**BEARING CAPACITY OF REINFORCED **

**GRANULAR BEDS ON **

**SOFT NON-HOMOGENEOUS CLAY **

K. RAJYALAKSHMI

Doctoral Student and Lecturer, Department of Technical Education, Bheemunipatnam- 531163, Andhra Pradesh, India.

dhanista123@yahoo.com +91- 9848369275

K. RAMU

Associate Professor, JNTU Kakinada, A.P., - 533033 India. kramujntu@gmail.com

+91-9848282931
**Abstract **

Most naturally deposited clays have induced non-homogeneity. Neglect of this increase of undrained strength would lead to conservative estimate of bearing capacity of foundations laid on top. The two layered foundation bed considered for the study, consists of a layer of dense reinforced granular fill overlying soft non-homogeneous clay whose undrained strength increases with depth. The paper presents a method developed to estimate the bearing capacity of a strip footing on the surface of a reinforced granular bed over a finite layer of clay whose undrained strength increases linearly with depth, incorporating the contribution of granular fill, that of soft ground based on the Davis and Booker’s theory and the axial tension in reinforcement. Parametric studies presented quantify the improvement in bearing capacity over that by the conventional Meyerhof’s approach for homogeneous deposit.

**Key words: Bearing capacity, non-homogeneous clay, granular fill, ***BCR*

**1. Introduction **

Rapid Urbanisation has pushed the need for exploitation of lands which were regarded unsuitable for construction earlier. Reclamation of deltaic or tidal lowlands with dense granular fill is the first step in improving soft marine deposits. The fill is necessitated for two reasons, viz., elevating the ground above the tide level and to provide a working platform for further development of the site. A geosynthetic layer (geogrid or geotextile) is also provided these days to further increase the load carrying capacity of the system. The soft ground is further improved by vertical drains to accelerate the consolidation or by stone columns/granular piles to reinforce and consolidate the initially soft deposit. Recent (geologically speaking) marine deposits may exhibit undrained strength increasing linearly with depth (Fig. 1a). If the deposit gets aged or gets weathered, the deposit may develop strength over the full depth in Fig. 1b or have relatively high but nearly constant undrained strength over the thickness of the crust while retaining the original linearly increasing undrained strength at further depths (Fig. 1c). In spite of these possible strength variations, most solutions for bearing capacity of footings on clay consider only homogeneous deposits.

Figure 1:Idealised undrained strength versus depth profiles (Davis and Booker, 1973): a) Newly deposited and consolidated clay, b) Normally consolidated deposit and

c) Normally consolidated deposit with crust.

The ultimate bearing capacity, *qbL*, of a strip footing on the surface of a deposit with strength increasing linearly

with depth is

] 4 1

[*s* *N* *B*

*F*

*q _{bL}*=

_{uo}*+*

_{c}### ρ

(1)where *suo *= undrained strength of clay at the base of foundation; ρ* = dsu/dz* is the rate of increase of undrained

strength, *su *of clay with depth; B = width of the footing; F = *f *(ρ*B/suo***) - a correction factor as obtained from **

Fig.2.

Figure 2: Correction factor ′*F′ (Davis and Booker, 1973) *

Meyerhof (1974) proposed a punching mode of failure for a footing on a granular bed of thickness, *H*, and angle
of shearing resistance,ϕ, overlying a soft homogeneous clay layer. The mechanisms of possible failure modes,
punching shear through granular bed or general shear within the granular bed alone, are shown in Fig. 3. The
bearing capacity, *qu,*of a footing at depth, *D*,is

*D*
*B*
*K*
*H*
*D*
*H*

*cN*

*qu* *c* *s* γ

ϕ

γ + +

+

Figure 3:Bearing Capacity Analysis for Sand Overlying Clay (Meyerhof, 1974)

where *Ks* is punching shear coefficient. *qu* is limited to the ultimate bearing capacity of the granular layer:

*q*
*DN*
*BN*

*q _{u}*

### γ

### γ

### γ

+=0.5

(3)
where *Nq* and* Nγ*are the bearing capacity factors for granular deposit. This paper presents a method for the

estimation of bearing capacity of footing resting on a granular bed overlying a clay deposit whose undrained shear strength increases linearly with depth.

**2. Problem definition and Formulation **

A strip footing (Fig. 4) of width, *B*, rests on the surface of a sand stratum of thickness, *H*, overlying
clay deposit, whose undrained shear strength, su, increases linearly with depth, with geosynthetic reinforcement

placed in the overlying granular bed. The single layer of reinforcement is placed in the granular bed. The unit
weight and the angle of shearing resistance of granular stratum are γ and ϕ respectively while *su 0* is the
undrained shear strength of soft ground at the top of the layer and ϕ

*r*is the interface/bond resistance between

geosynthetic layer and the granular fill.

