Limit analysis of cohesive slopes reinforced with geotextiles

Computers and Geotechnics 7 (1989) 53~6

LIMIT ANALYSIS OF COHESIVE SLOPES REINFORCED WITH GEOTEXTILES

Andrzej Sawicki and Danuta Lesniewska Institute of Hydroengineering,IBW PAN ul.Cystersow 11, 80-953 Gdansk-O1iwa,POLAND

ABSTRACT A method of plastic limit analysis of cohesive slopes reinforced with geotextiles is presented. First, the theoretical model of reinforced cohesive soil is presented, then the formulation of boundary value problems by a method of characteristics described.The bearing capacity of reinforced slopes and the failure surfaces are obtained as the solution to the system of governing equations.The method proposed allows for studying the influence of design parameters, like the unit weight of the soil, the angle of internal friction, cohesion, and the amount of reinforcement, on the stability of reinforced soil structures.

INTRODUCTION

R e i n f o r c e d s o i l i s a c o m p o s i t e m a t e r i a l formed by t h e a s s o c i a t i o n o f granular

fill

geotextiles, be t r e a t e d

and t h e r e i n f o r c e m e n t , which i s geogrids,

etc.

of the

form o f metal

From a m a c r o s c o p i c v i e w p o i n t r e i n f o r c e d

as a homogeneous and a n i s o t r o p i c m a t e r i a l ,

the properties

strips, soil

can

o f which

53

Computers and Geotechnics 0266-352X/89/$03.50 © 1989 Elsevier Science Publishers Ltd, England. Printed in Great Britain

54 depend on t h e p r o p e r t i e s geometrical

arrangement.

p r o p o s e d by S a w i c k i of

a

reinforced

solutions

of t h e

~l]e r i g i d - p l a s t i c

[1],

cohesionless

for cohesionless

with

examples

the

plastic

presented

subsoil

reinforced

further soil

that

respective

see the

soil

proportions

such material

has

and tmen

a

footing.

Some

simple

w a l l s have been o b t a i n e d

of

reinforced with

soil

both

slopes.

weightless

Numerical

and

weighty

slopes. p e r i o d o~ r e i n f o r c e d

[5].

cost

stimulated

reinforced

soil

cohesive fills

application,

locally

available [6].

extensive

structures,

see

materials

is

for using

such

much lower

than

Such w i d e r a p p l i c a t i o n s

research

in

[6-13].

and

can a l s o be u s e d i n r e i n f o r c e d

One of t h e most i m p o r t a n t r e a s o n s of

the cohesive

However, t h e p r a c t i c e

the

A nmnber

field of

of

of r e i n f o r c e d mechanics

proposed

of

models

was

r e v i e w e d by Burd [14]. The aim of t h a t

reinforced rather

soil

assumed

,

and the

reasonable

research

structures,

simple failure

considering quite

by

retaining

deal

cost for imported ones,

have

briefly

soil

paper

r e s e a r c h h a v e shown t h a t

is

soil

of

had n o t b e e n recommended f o r s u c h a u s e .

structures,

soils

loaded

analysis

this

During t h e f i r s t materials

model

relative

S u b s e q u e n t p a p e r of S a w i c k i and L e s n i e w s k a [4]

limit

in

non-cohesive reinforced

their

and t h e n a p p l i e d by K u l c z y k o w s k i [2] t o t h e a n a l y s i s

by S a w i c k i and L e s n i e w s k a [ 3 ] . deals

constituents,

is to provide simple design procedures for

since

most of t h e

approaches

proposed deal

m e c h a n i s m s , i n which t h e s h a p e o f t h e f a i l u r e

the

internal

equilibrium

forces of t h e

predictions,

in

the

failing

structure

soil

mass.

v e r y much s a t i s f a c t o r y

are

with

surface is

calculated

Such models

from t h e

by

can g i v e

view p o i n t

of

designer. We would l i k e t o limit plasticity cohesive slopes load.

contribute

to this

d e v e l o p m e n t by s h o w i n g how t h e

a p p r o a c h can h e l p i n p r e d i c t i n g at

failure,

as well

The a p p r o a c h p r e s e n t e d i n t h i s

as

in the

the slip

lines

determination

paper is rigorous

in reinforced

of t h e

collapse

from t h e view p o i n t

of

applied mechanics.

