0-0 for X = 0.0 & LIB
(9a)
and T*=0.0
forX=L/B
(9b)
The first boundary condition comes directly from the symmetry of the problem about the centre of the loaded footing. The second boundary condition comes from the fact that the prestressed geosynthetic layer is generally fixed at its edge either by placing stabilising berms on it (Broms, 1987) or by anchoring it in trenches or sometimes by folding it back. The third boundary condition is an assumption for simplicity because the mobilised tensile force at the edge of the reinforcement is very small. To solve eqns (6) and (7) a set of values for Wi along the x-axis are assumed initially. New values of Ti are obtained from eqn (6) and substituted into eqn (7) from which a new set of values of Wi is obtained. The iteration is continued until the change in the current estimate of the displacement is small enough, that is, within the convergence tolerance as specified.
RESULTS A N D DISCUSSIONS A computer program, based on the formulation as described above, was developed and the results were obtained using HP 9000/850 computer system. Due to the symmetry of the problem analysed, only half the region of the problem (x >I 0) is considered (Fig. 2(b)). The solutions were obtained with a convergence criterion of 0.0001. For simplicity, the nondimensionalised settlement W, mobilised tension T*, and prestress T*p' were normalised with respect to applied nondimensionalised load, q*. The ranges of parameters studied are: • • • • •
Prestress in the geosynthetic reinforcement, Tp. 0.0-l.0 Load intensity, q*: 0.01-1.0 Width of reinforced zone, L/B: 1-0-2.5 Shear modulus of granular fill, G t or Gb: 0.0-1.0 Interface friction coefficient, Pt or Pb: 0-0-1.0
Figure 3 shows the settlement response of a prestressed geosyntheticreinforced soil for several values of prestress and compares the results with
538
Sanjay Kumar Shukla, Sarvesh Chandra Distance f r o m Centre of L o a d i n g , X 01
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
I
I
I
I
J
I
I
I
I
Gt*'=
Gb ~=
0.1
"
~'-...~'~
2.0
- ~
0.2
L / e = 2.0 q "--0.5 "-
L
j,~.
".,~.~..-.-~-~.-.
.~.jl~'~ ' ~ "
0.4 .........
-
~ 0.6 ...... ~ ...... ~j.-~"E
.
.
-
.
.
-
-
...... .....P r Q
-
~
s
~
e
-
n
t
.......
1.0
~,,.,t.;~'nok
.......
------'-. . . . . . . .
.....
~-~;~ Poorooshosb Study Tp *
0.01 0.05 0.1 0.3 0.5
1.0
12 Fig. 3. Settlement~listance profiles effect of prestressing compared with existing foundation models.
those obtained using the model of Madhav and Poorooshasb (1988) for granular fill-geosynthetic-soft soil system and with Winkler and Pasternak models for general soil behaviour. It is observed that the settlement within the loaded region (X ~< 1.0) reduces as the prestress in the geosynthetic layer is increased but there is an increase in settlement slightly beyond the loaded region. The settlement reductions for nondimensionalised prestress values of 0.01, 0.05, 0.1, 0.3, 0.5, and 1.0, compared with no prestressing (Madhav & Poorooshasb, 1988) are respectively 0.55, 2.48, 4-54, 11.69, 17.33 and 27.65% at the centre of the footing whereas at the edge of the footing reductions are 0-00, 0.00, 0-00, 1.15, 3.23 and 9.24%. This indicates that the reductions in the settlements at the centre of the footing due to prestressing is more significant than at the edge of the footing. Thus the differential settlement of the loaded footing is reduced as a result of prestressing the geosynthetic reinforcement. Figure 4 shows the effect of prestressing the geosynthetic reinforcement on the settlement-distance profiles of geosynthetic-reinforced soil for various nondimensionalised load intensities. It is noted that at any location within the loaded footing, settlement reduction due to prestress (Tp -- 0.3) is more for lower values of q*. As q* increases from 0.01 to 1.0 the settlement reduction at the centre of the footing reduces from 15.91 to 9.05%. Hence it can be concluded that to achieve a particular reduction in the settlement, less prestress in the geosynthetic reinforcement is required for lower nondimensionalised load intensities as compared to higher load intensities. This conclusion indicates that in the case of soft soils where
Prestressing and settlement o f geosynthetic-reinforced soil
539
Distance f r o m Centre of L o a d i n g , X 0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
I
I
I
I
I
I
I
J
I
Gt" = S ; ~t
0.2
-/
=0.1
• ~b .
2.0
= o.s .
.
• u = z.u
.
.
~~~..~=_~
~"~*"
~ "
""~ " - - " ' ~ - ~ : ~
<:>.;~./...~""--
"
~
o" .
0.4 ~-~.'.~j"~h
~..../.y// .
.
.
.
-.~ 0.6 -
0.8
-
. . / /
II
J."
~#,/~
~_.~s.-=-~.->~"
~ -
q°
- - -
....~'.'.'~""
=~'"=~"
ut Prestress t s (tTp - ~ =0.0) -)
~
.// / y
---- - . -
O. I
o.s
1.0 . . Prestrlss (Tp" = 0.3)
................
h
- - - _
o,ol r
. . . .
