The Mechanics of Reinforced Embankments on Soft Soils* PDF

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Geotextiles and Geomembranes 7 (1988) 237-273 The Mechanics of Reinforced Embankments on Soft Soils* R. A. Jewell University of Oxford, Department of Engineering Science, Parks Road, Oxford OX1 3PJ, UK (Received 9 June 1988; accepted 20 July 1988) A BSTRA CT The mechanics of reinforced embankments o...

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Geotextiles and Geomembranes 7 (1988) 237-273

The Mechanics of Reinforced Embankments on Soft Soils* R. A. Jewell University of Oxford, Department of Engineering Science, Parks Road, Oxford OX1 3PJ, UK (Received 9 June 1988; accepted 20 July 1988)

A BSTRA CT The mechanics of reinforced embankments on soft foundation soils are examined to try to establish appropriate methods for their analysis and design. The focus is the bearing capacity of the foundation under the combined vertical and shear loading derived from the embankment fill. Lower bound plasticity solutions exist for this case, and indicate the magnitude of the reduction in bearing capacity due to outward shear stresses, compared to the 'smooth' case, and the improvement due to inward shear stresses. The improvement is greatest for soil with strength increasing with depth, or relatively thin layers of soft soil. The action of the reinforcement can be described in terms of the reinforcement firstly acting to carry the outward shear stresses generated by the embankment fill, and secondly providing inward shear stresses to restrain the foundation soil from lateral displacement. The slip circle analysis for an embankment on soft soil can now be examined using the plasticity solutions as the benchmark. To calculate foundation stability the slip circle is used only in the foundation, with vertical and shear stresses applied on the foundation surface. In the unreinforced case the outward thrust in the fill must be included for the assessment of overall stability, and it is suggested that the thrust is best calculated directly rather than with the same slip circle used in the foundation carried through the fill. The conclusion is that the slip circle analysis is satisfactory in the case of deep deposits of soil with strength increasing with depth. Where the depth of the soft soil is limited, however, the slip circle analysis appears to overestimate stability and the use of the plasticity solutions as a basis for design is recommended. This paper was delivered at the 'Prediction Symposium on a Reinforced Embankment', King's College, London, September 1986. 237 Geotextiles and Geomembranes 0266-1144/89/$03.50 © 1989 Elsevier Science Publishers Ltd, England. Printed in Great Britain

238

R. A. Jeweil

1 INTRODUCTION There are two separate ways that reinforcement may be used in embankments. Firstly, reinforcement placed across the base of the embankment may improve the bearing conditions in the foundation to allow a higher or steeper embankment to be built. Secondly, reinforcement incorporated in the embankment slope can enable a stable slope to be built steeper than the natural angle of repose of the fill. One major difference in the role of the reinforcement in these two cases is illustrated by Fig. 1. For an embankment on soft soil the reinforcement is only required to maintain stability during construction and during the subsequent consolidation until the shearing resistance of the foundation soil has increased sufficiently to maintain stability without the additional benefit of the reinforcement (Fig. lb). In a steep reinforced slope the reinforcement forces are required to maintain stability throughout the life of the slope (Fig. ld). The design of reinforced embankments on soft soil is discussed in this paper. Emphasis is placed on identifying the mechanics of how the reinforcement acts to improve the foundation bearing capacity and the embankment stability. The aim is to describe clearly the benefit that can be

(a)

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(c)

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(d) .....

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Steep reinforced slope

Fig. 1. For an embankment on soft soil the reinforcement is only required during consolidation--(a) and (b); for a steep slope the reinforcement is required for the full design life--(c) and (d).

The mechanicsof reinforcedembankmentson soft soils

239

gained from reinforcing an embankment on soft soil and to present simple calculations that give the magnitude of the reinforcement force required to gain the benefit. The application of slip circle analysis is described, and compared with the existing plasticity solutions relevant to the embankment on soft soil problem. Simple, approximate dosed form solutions are introduced that represent the mechanics of reinforced embankment behaviour and are useful for initial design studies for both unreinforced and reinforced embankments.

2 IMPROVEMENT OF EMBANKMENT FOUNDATION BEARING CONDITIONS In a reinforced embankment on soft soil the reinforcement is used to improve the bearing capacity of the foundation soil. The stability is most critical at (or immediately following) the end of a stage of construction when the new loading has been applied rapidly with respect to the drainage time in the foundation. The clay foundation soil can only drain, consolidate and improve in strength with time. To improve stability, reinforcement can be placed across the base of the embankment close to the foundation surface as shown in Fig. la. If the stabilising forces of the reinforcement were ignored, the factor of safety on the soil shearing resistance alone would fall to below unity at the end of construction, rising to well above unity as consolidation in the foundation takes place. In other words, the reinforcement is only required to maintain the factor of safety above unity for the reinforced embankment until the clay foundation has consolidated sufficiently to maintain stability without the assistance of the reinforcement (Fig. lb). 2.1 R e i n f o r c e m e n t action