RIGID-PLASTIC MODEL OF REINFORCED SOIL

Reinforced anisotropic properties the

soil

material,

the

and interactive

reinforcement.

We

is

treated

as

macroscopically

homogeneous

and

g r o s s b e h a v i o u r of which d e p e n d s on t h e m e c h a n i c a l contributions

consider

the

soil

of constituents, unidirectionally

i.e. the soil reinforced,

and the

55 vector n indicating the direction of reinforcement,

see Fig.l. 8 is the angle

between the x axis and the direction of reinforcement. Both constituents of reinforced

soil

are

assumed

to

work

together,

that

is

slippage

at

the

interfaces between the soil and the reinforcement is neglected.

x

Fig.1. Reinforced soil - co-ordinate system.

Three stress tensors are defined at every point of reinforced soil; one tensor of macrostress q and two tensors of microstresses, qs and G r

in

the soil and reinforcement respectively. In indicial notation, these tensors are related by, see [1,4]: a

" 1= [~s ax - ~a°COS20 1

x

a'y

= ~sl [~y

- ~GoSin2e]

Y

,

(i)

G" =!. [Oxy-~aoSinScosO ] , xy W where W

is a volumetric fraction of the soil, ao=WrR, R is a plastic locus

for the

reinforcement

reinforcement,

and

~

in extension, is

a

Wr

parameter

is a volumetric describing

the

fraction behaviour

of the of

reinforcement (~=-i means that the reinforcement works in a plastic state). The soil is assumed to obey the Coulomb-Hohr yield condition:

where H = c/sin~, c denoting cohesion.

the

56

Substitution following

yield

of

Eqs

condition

f =

a x- ~

where Hk= ~ s H

y

(1)

into

expressed

- ~a 0

-

the

yield

in terms

x+ a

condition

- t O O + 2H k

y

(2)

leads

to

the

of macrostresses:

sin2~

+ 4a 2 + xy

for abbreviation.

The associated flow rule is assumed to be valid for the soil:

Oas

j

i

ij

where that

i s

denotes

Eq.(4)

is

a non-negative

equivalent

to the

ij

where

~

and

ij

respectively.

~

ij

denote

The c o n d i t i o n

scalar

function.

associated

Oa

strain that

Of

-- X ~

for the

[15]

has

reinforced

shown soil:

,

(5)

ij

rates

the

Lesniewska

flow rule

soil

in

the

and the

soil

and

reinforcement

the

composite

w ork t o g e t h e r

can be expressed as follows:

ij

ij

It must be stressed that in a general case (4 ~ O) the principal directions o f the

tensor

~ do n o t

coincide

with

the

principal

directions

characteristic feature of anisotropic materials,

of

6,

what

is

a

[16].

The following relations describe the behaviour of reinforcement: n

n

n

where ~ = ~ n

ij

n n i

j

is a strain

T h e r e a r e two b a s i c mechanism depends reinforcement,

the

on t h e last

< 0

extension,

> 0

compression,

= O

rigid

rate

(7)

reinforcement

in the direction

of r e i n f o r c e m e n t .

mechanisms of reinforced

simultaneous working

in

plastic

extension

flow (~

n

soil of

< 0).

both

failure. the

In this

soil case

The first and

the

there

is

57 obviously

~

= -1.

In the

second mechanism

whilst the soil becomes plastic.

the

reinforcement

remains

rigid

In this case the parameter ~ describing the

behaviour of reinforcement can be determined with the help of Eq.(7c) and the associated with

those

because

flow rule

mentioned

the

(4). The case

above,

reinforcement

(7b) is not important

especially

does

for

not work

geotextile

generally

in comparison

reinforced

in compression.

soils, In

such

cases the reinforced soil behaves like a pure soil with no reinforcement.

PLANE PLASTIC FLOW OF REINFORCED SOIL

We

deal

with

the

plane

plastic

flow

of

reinforced

soil.The

equilibrium equations are of the form: @a

Oa

ax

+ ~ =X ¥

@a

aa

X

0 ,

(8) +x----O--~~ =

y ,

where y denotes the unit weight of reinforced soil (the y direction is assumed as a vertical one). Eqs.(3) macrostresses a

and , a

x

(8)

form

and a y

the

system

of

equations

with

respect

to

. There are two differential equations (8) and one xy

algebraic equation (3). It is possible to reduce the number of unknowns down to the two using the following parametrization:

a

x

Y

= a = a

~x~

=

l

( 1 + sin~cos2p ( 1 -

) + ¥ ~ ~o t

sin¢cos2p

) - ¥

( cos28

~ ao

- sin~cos2p

( cos2e

- sin~cos2p

) - H

k

) - Hk

(9)

i

asinCsin2p + ~- ~ o ° ( sine - sinCsin2p)

where p denotes the angle between the x axis and the direction of a bigger principal microstress in the soil, and

.'I

O" --- ~

Substitution

of

Eqs.(9)

into

the

(3

%0" x

yield

% y

2"I

condition

(3)

gives

an

identity.