1.0
------
1.0 Fig.
4. S e t t l e m e n t ~ l i s t a n c e profiles - - effect o f prestressing for various load intensities.
more membrane effect is felt, more prestress is required in the geosynthetic reinforcement to obtain a particular reduction in the settlement as compared to stiff soils. The effect of prestressing on the settlement behaviour of geosyntheticreinforced soil for various values of nondimensionalised width of the reinforced zone is shown in Fig. 5. It is noticed that the improvement in settlement characteristics at any location within the loaded footing due to prestress in the reinforcement increases with increase in width of the reinforced zone up to L/B = 2.0 but further increase in the values of L/B brings no significant improvement. For values of L/B of 1-2, 1-6, 2.0 and 2.4 the settlement reductions at the centre of footing due to prestress (T~ = 0.3) are respectively 5-62, 8.14, 9-76 and 10.19%. Hence it is not very beneficial to extend the width of the reinforced zone beyond 2B on either side of the centre of footing. Madhav and Poorooshasb's (1988) results exhibit a very similar trend for the case when there is no prestress in the geosynthetic reinforcement. The effect of prestress in the geosynthetic reinforcement on the settlement~listance profiles of geosynthetic-reinforced soil for various values o f the nondimensionalised shear parameter of a granular layer is shown in Fig. 6. It is observed that, due to prestress, settlement improves significantly within the loaded footing for lower values of the shear parameter. For values of the shear parameter of 0.01, 0.1, 0.5 and 1.0 the settlement reductions at the centre of the footing, due to prestress (T~ - 0.3), are respectively 14.64, 11-69, 6.88 and 5.18%. This indicates that prestressing the geosynthetic reinforcement might be an effective tool for further
540
Sanjay Kumar Shukla, Sarvesh Chandra Distance from Centre of Loading, X 00
0.2
0.4
0.6
0.8
1.0
1.2
1./-,
1.6
1.8
2.0
2.2
I
I
I
]
I
I
I
1
I
I
I
Gt ~ , Gb~ = 0.2
...-.-'"
P t = P b = 0.5 qi, • 0 5
0.2
2.l,
.......................
. ~ ~ ' - - - - ' ~ ~'~'-"~ ....
"Ill7
0.4
-d
~...~-~f.rp4""
¢'~- 0.6
.i.,,
= L ; ~ - ~ ;-~-'" ...---S~'--
U'I
. . . . . .
0.8
.
""'- "
.
Without
--.--
~
.
................ With Prestress . ....... .
(Tp =0.01
Prestress
.
.
.
. . . .
2;0 2X., (Tp ~= 1,2
0.3)
16
2.0 2.'-
1.0
Fig. 5. Settlement-distance profiles - - effect of prestressing for various widths of reinforced zone.
00
Distance from Centre of Loading, X 0.4 0.6 0.8 1.0 1.2 1.4 1.6
0.2 I
I
1
I
I
0.4
--"
~
7~ . . .-:7~T.. . .'. . ; ~
.............
": .........
~
........--'j-
~
m
m
I __ " i
....... - - -
~
~" "
.....--
.
7
i"" -"
1
/ I
,,,
0
t P r e s t r j i s s (To%0.O)
.
ooi
.
.
.
--.-.............
Oi I
o.s 1.0
. . . . . . .
0.8-
2.0
I
. . . . -----:
-
. . . . . . .
_.~ 0.6
1.8
~.J...~l
/
0.2
C
I
0.01' ....... . . . . . . . .
0.3)
0.1 0.5 1.0
1.01 Fig. 6. Settlement~distance profiles - - effect of prestressing for various shear parameters of granular fill.
reduction in settlement where granular fill of low shear modulus (G) or low thickness ( H = Ht + Hb) due to limited availability of granular material is used. Figure 7 shows the effect of prestressing on the settlement response of geosynthetic-reinforced soil for various values of interface friction coefficient. It is noted that at any location within the loaded region the influence of prestressing is significant for lower values of #t and/or/t b. For
Prestressing and settlement of geosynthetic-reinforced soil
541
Distance from Centre of Loading, X 0I
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
I
I
I
I
I
I
I
I
I
]
..~...------
G~'. % * . o.1 LIB
0.2
. . ~
• 2.0
......___~.
o"
0.4
...~...~t
c
E
0.6
. . . . . . _
0.8
--
..........
----""
~,,.~
....~;~/ ~,~7.//
_........--"'~
,...t~... (r~=0 o)
-- -- - .- -- --
0/ -
E3
-
With Prestress (Tp'= 0.3} :-- :-- - --- _-_ - 0 1 . . . . . . . .