Figure 4:Definition Sketch

**2.1. Bearing capacity of granular bed on soft non-homogenous soil **

*t*
*q*
*b*
*q*

*q _{ug}* = + (4)

where *qb* is the ultimate bearing resistance of clay layer,* qt* is the resistance from shear developed due to

punching failure of granular layer.

For clay deposit with undrained strength increasing linearly with depth (Davis and Booker, 1973) (Fig. 1), Eq. (1) reduces to

*c*
*uo*
*c*
*uo*

*b* *s* *N*

*N*
*s*

*B*
*F*

*q* * ]

4
1
1
[ + ρ
=
** (5) **
For punching shear failure (Fig. 5a), shearing resistance developed in the granular fill is

### φ

### γ

### 2

_{tan}

*B*

*H*

*s*

*k*

*T*

*q*

_{t}### =

### =

(6)where *ks* = punching shear coefficient; γ = unit weight of the granular fill; *H* = thickness of the fill; φ is the

angle of shearing resistance of the fill.

Figure 5: Stresses on a) Sand Column & b) Reinforcement

Substituting Equations (5) & (6) in Eq. (4) one can get

φ
γ
ρ
tan
2
0
0
4
1
1
*B*
*H*
*s*
*k*
*c*
*N*
*u*
*s*
*u*
*s*
*B*
*F*

*q _{ug}* = + +

###

###

###

###

###

###

###

###

(7)Normalizing Eq. (7) with s*u0*, one can get,

φ γ ρ tan 2 0 0 4 1 1 ,

###

###

###

###

###

###

###

###

###

###

###

###

###

###

+ + =*B*

*H*

*u*

*s*

*B*

*s*

*k*

*c*

*N*

*u*

*s*

*B*

*F*

*N _{c}_{g}* (8)

where *Nc,g* = *qug/su0*

The axial tensile force, *Tr*, developed in the reinforcement layer due to shear stresses developed on either side of

the reinforcement layer at the interface with the soil (Fig. 5b) is

where *(Lr-B)/2* is the length of reinforcement beyond the footing.

**2.2. Bearing capacity of reinforced granular bed on soft non-homogenous soil **

The bearing capacity of the reinforced granular bed of soft soil can be obtained by adding the bearing capacity of the two layer system consisting of granular bed overlying soft non-homogeneous clay, whose strength increases with depth as obtained in Eq. 7 and the mobilized tensile force (pure axial tension is assumed) in the reinforcement layer at the edge of the footing as obtained in Eq. 9 as

∗= + + + − (10)

Normalising Eq. (10) by undrained shear strength, ‘*su0*’ one gets

∗ = + + + − (11)

where *Ncr* *= *qur*/su0*.

The ratios of bearing capacities, *BCR*, are defined as:

*RNcg* = *Nc,g(ρB/su0)/ Nc,g(ρB/su0= 0) *is the ratio of bearing capacity of the unreinforced two layered system of

granular fill overlying soft non-homogeneous ground, at a specific value of ρ*B/su0 *to the bearing capacity of the

unreinforced two layered system of granular fill overlying soft homogeneous ground, i.e., ρ*B/su0 *equal to 0.

This ratio quantifies the improvement in bearing capacity of the footing on an unreinforced two layered system of granular fill over soft non-homogeneous ground to that over a soft homogeneous ground.

*RNcr** = *Ncr*(ρB/su0)/ Ncr*(ρB/su0= 0) *is the ratio of bearing capacity of the reinforced two layered system

(considering the effect of axial tension only) of granular fill overlying soft non-homogeneous ground, at a
specific value of ρ*B/su0 *to the bearing capacity of the reinforced two layered system (considering the effect of

axial tension only) of granular fill overlying soft homogeneous ground, i.e., ρ*B/su0 * equal to 0. This ratio

quantifies the improvement in bearing capacity of the footing on a reinforced two layered system of granular fill over soft non-homogeneous ground to that over a soft homogeneous ground.

*(BCR)ug *= *Nc,g/Nc*is the ratio of bearing capacity of the unreinforced two layered system to that of footing on

clay alone. This ratio quantifies the contribution of the granular layer to the bearing capacity of the footing.

*(BCR)ax*= N*cr*/Nc* is the ratio of bearing capacity of the reinforced two layered system (considering the effect of

axial tension only) to that of footing on clay alone. This ratio quantifies the contributions of the granular layer
and the axial tension mobilized in the reinforcement to the overall bearing capacity of the footing.* *

*(BCR)ax** = *Ncr*/Nc,g*is the ratio of bearing capacity of the reinforced two layered system (considering the effect

of axial tension only in the reinforcement) to that of an unreinforced two-layered system*.(BCR)ax** quantifies

the improvement of bearing capacity of the two-layered system due to axial force in the reinforcement.