58 Lesniewska (1988) has shown t h a t t h e r e l a t i o n s = -I e

for

p - 0 - ~ > 0

(-1,0)

= 0

for

for

(7) can be r e p l a c e d by:

(reinforcement

p - 0 - ¢ = 0

p - e - ~ < 0

yields in extension),

(reinforcement

(reinforcement

remains rigid),

(lO)

works in compression),

n

where 6 = - - 4 2 Eqs.(lO)

are equivalent

to the following

~ =-HIpwhere

H()

denotes

the

into the equilibrium

Heaviside

equations

e-

(1.1)

~I

function.

(8) gives

formula:

Substitution

the following

of

Eqs.(9)

system

and

(ii)

of differential

equations with respect t o ~ and p:

go

+ sintsin2p--~-

+

= O,

(12) 0(7

sin@ s i n 2 p - - ~

+

8

Io 1]

I[

j j ~

-O-~

~

+

Oo + I I - s i n ¢ cos2p] ~ +

+

[I

2o-~a °

1

sin¢cos2p+ 7 ao

The system of e q u a t i o n s Sokolovski function.

[17]

for

an i d e a l

I

cos2e-sin~bsin2p 6 p - e -

= •.

(12) i s more g e n e r a l t h a n t h a t p r e s e n t e d by

soil

with

no r e i n f o r c e m e n t .

6()

is

a Dirac

59 We have to complete the system of Eqs.(12) by adding the following expressions for respective differentials:

~cr

@a@x dx + - ~ y

y = do,

(13) - - ~ x x + --~-dy = do. uy The system of partial differential equations (12) and (13) can be analysed using standard procedures, [17]. This system is of a hyperbolic type provided that the following relations are not satisfied simultaneously: ~=0 and ~=0 (or ~o=0)" From the characteristic polynomial of Eqs.(12) and (13) we obtain the following differential equations for stress characteristics:

dy

[

I [

]

(14)

[

2a-~a ° sin~ sin2o±cos~ + ~oCOS~ c o s ( ~ - 2 e ) e c o s ~ 6

--4-~=

p Ool.,o,I°o..o÷s,o,l

-e-~

o '1

There are two cases that have to be considered separately. The first one corresponds to the case p,O+~.

In this case the stress characteristics are

given by: dy

~ =

sin2p± cos# =tan(p±~ ). cos2p+sin#

(15)

In the second case, when p is approaching ()+~ (p ~ ()+~) we have: dy _- c o s ( # - 2 e ) ± c o s # dx s i n ( ~ - 2 e ) +sin#

In

both

cases,

( 1 5 ) and

(16), %he

=tan(e+E±c).

differential

(16)

equations

for

stress

characteristics are of the final form: dy -tan(p±£)

(17)

--d-Z--

which is similar to that for a pure soil. Eq.(17) means that there is a continuous transition from extended and rigid reinforcement, as well as from the rigid reinforcement and that compressed. In the

case

(15) the

following

relations

are

satisfied

along

characteristics: da±(2a-~ao)tan~d~=F(dy±tan~dx),

(18)

60

where

for

similar

the

reinforcement

working

to those for a pure soil. dal

In a way s i m i l a r equations for velocity

compression

(~=0)

For t h e c a s e (16) t h e r e

we g e t

formulae

is:

~ o d~ =~ (dy± t a n O d x ) . to

that

presented

(19)

above we o b t a i n

the

respective

characteristics:

dy dx Eqs.(20)

in

= tan(p±e),

are valid for arbitrary

dv + dv t a n ( p ± 6 ) × y

= O.

(20)

~. It follows from above considerations

the stress and velocity characteristics

that

coincide.