0.5 1.0
1.0
Fig. 7. Settlement~listance profiles - - effect of prestressing for various interface friction
coefficients. values of ,ut /Ab of 0"1, 0"3, 0"5 and 1.0 the settlement reductions at the centre of the footing as a result of prestress (Tp = 0.3) in the reinforcement are respectively 14.96, 13.08, 11.69, and 9.05%. These results are in accordance with the fact that the mobilised tension in the reinforcement is more for higher values of interface friction coefficient. It can be concluded that, if the geosynthetic layer is placed directly on the soft soil, prestressing will be more effective in settlement reduction, compared to the case when it is placed inside the granular flU, because of the lower interface friction coefficient below the geosynthetic layer in the former case. The effect of prestressing on the mobilised tensile force distribution is shown in Fig. 8. It is noticed that prestressing affects the mobilisation of tensile force in the geosynthetic reinforcement. With the increase in prestress (Tp) mobilised tensile force (T*) in the geosynthetic reinforcement increases at all locations but the increase is relatively more near the edge of the loaded footing. The mobilised tensile force at x/B = 2.0 has been assumed to be zero for simplicity. =
CONCLUSIONS On the basis of the results and discussions presented in the previous section, the following general conclusions can be drawn. (i)
Improvement in the settlement response increases with the increase in prestress in the geosynthetic reinforcement within the loaded
542
Sanjay Kumar Shukla, Sarvesh Chandra Distance from Centre of Loading, X
\ o"
0.8
0.2 0.4 I I
0.6
0.8
1.0
1.2
1.4
1.6
1.8
I
I
I
I
I
I
I
":' ¢-
.9 0.6 r'. I,,-
0z. r 0
x
0.2
w',t:qtor'"r"" With Prestress 1"P~
~'e,,&.
~'~... ~
2.0
• 0.01 ..
• 0.1
~.
................ 0.3 " ~
~:.,. ~"-. ~ : .
6t"
= Gb~ = 0.05
~t
= ~b • o.s
L / B = 2.0 q ~ = 0.5
.~':
Fig. 8. Mobilised tensile force distribution -- effect of prestressing.
(ii)
(iii)
(iv)
(v)
footing and is most significant at the centre of the loaded footing which reduces differential settlement. On soft soils or at higher load intensities more prestress is required in the geosynthetic reinforcement to achieve a particular settlement reduction compared with stiff soils or lower load intensities. Influence of prestressing increases with the increase in width ( = 2L) of the reinforced zone up to L I B = 2.0. Beyond this width there is no significant improvement in the settlement characteristics. Effect of prestressing is significant at lower values of shear parameter of granular fill and interface friction coefficients at top and bottom of geosynthetic reinforcement. Mobilised tensile force in the geosynthetic layer increases at all locations with the increase in prestress but the increase is relatively more near the edge of the loaded footing.
REFERENCES Aboshi, H. (1984). Soil improvement techniques in Japan. In Proc. of Seminar on Soil Improvement and Construction Techniques in Soft Ground, Singapore, pp. 3-16. Andrawes, K. Z., McGown, A., Wilson-Fahmy, R. F. & Mashhour, M. M. (1982). The finite element method of analysis applied to soil-geotextile systems. In Proc. of Second lnt. Conf. of Geotextiles, Las Vegas, USA, Vol. 3, pp. 695-700.
Prestressing and settlement of geosynthetic-reinforced soil
543
Broms, B. B. (1987). Stabilization of very soft clay using geofabric. Geotext. & Geomembr., 5, 17-28. Giroud, J. P. & Noiray, L. (1981). Geotextile-reinforced unpaved road design. J. Geotech. Engng Div., ASCE, 107(9), 1233-54. Guido, V. A., Biesiadecki, G. L. & Sullivan, M. J. (1985). Bearing capacity of a geotextile-reinforced foundation. In Proc. of llth Int. Conf. on SMFE, San Francisco, Vol. 3, pp. 1777-80. Hausmann, M. R. (1990). Engineering Principles of Ground Modification. McGraw-Hill, New York. Horvath, J. S. Historical review of subgrade models. Geotechnique (in press). Kerr, A. D. (1964). Elastic and viscoelastic foundation models. J. Appl. Mech., ASME, 31,491-8. Koerner, R. M. (1990). Designing with Geosynthetics, 2nd edn. Prentice Hall, Englewood Cliffs, N J, USA. Madhav, M. R. & Poorooshasb, H. B. (1988). A new model for geosyntheticreinforced soil. Computers & Geotechnics, 6, 277-90. Milligan, G. W. E. & Love, J. P. (1984). Model testing of geogrids under an aggregate layer in soft ground. In Proc. Symp. Polym. Grid Reinforcement in Civil Engng, ICE, London, Paper No. 4.2. Poorooshasb, H. B. (1989). Analysis of geosynthetic-reinforced soil using a simple transform function. Computers & Geotechnics, 8, 289-309. Rowe, R. K. & Soderman, K. L. (1987). Stabilization of very soft soils using high strength geosynthetics: the role of finite element analyses. Geotext. & Geomembr., 6, 53-80. Selvadurai, A. P. S. (1979). Elastic Analysis of Soil-Foundation Interaction. Elsevier, Amsterdam, pp. 13-42. Watary, Y. (1984). Reclamation with clayey soils and method of earth spreading on the surface. In Proc. of Seminar on Soil Improvement and Construction Techniques in Soft Ground, Singapore, pp. 103-19.
Geotextiles and Geomembranes
ELSEVIER
The Effect of Prestressing on the Settlement Characteristics of Geosynthetic-Reinforced Soil
Sanjay Kumar Shukla & Sarvesh Chandra Department of Civil Engineering, Indian Institute of Technology, Kanpur 208016, I n d i a (Received 22 December 1993; accepted 4 February 1994)
ABSTRACT In this paper, the effect of prestressing the geosynthetic reinforcement on the settlement behaviour of geosynthetic-reinforeed granular fill-soft soil system is studied. The foundation model element proposed by Madhav and Poorooshasb (Computers & Geotechnics, 6, 277-90, 1988), which has a rough membrane embedded in a granular layer, has been modified to include the prestressing effect in the geosynthetic reinforcement. Parametric studies reveal that the settlement reductions within the loaded region are observed even for low prestress in the reinforcement. It is concluded that prestressing the geosynthetic reinforcement is a significant ground improvement technique to enhance the settlement characteristics of the soft soils where the membrane effect of reinforcement is felt.