Reinforcement improves the shearing resistance of soil in two separate ways - - b y reducing the forces causing failure - - b y increasing the forces resisting failure. This fundamental action of reinforcement is illustrated in Fig. 2 for a direct shear test on reinforced soil. The reinforcement force PR at an orientation 0 in the soil directly reduces the applied shear loading ~ that the soil must support on the soil shear surface As ~"= Ty~

PasinO A~

(1)

240

R. A. Jewell O'yy I I L,.

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, z/L (b)

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l:y x

r PRsin 8 The effect of reinforcement is twofold: {1) To reduce the stresses causing failure PRsin e 1;=l:yx As 12) To increase the stresses resisting failure PRCOSO O = Gyy + As

Fig. 2. Reinforcement acts by reducing the stresses causing failure and increasing the stresses

resisting failure. T h e reinforcement force also increases the normal effective stress o- on the soil shear surface so that greater frictional shearing resistance may be mobilised cr = O'yxJr

PRcos 0

A-------~

(2)

T h e function of reinforcement at the base of an embankment on soft soil can usefully be described in similar terms of reducing disturbing forces and increasing resisting forces. As will be shown later, for the e m b a n k m e n t on soft soil the reinforcement has first to complete the function of reducing the disturbing forces before it can begin the function of increasing the resisting forces.

2.2 Reduction of embankment disturbing forces T h e main disturbing force for an embankment on soft soil is the vertical self weight loading of the embankment fill on the foundation surface (Fig. 3a).

The mechanics of reinforced embankments on soft soils

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Vertical loading

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241

Outward shear stress

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(c)

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Fig. 3. Illustration of the disturbing forces in an unreinforced embankment and the role of the reinforcement to support the outward disturbing shear stresses.

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0-2 0-4 0-6 0-8 1.0 I/s u Reduced bearing capacity from outward shear stress

Fig. 4. The influence of outward shear stress in reducing the bearing capacity for a surface footing.

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R. A. Jewell

The other significant disturbing force is the outward lateral thrust in the embankment caused by the horizontal stresses in the fill required to maintain local equilibrium under self weight (Fig. 3b). The resulting outward shear stress at the base of the embankment reduces the capacity of the foundation to carry the vertical loading of the embankment fill (Fig. 3c). The influence on foundation beating capacity of combined vertical and shear loading is illustrated in Fig. 4a for a footing on the surface of a uniform deposit of clay with an undrained shear strength s~. The soil resistance to the applied vertical stress q is reduced when an outward shear stress r = ~s~

(3)

acts on the footing. The maximum vertical stress that can be supported is given by the equation q = su

/

1 +-~-+eos-l(fl)+x/(l-/3 2)

/

(4)

derived by the lower bound method of analysis (see, for example, Bolton~). The variation in the ratio q/su with the magnitude of the outward sheafing stress 0 < z/su < 1-0 is plotted in Fig. 410. The results show that the bearing capacity of the soil can be reduced to one half the normal value by the outward shear stress. Reinforcement placed across the full width of the embankment can support the outward shear force, balancing the force from either side of the embankment with a tensile force, as shown in Fig. 3d. If the reinforcement is sufficiently stiff and strong all the lateral thrust in the embankment fill Pau can be counterbalanced by the reinforcement. Any extension in the reinforcement, as it takes up the lateral force exerted by the fill, that results in relative outward deformation with respect to the underlying soil surface would cause some of the lateral force to be transmitted directly to the foundation as an outward shear stress. 2.3 Increase of foundation resisting forces An unreinforced embankment cannot support lateral tensile forces and therefore cannot restrain the foundation soil from displacing laterally under the self weight loading from the embankment fill (Fig. 5a). Restraining the lateral movement at the surface of a foundation can improve the bearing capacity (Fig. 5b). The difference between the unrestrained and the restrained cases is similar to the difference between a smooth foundation and a rough foundation. The two main cases where

The mechanics of reinforced embankments on soft soils (O)

Unreinforced

(b)

243

Reinforced

Lateral displacement

Fig. 5. In an unreinforced embankment (a), there is no restraint against lateral displacement in the foundation. Reinforcement (b) can provide a restraining shear stress on the foundation surface. (a)

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Fig. 6. (a) Restraining shear stress on the surface of a soft clay foundation improves the bearing capacity, where (b) the strength increases with depth, and (c) the depth of the foundation soil is limited. f o o t i n g r o u g h n e s s has an i m p o r t a n t beneficial influence on bearing capacity are: C a s e 1: a f o u n d a t i o n with strength increasing with d e p t h (Fig. 6b) 2 a n d C a s e 2: a f o u n d a t i o n o f limited d e p t h above a strong layer (Fig. 6c) 3 or, i n d e e d , a c o m b i n a t i o n o f these two cases.

244

R. A. Jewell

(a)

2B Rough footing

Smooth footing

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SUO

Su

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(b)

12 Bearing capacity factor Nc

10 8

4

[]Improvement in bearing capacity due to lateral restraint on the foundation

2 0~

0

1

2

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5

Geometric ratio pB

SUO

Fig. 7. The influence of strength increasing with depth on bearing capacity, and the improvement resulting from restraining shear stress at the foundation surface (after Davis & Booker, 2 and Houlsby & Wroth4).