BEARING CAPACITY OF REINFORCED SLOPES AND SLIP LINES

The presented of reinforced slope,

slopes.

i.e. the height

properties

theory has been applied

As the initial

to the analysis

of stability

data we have to know the geometry of the

h and the angle B

(see Fig.2),

of the soil (~, c) and the reinforcement

as well

(~o)'

as mechanical

and the unit weight

of the soil y.

Y

I

Fig.2.

Fig.3 the following

shows t h e

data:

p {x)

Reinforced soil

stress

characteristics

h = 5 m, ~ = 70 ° , ~

= 400 kPa. The case "a" corresponds o assumption that the slip surface passes regions

I and

III the

stress

and s l i p

lines

computed f o r

= 25 ° , c = 50 kPa, y = 21.6 kN/m 3, to

the

through

(I,II and III) in which the reinforced

the regions

slope

slope the

failure

toe.. There

soil is in a plastic

characteristics

are straight

under are

the three

state.

lines.

In

In the

61 region

II

the

lines,

the

second

first

family

one by

stress characteristics one curvilinear

of

characteristics

logarithmic

spirals.

is

represented

According

the shape of line "a" is represented

sectors,

by

straight

to the character

of

by two linear and

as shown in Fig.3.

vertical stress

IilII11111111 lll slip line o'"

Fig.3. Stress characteristics, for

reinforced

cohesive

slip lines and distribution

slope,

h

= 5 m,

y = 21.6 kN/m 3, o

A part stresses

is

solution

of this P

=

distribution

distribution

5616

kN/m

for

gives

the

is

the

distribution

the value

of total

shown

Fig.3.

case

In many practical

slip

characteristics,

line

in

is not a boundary

In general this distribution

slope are distributed The

obtained

on the upper plateau

the solution!

"b".

o

= 70 ° , ~b = 250 , c

stress

-- 50

kPa,

= 400 kPa.

on the upper plateau of the slope that corresponding

Integration which

of the

B

of vertical

of

vertical

to the failure. load at

Note

condition

failure,

that

the

but a part of

is not uniform.

cases the loads acting on the upper plateau of the

on the limited area, as for example shown in Fig.3, is,

p

in

this

case,

also

defined

by

the

and is similar to that in the case "a". The total

is, in the case "b", P = 2906 kN/m.

net

case of

limit load

62

Fig.4.Stress characteristics f o r B=90 °, h=5 m, ~=25 °, c=50 kPa, y=21.6kN/m 3, a

0

:i00

kPa

)

lm

q

Fig.5.Stress characteristics for B=80 °, and data as in Fig.4

)

Im

!

Fig.6,Stvess characteristics for B:70 °, and data as shown in Fig.4.

63 Figs. in the

4 - 6 show t h e s t r e s s

previous

three

values

total

limit

example,

of t h e

except

slope

characteristics

for a o

inclination:

load is respectively

now e q u a l

90 ° ,

and 70 °

80 °

u s a l s o an i n f o r m a t i o n a b o u t t h e i n f l u e n c e (5616 a g a i n s t

The v a l u e o f a o i s the

reinforcement

geotextile the

R (in

I00 kPa,

and

respectively.

The how

Comparison o f F i g s . 3 and 6 g i v e s o f t h e amount o f r e i n f o r c e m e n t on

1763). calculated

kN/m) by t h e

by d i v i d i n g s p a c i n g Ah

the tensile (m).

For

STABILENKA 1000/800 i s u s e d a s t h e r e i n f o r c e m e n t

length-wise direction,

data to those

to

997, 1355 and 1763 kN/m, so i £ i s v i s i b l e

the angle B influences the bearing capacity.

bearing capacity

for similar

which i s

[18]),

with the

strength

example,

if

of the

(R = 1000 kN/m i n

s p a c i n g &h=l m, we h a v e g

=i000 o

kPa. For t h e g e o t e x t i l e

STABILENKA 200/45 we h a v e r e s p e c t i v e l y

a

=200 kPa.

If

0

we u s e t h e g e o t e x t i l e

LOTRAK 3 2 0 / 6 0 , w i t h t h e s p a c i n g Ah=0.5 m, t h e f o l l o w i n g

v a l u e of a ° i s o b t a i n e d : g o = 3 1 8 / 0 " 5 = 636 kPa, e t c . In g e n e r a l , linearly

f o r a g i v e n g e o m e t r y of t h e s l o p e ,

i n c r e a s e s w i t h i n c r e a s i n g v a l u e s of g

2 34

5 6789

o

the bearing capacity

.