NOTATION B
Gb Gb at
Gt
Ht Hb
Half width of strip footing (m) Shear modulus of granular fill below reinforcement (kN/m 2) Nondimensionalised shear parameter of granular fill below reinforcement Shear modulus of granular fill above reinforcement (kN/m 2) Nondimensionalised shear parameter of granular fill above reinforcement Thickness of granular fill above reinforcement (m) Thickness of granular fill below reinforcement (m) 531
532
i ks L q q*
T T*
Tp Tp w
W x
X
0 ]At Pb
Sanjay Kumar Shukla, Sarvesh Chandra
Subscript referring to a nodal point Modulus of subgrade reaction for soft soil (kN/m 3) Half width of reinforced zone (m) Applied load intensity (kN/m 2) Nondimensionalised applied load intensity Mobilised tensile force in the reinforcement (kN/m) Nondimensionalised mobilised tensile force in the reinforcement Prestress in the reinforcement (kN/m) Nondimensionalised prestress in the reinforcement Vertical surface displacement (m) Nondimensionalised vertical surface displacement Distance from the centre of footing along x-axis (m) Nondimensionalised distance from the centre of footing along x-axis Slope of the surface deformation profile (degrees) Interfacial friction coefficient at the top of reinforcement Interfacial friction coefficient at the bottom of reinforcement
INTRODUCTION The use of geosynthetics, mainly geotextiles and geogrids, to reinforce soft soil in order to improve its bearing capacity and settlement characteristics is becoming increasingly popular in present-day geotechnical engineering. It has now been well established that geosynthetics, particularly geotextiles, show their beneficial effects only after relatively large settlements (Andrawes et al., 1982; Milligan & Love, 1984; Guido et al., 1985; Rowe & Soderman, 1987; Madhav & Poorooshasb, 1988; Poorooshasb, 1989) which may not be a desirable feature for shallow footings, paved and unpaved roads, and embankments. Andrawes et al. (1982) reported measured and predicted data from which they concluded that the influence of the geotextile on the loadsettlement behaviour of the strip footing on sand is very limited up to settlements equal to approximately 8% of the footing breadth. This suggests that up to that level of settlement, strains in the soil are insufficient to mobilise significant tensile load in the geotextile. From large-scale laboratory tests, Milligan and Love (1984) showed that there is a marked improvement in load-carrying capacity with a geogrid at high deformation and only nominal beneficial effect at low deformation. Poorooshasb (1989) found that at lower settlement level (less than 2.5 cm) the presence of geogrids had no effect at all. Hence there is a need for a technique which can make geosynthetics more beneficial without the occurrence of large settlements. It was thought that
Prestressing and settlement of geosynthetic-reinforced soil
533
prestressing the geosynthetics might have improved the settlement characteristics significantly. The idea of prestressing has been recognised in the recent past. Aboshi (1984) and Watary (1984) described a method to stabilise very soft clay, developed in Japan called 'Rope sheet method' in which the ropes are preloaded to 0-5-0.6 kN in order to increase their effectiveness. For stabilisation of very soft clay using geotextile, Broms (1987) has suggested that the geotextile should be stretched as much as possible before the stabilising berms are placed along the perimeter of the geotextile sheet in order to limit the penetration required to develop the necessary tension in the geotextile. Koerner (1990) expressed the view that a method of prestressing the geotextile would be a significant step forward in ground improvement. Hausmann (1990), while developing construction guidelines for geotextile applications in various geotechnical constructions, pointed out that simple procedures such as pretensioning the geotextile might enhance the reinforcement function in some applications. From the available literature, it can be observed that very little study has been carried out on the prestressing of geosynthetics and its effect on settlement characteristics. Most of the earlier workers have realised the importance of prestressing the geotextile but analytical work is scarce. In this paper the effect of prestressing has been included in the existing foundation model element, the rough membrane proposed by Madhav and Poorooshasb (1988), to represent the response of a prestressed geosynthetic. Using this foundation model element, a model for prestressed geosynthetic-reinforced soil is proposed. The parametric studies were carried out to determine the effect of prestressing on settlement characteristics over a wide range of parameters. MODELS FOR G E O S Y N T H E T I C - R E I N F O R C E D SOIL There are several physical models e.g. Winkler, Filonenko-Borodich, Pasternak, etc. (see Kerr (1964), Selvadurai (1979) and Horvath (in press)) available to represent the behaviour of soils as subgrades. Kerr (1964), Selvadurai (1979) and Horvath (in press) present excellent surveys of the existing foundation models for soils but very few physical foundation models are available for the geosynthetic-reinforced soils. One of the widely used models is that proposed by Madhav and Poorooshasb (1988) for a geosynthetic-granular fill-soft soil system (Fig. 1). The response function of the model is dZw
ks w - (Gt Ht h- Tcos0 + Gb Hb) ~X~X 2=
q(x)
(1)
Sanjay Kumar Shukla, Sarvesh Chandra
534
Parternak
c
Fig. 1. Definition
Shear
Rough Membrane
sketch - foundation model for geosynthetic-granular system. (From Madhav & Poorooshasb, 1988.)