The bearing capacity of strip footings on non-homogeneous deposit (Davis and Booker 1973) depends
on normalized rate of increase of undrained shear strength of the clay, ρ*B/suo*, with depthand is obtained by

incorporating the correction factor ‘*F*’ for different values of ρ*B/suo*. (Fig. 2). The bearing capacity of a footing

resting on reinforced granular bed overlying a non-homogeneous clay layer also depends on φ and *H/B* related
to the granular layer, γ*B/su0*, related to unit weight of granular fill, width of the footing and undrained strength of

the clay layer at the top, φ*r/φ - bond strength relative to angle of shearing resistance of granular layer, Lr/B* -

relative length of reinforcement for axial tension in the reinforcement. Parametric study is carried out for the
following ranges of parameters: ρ*B/su0*: 0 to 24, γ*B/su0*: 5 to 35; and *H/B*: 0 to 5.0. The computations are made

for *φ* equal to 350,*φr/φ: 0.75, H/B* of 0.5 and *Lr/B* of 3.0. The paper investigates the contributions of these

parameters.

**3. Results and Discussion **

Fig.6 illustrates the variation of ratio of bearing capacity of an unreinforced two layer system underlain
by soft non-homogeneous ground (at a specific value of *ρB/su0) *to that of an unreinforced two layer system

underlain by a soft homogeneous ground *(ρB/su0,0),Ncg(ρB/su0)/Ncg(ρB/su0,0) *represented by *RNcg*with ρ*B/su0,* for

Thebearing capacity ratiovalues,* RNcg* increase from 1 at ρ*B/su0*equal to 0 to 3.1 at ρ*B/su0*equal to 24,

for γ*B/su0*equal to 5.0. Correspondingly, the bearing capacity ratio values,* RNcg* increase to 2.0 at ρ*B/su0*equal to

24, for γ*B/su0*equal to 35.0 i.e, for relatively soft clays or relatively wide footings. The bearing capacity ratio

values,* RNcg* are equal to 2.0, 1.7 and 1.5, at ρ*B/su0*equal to 8, for values of γ*B/su0*equal to 5.0, 15.0 and 35.0.

Figure 6:*RNcg* versus*ρB/su0*- Effect of γ*B/su0 *

Figure 7: *RNc,r** versus*ρB/su0*- Effect of γ*B/su0 *

Fig. 7 depicts the variation of ratio of bearing capacity of a reinforced two layer system underlain by soft
non-homogeneous ground, (at a specific value of*ρB/su0) *to that of a reinforced two layer system underlain by a soft

homogeneous ground *(ρB/su0,0),Ncr*(ρB/su0)/Ncr* (ρB/su0,0) *represented by *RNcr* *with ρ*B/su0,* for a granular fill

with*φ of 35*0,*φr/φ = 0.75, Lr/B* =3 and *H/B *of 0.5, for values of γ*B/su0* equal to 5.0, 15.0 and 35.0.Thebearing

capacity ratiovalues,* RNcr** increase from 1 at ρ*B/su0*equal to 0 to 2.6 at ρ*B/su0*equal to 24, for γ*B/su0*equal to

5.0. Correspondingly, the bearing capacity ratio values,* RNcr** increase to 1.5 at ρ*B/su0*equal to 24, for γ*B/su0*

equal to 35.0 i.e, for relatively soft clays or relatively wide footings. The bearing capacity ratio values,* RNcr* *are

equal to 2.7, 1.4 and 1.2, at ρ*B/su0*equal to 8, for values of γ*B/su0*equal to 5.0, 15.0 and 35.0.

The variation of *(BCR)u,g*, the ratio of bearing capacity of footing on a granular bed over soft soil to

that of on clay alone, with ρ*B/su0*, for φof* *350, *H/B *of 0.5, for values of γ*B/su0 *equal to 5.0, 15.0 and 35.0 is

depicted in Fig. 8. *(BCR)u,g*values decrease for 0<ρ*B/su0*≤*4* and gradually thereafter, for 4<ρ*B/su0 *<2*4*. The rate

of increase in undrained strength with depth, i.e., the bearing capacity of soft soil alone increases with values of
*ρB/su0 *increasingfrom 0 to 24. For 0<ρ*B/su0*≤*4,* the increase in the correction factor, *F* suggested by Davis and

Booker is pointed and therefore, a sharp increase in* Nc,g*values is reflected, resulting in a steep decrease of