1

10

Fig.7.Influence h=lO m,

~=25 ° ,

(5)c=80

kPa;

( i 0 ) c = 5 0 0 kPa; Fig.7 c o h e s i v e c u t of

c=50

of ~o on s l i p kPa,

(6)c=120

(1)c=0,

kPa;

(11)c=1000 kPa. shows t h e

lines for cohesive vertical ~=0;

(7)c=160

(2)c=0; kPa;

(3)c=20

(8)c=200

I n c a s e s Nos 2-11 t h e r e

influence

of

a°

on

slip

kPa;

kPa;

cut. (4)c=30 (9)c=300

kPa; kPa;

i s 7 = 2 1 . 6 kN/m3 . lines

for

the

vertical

d e p t h h=lO m. We have a s s u m e d t h e f o l l o w i n g d a t a : ~=25 ° , c=50

64 kPa

and

y=21.6

respectively. where

kN/m 3 . T h e r e

The c a s e

the

slip

corresponds

line

are

"1" c o r r e s p o n d s

to the by

represented

to the unreinforced

weighty

failure

wedge, whilst

surface

similar

to the so-called

For

small

by t h e

reinforcement

(~o

It

It

zone is

seems that

state.

this

vertical

cut

influence values is a

O

for

is

that

the

slip

lines

lines

for

should

the

The

is

of cohesion

of ~

O

similar

[19].

are

similar to

to

the

slopes

that

the

into

amount

( s a y ~ o > 2 0 0 kPa)

of

the

(say ~o<50 kPa).

account

in

elaborating

c on b e a r i n g

capacity

capacity

on t h e

expands

slip

with

increases lines

with

of the

values

P [kN/m]

120(

80(

40C c [kPa] . .40. .

o f c on b e a r i n g

60 capacity

of a vertical

cut.

This

increasing

i s shown i n F i g . 9 .

increasing

160(

Fig.8.Influence

that

stronger

and the reinforcement

= const.

:~0

"2"

to the

, a n d h=5 m, y = 2 0 kN/m 3 , @=10 ° .

bearing

zone

'

slope,

case

"1".

theory

taken

"2"

by t h e b i - l i n e a r

weak r e i n f o r c e m e n t

be

and

failure.

of cohesion

active

line

"1"

weightless

corresponding

reinforced

that

values

strong:

see

in which both the soil

influence

o f c . The i n f l u e n c e

visible

zone,

presented

slope

various

very

slip

the

observation

by

sector.

The "1" c a s e

approach the slip

than

shows the

linear

slope.

the

O

For strongly

simple models of reinforced Fig.8

o

the area

much b i g g e r

denoted

unreinforced,

the

French failure

The

from

influences

cases

"2" o n e may be a p p r o x i m a t e d

of

"2".

increases)

work i n a p l a s t i c active

the

values line

follows

reinforcement

special

is

British

represented

two

of

c,

It for

65

Fig.9.Influence of c on slip lines for a vertical cut.

h=5 m, ~=10 ° , ¥=20 kN/m3 , o =100 kPa. (1)c=20 kPa; (2)c=40 kPa', (3)c=60 kPa. o

CONCLUSIONS

The r e s u l t s

p r e s e n t e d i n t h i s p a p e r g i v e some b a s i c m a t e r i a l ,

example e q u a t i o n s f o r c h a r a c t e r i s t i c s , a p p l i e d by t h o s e who a r e part

of the t e x t

familiar

which can be e a s i l y

w i t h t h e methods of

i s v e r y much s u b s t a n t i a l

reinforced soil,

limit

analysis.

from t h e view p o i n t

as well as from t h e p r a c t i c a l

as f o r

checked and t h e n This

of t h e o r y of

p o i n t o f view s i n c e i t

leads to

s o l u t i o n s o f e n g i n e e r i n g p r o b l e m s . The a p p r o a c h p r o p o s e d i s r i g o r o u s from t h e view

point

of

limit

plasticity

d i s c u s s i o n of other e x i s t i n g p r e s e n t e d f o r a few t y p i c a l

and

provides

a

framework

models can be p e r f o r m e d .

inside

which

Such a d i s c u s s i o n

a is

l i m i t e q u i l i b r i u m models by Sawicki and Lesniewska

[20]. Numerical possibilities

of

the

results theory

presented proposed,

in as

this well

paper

as

allow

illustrate for

drawing

some some

conclusions important for designers. Some of these conclusions regarding the influence of the amount of reinforcement and cohesion on bearing capacity of reinforced slopes and the slip lines are presented in Section 4. It is realized that the approach presented from

some

shortcomings.