fill-soft
soil
where q is the applied load intensity; G, Ht and GbHb are respectively shear parameters for the soil above and below the membrane; k, is modulus of subgrade reaction for the soft soil; T is the tensile force per unit length mobilised in the membrane; 0 is the slope of the surface deformation profile with respect to the x-axis; and w is the vertical surface displacement. The expression for the variation of the mobilised tension in the membrane with its length measured from the centre of footing is dT - = - (pLtset 0 + sin 0) dx
- (p,, set 0 - sin 0) >
where ,&qand PU,are respectively the interfacial top and bottom of the membrane.
A M6DEL
(2)
friction
coefficients
at the
FOR PRESTRESSED GEOSYNTHETICREINFORCED SOIL
The membrane used in the model proposed by Madhav and Poorooshasb (1988) is a rough elastic one while, the Filonenko-Borodich model uses a thin smooth elastic membrane under a constant tension in all horizontal directions to achieve the continuity between the individual springs in the Winkler model. In the present paper these two foundation model elements have been combined into one as a stretched rough elustic membrane to idealise the behaviour of a prestressed geosynthetic. Further stretching of the membrane may occur because of the tension mobilised
Prestressing and settlement of geosynthetic-reinforced soil
~
q
14
~
2B
=1
/
[ Ht T IIILIIIIIlllllll'rlll
T
~ S t (. • <~ ~> ~.~
r e • <~ ~
t < <~ ~.~
c < <~ ~,
r/F~r~/[
~ <" ~_~
T Ht
I ~ B .-hi I"-1"T'I-1 q It • • • •
Tp I
h e d Rough ..t2 <~ Etastic Membrane <. (Prestressed Geosynthetic ~_~ Layer} I
~ ~ ~ ~ ~
( <" ~, ,~
~ - Pasternak Shear Layer (Granul.ar Fitt) T
<" < ' ~ W i n k t o r Springs ~.~_ (Soft Soi[)
r[ / / I t / / ~ [ r r
(a)
///
i I [
x ~
535
Prestressed
/Geosynthetic Layer
TopGranulorLayer(Gtl/(pt,Pb,Tp) o,,o
o....
,or
Soft Soil
(ks)
~///1//////////[/t///]//I
(b)
Fig. 2. Definition sketch, (a) foundation model proposed for prestressed geosyntheticreinforced granular fill-soft soil system, (b) foundation system analysed. by the transference of shear resistance acting at the top and bottom of the geosynthetic reinforcement. Hence the load coming from the structure is distributed on a wider area without causing excessive settlement, resulting in reduction of subgrade stress which also occurs because of sharing the load by the membrane through structural action commonly called membrane effect as explained by Giroud and Noiray (1981). Combining the modified foundation model element with Winkler springs and Pasternak shear layer representing respectively soft soil and granular fill, a foundation model is proposed to represent the response of a granular fill-prestressed geosynthetic-soft soil system (Fig. 2(a)). Considering equilibrium of the fill and reinforcement elements the response function of the model is derived as: k s w - {GtHt + ( T +
d2 W Tp)cOs 0 + GbOb} ~ ----q(x)
(3)
where Tp is the pretension per unit length applied to the geosynthetic reinforcement. For no prestressing the present model reduces to the model proposed by Madhav and Poorooshasb (1988) whereas for a stretched smooth membrane and no shear layer this model reduces to the Filonenko--Borodich model. Pasternak and Winkler models are also particular cases of the present model. The expression for variation of the mobilised tension in the reinforcement remains the same as eqn (2). M E T H O D OF ANALYSIS The basic eqns (2) and (3), governing the response of the present model, are coupled and solved by a nondimensionalised finite difference scheme, iteratively, in a convenient way. Nondimensionalising with
536
Sanjay Kumar Shukla, Sarvesh Chandra
X = x/B, W = w/B, G t = Gt Ht/ks B 2, G b =- Gb Hb/ks B 2,
q* = q/ks B, T* = T/ks B 2 and Tp = Tp/ks B 2,
eqns (2) and (3) become
(q*+G~ d2W d X Z J - (#b sec 0 -- sin 0)
dr*_dX
(Ptsec0+sin0)
(
.d2W )
(4)
W -- G b -d-~
and d 2 W q, W - {G t + ( T * + Tp)COsO+G;} d X 2 --
(5)
Writing eqns (4) and (5) in finite difference terms leads to T 1 =T~+ l + A X/2 {
*
sec 0i + sin 0i) (d2W i
(q~+qi+l)+Gt \~--/
d2W +d-X-2-
i+l
)}+(#bsec0i_sin0i)
(d2W d2W { ( W i + W i + , ) - G ~ , k d X 2 i+~-~-~ i + , ) } ]
(6)
and Wi-{a~+(r;+Tp)COsOi+6~,}"
{
Wi_,
2Wi + Wi+, (AX)2
}
= qi
(7)
Values of sin 0i, cos 0i & sec 0i at each node along x-axis in eqns (6) and (7) are obtained from tan0i = d W / d X l i . In order to minimise the numerical error, average values of q*, W and d 2 W / d X z for each element are taken in eqn (6). Solutions are obtained for a uniformly loaded flexible strip footing. Loading conditions
The loading conditions considered are q~ (X) = q*
for IX[ < 1.0
(8a)
=0-0
for I X I > 1.0
(8b)
Prestressing and settlement of geosynthetie-rein['orced soil
537
Boundary conditions Boundary conditions considered at the centre and at the edge of the reinforcement/shear layer are
dW/dX = 0-0 for X = 0.0 & LIB
(9a)
and T*=0.0
forX=L/B
(9b)
The first boundary condition comes directly from the symmetry of the problem about the centre of the loaded footing. The second boundary condition comes from the fact that the prestressed geosynthetic layer is generally fixed at its edge either by placing stabilising berms on it (Broms, 1987) or by anchoring it in trenches or sometimes by folding it back. The third boundary condition is an assumption for simplicity because the mobilised tensile force at the edge of the reinforcement is very small. To solve eqns (6) and (7) a set of values for Wi along the x-axis are assumed initially. New values of Ti are obtained from eqn (6) and substituted into eqn (7) from which a new set of values of Wi is obtained. The iteration is continued until the change in the current estimate of the displacement is small enough, that is, within the convergence tolerance as specified.
