Unit Cell Testing of Reinforced Soils - Reinforced Soil Engineering: Advances in Research and Practice - page 47

That is, the major principal stress in it is s 1R ¼ K p s 3R :

Note that these are the
averaged values in the composite due to the nonuniform stress distribution in it.
The reinforcing ratio is thus defined as

s 1R Ds 3

s 3

R ¼

s 1 2 1 ¼

ð 14 Þ

If the lateral strain in the composite, 1 3R , and that in the soil, 1 xR , are
considered rather close, the tensile force per unit width developed in
the reinforcement with Young's modulus E and thickness t will be

Ds 3 DH T ¼ ¼ð 1 xR 2 1 3R Þ Et ð 15 Þ

The reinforcement lateral strain is determined by considering it to be
compressed by s 1R at its plane, subject to a confining pressure s 30 : Consider

the composite with reference to Hooke's law at the plane strain condition,

1
E ½ð

s 2 2 s 30 Þ 2 s 1R 2 s 30 Þ ¼ 1 2R ¼ v ð 0 ð 16 Þ

On the other hand, for the reinforcement, its lateral strain is

1
E ½2

v
E ð

s 1R 2 s 30 Þþð s 2 2 s 30 Þ ¼ 2 s 1R 2 s 30 Þð

1 xR ¼

ð þ Þ ð Þ

v 1 v 17

Substituting Eq. (16) into Eq. (17) gives

1 xR ¼ 2 ð

þ Þ

1 v v

s 30 þ K p Ds 3

ð K p 2 1 Þ ð 18 Þ

E

By equating Eq. (17) with Eq. (15) for the lateral strain in a reinforcement,
the reinforcing ratio is obtained as

1 3R

s 30 2 ð

1 þ v Þ v

E

2 ð K p 2 1 Þ

Ds 3

R ¼

s 30 ¼

ð 19 Þ

D Et þ ð

þ Þ

1 v v

K p

E

The equation indicates clearly that a smaller value of v, DH, s 30 ;

and a large
value of Et would lead to a greater effect of reinforcing. A greater reinforcing
effect will be obtained if a reinforcement has (1) a large value of E with any value
of v, (2) a small value of v but a large value of E, (3) a small value of E and also a
small value of v. A testing program has been conducted to investigate the validity
of Eq. (19) using materials of different values of E and v with the results shown in