Fortunately, these two cases are typical of the conditions where embankments are constructed on soft soil. The two most common examples are deep deposits of normally consolidated clay, such as in an estuary, and a relatively thin stratum of lightly overconsolidated clay or peat overlying a harder stratum. Results from the plasticity solutions presented by Davis & Booker 2 for surface footings on clay with undrained shear strength increasing with depth are given in Fig. 7b for illustration. The bearing capacity factor No for a surface footing of width 2B on clay with shear strength S~oat the foundation surface and with strength increasing with depth Su = S~o+ pz

(5)

is shown in Fig. 7b. The bearing capacity factor is plotted against a nondimensional expression of the footing width pB/s~oand indicates that where the soil strength increases with depth the rough footing can support more

The mechanics of reinforced embankments on soft soils

245

load t h a n the s m o o t h footing. (Manipulation of the results in Davis & B o o k e r 2 is required to obtain the bearing capacity factors; these factors have b e e n i n d e p e n d e n t l y calculated and published by Houlsby & Wroth.4 ) 2.4 S u m m a r y o f t h e mechanics T h e mechanics of a reinforced e m b a n k m e n t on soft soil can be summarised as follows. A reinforced e m b a n k m e n t on a soft soil foundation is similar to a bearing capacity p r o b l e m with a surface loading. In conventional terms of a footing, an unreinforced e m b a n k m e n t exerts a worse loading on the foundation than a s m o o t h footing because the lateral thrust developed in the e m b a n k m e n t fill creates o u t w a r d shear stress which acts to reduce the bearing capacity of the f o u n d a t i o n (Fig. 8a--c). (O) Unreinforced

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(d) Reinforced

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(f)

Fig. 8. Illustration summarising the mechanics of a reinforced embankment on soft soil. Reinforcement improves stability by: (a) carrying the outward (disturbing) shear stress; and (2) providing inward (resisting) shear stress.

246

R. A. Jewell

The first purpose of the reinforcement is to hold the outward thrust of the embankmentfiU in equilibrium with a tensile force (Fig. 8d). As long as there is no relative outward movement between the reinforcement and the surface of the underlying foundation soil (the movement would be caused by the extension in the reinforcement as it takes up the thrust P~) then the foundation will not have to support any outward shear stress, and the embankment loading would be like a smooth foundation. The reinforcement is acting to reduce the forces causing failure.

The second purpose of the reinforcement is to restrain the surface of the foundation soil against lateral displacement. If the reinforcement bonds well with the foundation surface and is relatively inextensible then the reinforced embankment loading on the foundation is like a rough footing (Fig. 8d-f). For a foundation with strength increasing with depth, or where the depth of the soft soil is limited by a stronger stratum, the restraint at the foundation surface provided by the reinforcement improves the bearing capacity of the foundation and hence the stability of the embankment. The reinforcement is acting to increase the forces resisting failure.

3 CONSTRUCTION RATE AND D R A I N A G E Before considering the stability aspects of reinforced embankment design, the influence of construction rate and enhanced drainage in the foundation need to be mentioned. For an embankment on soft soil the reinforcement is only required to maintain stability until the excess pore water pressures in the foundation caused by the construction have dissipated. Any combination of embankment height and side slope that can be achieved by reinforcing an embankment on soft soil can equally always be achieved by building slowly to minimise the development of excess pore water pressure in the foundation. Slow construction allows the rate of increase of foundation strength to keep pace with the imposed embankment loads. There are many different cases where the use of reinforcement will still be attractive. Three examples are: (1) On very soft ground the reinforcement doubles as a construction expedient preventing local loss or intermixing of the fill and the soft ground, and improving the bearing capacity for earthmoving equipment. (2) In a choice between a reinforced and an unreinforced alternative for an embankment that needs to be built rapidly in a single stage, the reinforced embankment will be cheaper if the cost of the fill saved

The mechanics of reinforced embankments on soft soils

247

exceeds the cost of the reinforcement (which is often the case with current reinforcement prices). (3) For a major embankment on soft soil that will require construction in several stages the reinforced solution may be the most attractive because a higher embankment can be constructed at any stage reducing the number of stages and the construction time. This would apply whether or not any artificial drainage is used in the foundation, but is particularly attractive when combined with foundation drainage.

4 B O U N D S ON T H E R E Q U I R E D R E I N F O R C E M E N T FORCE 4.1 Lateral thrust in the fill

Before the reinforcement can offer any restraint to lateral deformation in the foundation it must first support the lateral thrust in the embankment fill (Fig. 8). Any proportion of the lateral thrust not carried by the reinforcement will be transmitted directly to the surface of the foundation as an outward disturbing force. An embankment on soft soil will naturally settle and spread, so it seems reasonable to estimate the magnitude of the lateral thrust in the embankment from the active earth pressure (Fig. 3a). The lateral thrust from the fill P~n that must be carded by the reinforcement is, for the sim...