RESULTS A N D DISCUSSIONS A computer program, based on the formulation as described above, was developed and the results were obtained using HP 9000/850 computer system. Due to the symmetry of the problem analysed, only half the region of the problem (x >I 0) is considered (Fig. 2(b)). The solutions were obtained with a convergence criterion of 0.0001. For simplicity, the nondimensionalised settlement W, mobilised tension T*, and prestress T*p' were normalised with respect to applied nondimensionalised load, q*. The ranges of parameters studied are: • • • • •
Prestress in the geosynthetic reinforcement, Tp. 0.0-l.0 Load intensity, q*: 0.01-1.0 Width of reinforced zone, L/B: 1-0-2.5 Shear modulus of granular fill, G t or Gb: 0.0-1.0 Interface friction coefficient, Pt or Pb: 0-0-1.0
Figure 3 shows the settlement response of a prestressed geosyntheticreinforced soil for several values of prestress and compares the results with
538
Sanjay Kumar Shukla, Sarvesh Chandra Distance f r o m Centre of L o a d i n g , X 01
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
I
I
I
I
J
I
I
I
I
Gt*'=
Gb ~=
0.1
"
~'-...~'~
2.0
- ~
0.2
L / e = 2.0 q "--0.5 "-
L
j,~.
".,~.~..-.-~-~.-.
.~.jl~'~ ' ~ "
0.4 .........
-
~ 0.6 ...... ~ ...... ~j.-~"E
.
.
-
.
.
-
-
...... .....P r Q
-
~
s
~
e
-
n
t
.......
1.0
~,,.,t.;~'nok
.......
------'-. . . . . . . .
.....
~-~;~ Poorooshosb Study Tp *
0.01 0.05 0.1 0.3 0.5
1.0
12 Fig. 3. Settlement~listance profiles effect of prestressing compared with existing foundation models.
those obtained using the model of Madhav and Poorooshasb (1988) for granular fill-geosynthetic-soft soil system and with Winkler and Pasternak models for general soil behaviour. It is observed that the settlement within the loaded region (X ~< 1.0) reduces as the prestress in the geosynthetic layer is increased but there is an increase in settlement slightly beyond the loaded region. The settlement reductions for nondimensionalised prestress values of 0.01, 0.05, 0.1, 0.3, 0.5, and 1.0, compared with no prestressing (Madhav & Poorooshasb, 1988) are respectively 0.55, 2.48, 4-54, 11.69, 17.33 and 27.65% at the centre of the footing whereas at the edge of the footing reductions are 0-00, 0.00, 0-00, 1.15, 3.23 and 9.24%. This indicates that the reductions in the settlements at the centre of the footing due to prestressing is more significant than at the edge of the footing. Thus the differential settlement of the loaded footing is reduced as a result of prestressing the geosynthetic reinforcement. Figure 4 shows the effect of prestressing the geosynthetic reinforcement on the settlement-distance profiles of geosynthetic-reinforced soil for various nondimensionalised load intensities. It is noted that at any location within the loaded footing, settlement reduction due to prestress (Tp -- 0.3) is more for lower values of q*. As q* increases from 0.01 to 1.0 the settlement reduction at the centre of the footing reduces from 15.91 to 9.05%. Hence it can be concluded that to achieve a particular reduction in the settlement, less prestress in the geosynthetic reinforcement is required for lower nondimensionalised load intensities as compared to higher load intensities. This conclusion indicates that in the case of soft soils where
Prestressing and settlement o f geosynthetic-reinforced soil
539
Distance f r o m Centre of L o a d i n g , X 0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
I
I
I
I
I
I
I
J
I
Gt" = S ; ~t
0.2
-/
=0.1
• ~b .
2.0
= o.s .
.
• u = z.u
.
.
~~~..~=_~
~"~*"
~ "
""~ " - - " ' ~ - ~ : ~
<:>.;~./...~""--
"
~
o" .