For

example,

the "soil

is

in this paper suffers assumed

to

obey

associated flow rule which is recognized rather as a rough approximation

the of

66 the real soil behaviour. Another difficult problem is the prolongation of the stress field outside the slip lines zone, which has not been discussed in this paper.

REFERENCES

i. Sawicki, A. (1983): Plastic limit behaviour of reinforced earth, Jnl Geot.Engng, ASCE, 109, 7, 1000-1005. 2. Kulczykowski, M. (1985): Bearing capacity analysis of the reinforced earth subsoil loaded by a footing, PhD Thesis, Institute of Hydroengineering, Gdansk, Poland. 3. Sawicki, A.,Lesniewska, D. (1987): Failure modes and bearing capacity of reiforced soil retaining walls, Geotextiles and Geomembranes Int.Jn],5, 29-44. 4. Sawicki, A.,Lesniewska, D. (1988): Limit analysis of reinforced slopes, Geotextiles and Geomembranes Int.Jnl, 6, in press. 5. Ingold, T.S. (1982): Reinforced Earth, Thomas Telford Lid, London. 6. Murray, R. (1982): Fabric reinforcement of embankments and cuttings, Proc.2nd Int.Conf. on Geotextiles, Las Vegas, 707-713. 7. Schneider, H.R., Holtz, R.D. (1986): Design of slopes reinforced with geotextiles and geogrids, Geotextiles and Geomembranes Int.Jn], 3, 29-51. 8. J e w e l 1 , R.A. (1985): M a t e r i a l p r o p e r t i e s f o r t h e d e s i g n o f g e o t e x t i l e r e i n f o r c e d s l o p e s . G e o t e x t i l e s and Geomembranes I n t . J n l , 2, 83-109. 9. J e w e l 1 , R.A. (1985): L i m i t e q u i l i b r i u m a n a l y s i s o f r e i n f o r c e d s o i l w a l l s , P r o c . l l t h I n t . C o n f . S o i l Mech.Found.Engng, San F r a n c i s c o , A.A. Balkema, 1705-1708. l O . J e w e l l , R.A. (1987): R e i n f o r c e d s o i l wall a n a l y s i s and b e h a v i o u r , R e p o r t No. OUEL 1701, U n i v e r s i t y of Oxford, Dpt.Engng S c i . l l . S t u d e r , J . A . , Meier, P. (1986): E a r t h r e i n f o r c e m e n t w i t h non-woven fabrics: Problems and computational possibilities, Proc. 3rd Int.Conf.on Geotextiles, 3, Vienna, 361-365. 12.Leshchinsky, D., Volk, J.C. (1986): Predictive equation for the stability of geotextile reinforced earth structure, Proc.3rd Int.Conf.on Geotextiles, 3, Vienna, 383-388. 13.Ruegger, R. (1986): Geotextile reinforced soil structures on which vegetation can be established,Proc.3rd Int.Conf.on Geotextiles, 3, Vienna, 453-458. 14.Burd, H. (1986): Soil reinforcement for Norwegian conditions, Internal Report of the Norwegian Geotechnical Institute, No. 52757-3. ]5.Lesniewska, D. (1988): Statics and kinematics of reinforced soil-an application to bearing capacity of slopes, PhD Thesis, Institute of Hydroengineering, Gdansk, Poland. 16.Hill, R. (1956): The Mathematical Theory of Plasticity, Clarendon Press, Oxford. 17.Sokolovski, V.V. (1965): Statics of granular media, Pergamon Press, New York. 18.1ngold, T.S., Miller, K.S. (1988): Geotextiles Handbook, Thomas Telford Ltd., London. 19.John,N.W.M. (1986):Geotextile reinforced soil walls it* a tidal environment, Proc.3rd Int.Conf.on Geotextiles, i, Vienna, 331-336. 20.Sawicki, A.,Lesniewska, D. (1988): Stability of fabric reinforced cohesive slopes, Geotextiles and Geomembranes Int. Jnl, submitted.