0.4 ~-~.'.~j"~h
~..../.y// .
.
.
.
-.~ 0.6 -
0.8
-
. . / /
II
J."
~#,/~
~_.~s.-=-~.->~"
~ -
q°
- - -
....~'.'.'~""
=~'"=~"
ut Prestress t s (tTp - ~ =0.0) -)
~
.// / y
---- - . -
O. I
o.s
1.0 . . Prestrlss (Tp" = 0.3)
................
h
- - - _
o,ol r
. . . .
1.0
------
1.0 Fig.
4. S e t t l e m e n t ~ l i s t a n c e profiles - - effect o f prestressing for various load intensities.
more membrane effect is felt, more prestress is required in the geosynthetic reinforcement to obtain a particular reduction in the settlement as compared to stiff soils. The effect of prestressing on the settlement behaviour of geosyntheticreinforced soil for various values of nondimensionalised width of the reinforced zone is shown in Fig. 5. It is noticed that the improvement in settlement characteristics at any location within the loaded footing due to prestress in the reinforcement increases with increase in width of the reinforced zone up to L/B = 2.0 but further increase in the values of L/B brings no significant improvement. For values of L/B of 1-2, 1-6, 2.0 and 2.4 the settlement reductions at the centre of footing due to prestress (T~ = 0.3) are respectively 5-62, 8.14, 9-76 and 10.19%. Hence it is not very beneficial to extend the width of the reinforced zone beyond 2B on either side of the centre of footing. Madhav and Poorooshasb's (1988) results exhibit a very similar trend for the case when there is no prestress in the geosynthetic reinforcement. The effect of prestress in the geosynthetic reinforcement on the settlement~listance profiles of geosynthetic-reinforced soil for various values o f the nondimensionalised shear parameter of a granular layer is shown in Fig. 6. It is observed that, due to prestress, settlement improves significantly within the loaded footing for lower values of the shear parameter. For values of the shear parameter of 0.01, 0.1, 0.5 and 1.0 the settlement reductions at the centre of the footing, due to prestress (T~ - 0.3), are respectively 14.64, 11-69, 6.88 and 5.18%. This indicates that prestressing the geosynthetic reinforcement might be an effective tool for further
540
Sanjay Kumar Shukla, Sarvesh Chandra Distance from Centre of Loading, X 00
0.2
0.4
0.6
0.8
1.0
1.2
1./-,
1.6
1.8
2.0
2.2
I
I
I
]
I
I
I
1
I
I
I
Gt ~ , Gb~ = 0.2
...-.-'"
P t = P b = 0.5 qi, • 0 5
0.2
2.l,
.......................
. ~ ~ ' - - - - ' ~ ~'~'-"~ ....
"Ill7
0.4
-d
~...~-~f.rp4""
¢'~- 0.6
.i.,,
= L ; ~ - ~ ;-~-'" ...---S~'--
U'I
. . . . . .
0.8
.
""'- "
.
Without
--.--
~
.
................ With Prestress . ....... .
(Tp =0.01
Prestress
.
.
.
. . . .
2;0 2X., (Tp ~= 1,2
0.3)
16
2.0 2.'-
1.0
Fig. 5. Settlement-distance profiles - - effect of prestressing for various widths of reinforced zone.
00
Distance from Centre of Loading, X 0.4 0.6 0.8 1.0 1.2 1.4 1.6
0.2 I
I
1
I
I
0.4
--"
~
7~ . . .-:7~T.. . .'. . ; ~
.............
": .........
~
........--'j-
~
m
m
I __ " i
....... - - -
~
~" "
.....--
.
7
i"" -"
1
/ I
,,,
0
t P r e s t r j i s s (To%0.O)
.
ooi
.
.
.
--.-.............
Oi I
o.s 1.0
. . . . . . .
0.8-
2.0
I
. . . . -----:
-
. . . . . . .
_.~ 0.6
1.8
~.J...~l
/
0.2
C
I
0.01' ....... . . . . . . . .
0.3)
0.1 0.5 1.0
1.01 Fig. 6. Settlement~distance profiles - - effect of prestressing for various shear parameters of granular fill.
reduction in settlement where granular fill of low shear modulus (G) or low thickness ( H = Ht + Hb) due to limited availability of granular material is used. Figure 7 shows the effect of prestressing on the settlement response of geosynthetic-reinforced soil for various values of interface friction coefficient. It is noted that at any location within the loaded region the influence of prestressing is significant for lower values of #t and/or/t b. For
Prestressing and settlement of geosynthetic-reinforced soil
541
Distance from Centre of Loading, X 0I
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
I
I
I
I
I
I
I
I
I
]
..~...------
G~'. % * . o.1 LIB
0.2
. . ~
• 2.0
......___~.
o"
0.4
...~...~t
c
E
0.6
. . . . . . _
0.8
--
..........
----""
~,,.~
....~;~/ ~,~7.//
_........--"'~
,...t~... (r~=0 o)
-- -- - .- -- --
0/ -
E3
-
With Prestress (Tp'= 0.3} :-- :-- - --- _-_ - 0 1 . . . . . . . .
0.5 1.0
1.0
Fig. 7. Settlement~listance profiles - - effect of prestressing for various interface friction
coefficients. values of ,ut /Ab of 0"1, 0"3, 0"5 and 1.0 the settlement reductions at the centre of the footing as a result of prestress (Tp = 0.3) in the reinforcement are respectively 14.96, 13.08, 11.69, and 9.05%. These results are in accordance with the fact that the mobilised tension in the reinforcement is more for higher values of interface friction coefficient. It can be concluded that, if the geosynthetic layer is placed directly on the soft soil, prestressing will be more effective in settlement reduction, compared to the case when it is placed inside the granular flU, because of the lower interface friction coefficient below the geosynthetic layer in the former case. The effect of prestressing on the mobilised tensile force distribution is shown in Fig. 8. It is noticed that prestressing affects the mobilisation of tensile force in the geosynthetic reinforcement. With the increase in prestress (Tp) mobilised tensile force (T*) in the geosynthetic reinforcement increases at all locations but the increase is relatively more near the edge of the loaded footing. The mobilised tensile force at x/B = 2.0 has been assumed to be zero for simplicity. =
CONCLUSIONS On the basis of the results and discussions presented in the previous section, the following general conclusions can be drawn. (i)
Improvement in the settlement response increases with the increase in prestress in the geosynthetic reinforcement within the loaded
542
Sanjay Kumar Shukla, Sarvesh Chandra Distance from Centre of Loading, X
\ o"
0.8
0.2 0.4 I I
0.6
0.8
1.0
1.2
1.4
1.6
1.8
I
I
I
I
I
I
I
":' ¢-
.9 0.6 r'. I,,-
0z. r 0
x
0.2
w',t:qtor'"r"" With Prestress 1"P~
~'e,,&.
~'~... ~
2.0
• 0.01 ..
• 0.1
~.
................ 0.3 " ~
~:.,. ~"-. ~ : .
6t"
= Gb~ = 0.05
~t
= ~b • o.s
L / B = 2.0 q ~ = 0.5
.~':
Fig. 8. Mobilised tensile force distribution -- effect of prestressing.
(ii)
(iii)
(iv)
(v)
footing and is most significant at the centre of the loaded footing which reduces differential settlement. On soft soils or at higher load intensities more prestress is required in the geosynthetic reinforcement to achieve a particular settlement reduction compared with stiff soils or lower load intensities. Influence of prestressing increases with the increase in width ( = 2L) of the reinforced zone up to L I B = 2.0. Beyond this width there is no significant improvement in the settlement characteristics. Effect of prestressing is significant at lower values of shear parameter of granular fill and interface friction coefficients at top and bottom of geosynthetic reinforcement. Mobilised tensile force in the geosynthetic layer increases at all locations with the increase in prestress but the increase is relatively more near the edge of the loaded footing.
REFERENCES Aboshi, H. (1984). Soil improvement techniques in Japan. In Proc. of Seminar on Soil Improvement and Construction Techniques in Soft Ground, Singapore, pp. 3-16. Andrawes, K. Z., McGown, A., Wilson-Fahmy, R. F. & Mashhour, M. M. (1982). The finite element method of analysis applied to soil-geotextile systems. In Proc. of Second lnt. Conf. of Geotextiles, Las Vegas, USA, Vol. 3, pp. 695-700.
Prestressing and settlement of geosynthetic-reinforced soil
543
Broms, B. B. (1987). Stabilization of very soft clay using geofabric. Geotext. & Geomembr., 5, 17-28. Giroud, J. P. & Noiray, L. (1981). Geotextile-reinforced unpaved road design. J. Geotech. Engng Div., ASCE, 107(9), 1233-54. Guido, V. A., Biesiadecki, G. L. & Sullivan, M. J. (1985). Bearing capacity of a geotextile-reinforced foundation. In Proc. of llth Int. Conf. on SMFE, San Francisco, Vol. 3, pp. 1777-80. Hausmann, M. R. (1990). Engineering Principles of Ground Modification. McGraw-Hill, New York. Horvath, J. S. Historical review of subgrade models. Geotechnique (in press). Kerr, A. D. (1964). Elastic and viscoelastic foundation models. J. Appl. Mech., ASME, 31,491-8. Koerner, R. M. (1990). Designing with Geosynthetics, 2nd edn. Prentice Hall, Englewood Cliffs, N J, USA. Madhav, M. R. & Poorooshasb, H. B. (1988). A new model for geosyntheticreinforced soil. Computers & Geotechnics, 6, 277-90. Milligan, G. W. E. & Love, J. P. (1984). Model testing of geogrids under an aggregate layer in soft ground. In Proc. Symp. Polym. Grid Reinforcement in Civil Engng, ICE, London, Paper No. 4.2. Poorooshasb, H. B. (1989). Analysis of geosynthetic-reinforced soil using a simple transform function. Computers & Geotechnics, 8, 289-309. Rowe, R. K. & Soderman, K. L. (1987). Stabilization of very soft soils using high strength geosynthetics: the role of finite element analyses. Geotext. & Geomembr., 6, 53-80. Selvadurai, A. P. S. (1979). Elastic Analysis of Soil-Foundation Interaction. Elsevier, Amsterdam, pp. 13-42. Watary, Y. (1984). Reclamation with clayey soils and method of earth spreading on the surface. In Proc. of Seminar on Soil Improvement and Construction Techniques in Soft Ground, Singapore, pp. 103-19.