*(BCR)u,g *and thereafterthe decrease issteady*.(BCR)u,g *values decrease from 1.3 at ρ*B/su0*equal to 0 to 1.2 at

1.0 2.5 4.0

0 4 8 12 16 20 24

**RN**

**cg**

**ρB/su0**

**γB/su0**

**= **

**5**

**15**
**35**

**φ****= 350**

**H/B ****= 0.5**

1.0 1.9 2.8

0 4 8 12 16 20 24

**RN**

**cr**

*****

**ρB/su0**

**γB/su0 = 5**

**15**
**35**

**φ****= 350**

*ρB/su0*equal to 4 and to 1.1 at ρ*B/su0*equal to 24, for γ*B/su0*equal to 5.0.* (BCR)u,g *values decrease from 2.8 at

*ρB/su0*equal to 0 to 2.0 at ρ*B/su0*equal to 4 and thereafter steadily to 1.5, at ρ*B/su0*equal to 24, for γ*B/su0*equal to

35.0.

Figure 8**. ***(BCR)ug *versus ρ*B/su0*- Effect of γ*B/su0 *

Fig. 9 illustrates the variation of *(BCR)ax*, the ratio of bearing capacity of footing on reinforced granular bed

(considering axial response of reinforcement to pullout) on soft soil to that of on clay alone, with ρ*B/su0*, for a

granular fill with*φ of 35*0, ϕ*r/*ϕ of 0.75, *Lr/B* of 3.0 and *H/B *of 0.5, for values of γ*B/su0* equal to 5.0, 15.0 and

35.0. *(BCR)ax *values decrease from 1.8 at ρ*B/su0*equal to 0 to 1.4 at ρ*B/su0*equal to 4 and to 1.2 at ρ*B/su0*equal to

24, for γ*B/su0*equal to 5.0.* (BCR)ax *values decrease from 6.1 at ρ*B/su0*equal to 0 to 3.9 at ρ*B/su0*equal to 4 and

thereafter steadily to 2.3, at ρ*B/su0*equal to 24, for γ*B/su0*equal to 35.0.

The variation of *(BCR)ax**, the ratio of bearing capacity of footing on reinforced granular bed

(considering axial response of reinforcement to pullout) on soft soil to that of on an unreinforced two layer
system, with ρ*B/su0*, for a granular fill with φ of 350, ϕ*r/*ϕ of 0.75, *Lr/B* of 3.0 and *H/B *of 0.5, for values of

*γB/su0* equal to 5.0, 15.0 and 35.0 is presented in Fig.10. *(BCR)ax* *values decrease for 0<ρ*B/su0*<*4* and gradually

thereafter.* (BCR)ax* *values decrease from 1.4 at ρ*B/su0*equal to 0 to 1.2 at ρ*B/su0*equal to 4 and to 1.1 at ρ*B/su0*

equal to 24, for γ*B/su0*equal to 5.0.* (BCR)ax* *values decrease from 2.2 at ρ*B/su0*equal to 0 to 1.9 at ρ*B/su0*equal

to 4 and thereafter steadily to 1.6, at ρ*B/su0*equal to 24, for γ*B/su0*equal to 35.0.

Figure 9: *(BCR)ax* versus ρ*B/su0*- Effect of γ*B/su0 *
1.00

1.95 2.90

0 4 8 12 16 20 24

**(BCR)**

**ug **

**ρB/suo **

**φ****= 350**

**H/B****= 0.5**

**γB/s _{uo }= 35.0**

**15.0**
**5.0**

1.00 3.70 6.40

0 4 8 12 16 20 24

**(BCR)**

**ax**

**ρB/suo **

**φ****= 350**

**φ****r****/****φ****= 0.75**
**L****r****/B****= 3.0**
**H/B ****= 0.5**

**γB/su0 **

**= **

**35.0**

Figure 10:*(BCR)ax** versus ρ*B/su0*- Effect of γ*B/su0 *

Fig. 11 depicts the variation of *Nc,g,* evaluated from Eq. 8 with *H/B*, for a granular fill with φ of 350

and *ρB/su0* of 4, for values of γ*B/su0*equal to 5.0, 15.0 and 35.0. The normalized bearing capacity of an

unreinforced two layer system, *Nc,g*, increases with increase in *H/B*, upto a critical value of *H/B* denoted by

*(H/B)cr*. For *H/B* >*(H/B)cr*, *Nc,g*remains constant as the bearing capacity of the two layer system is limited by the

bearing capacity of the granular layer. *Nc,g* values increase from 9.2 at *H/B *equal to 0 to a maximum value of

93.0 at relative granular layer thicknessequal to 3.6, for γ*B/su0*equal to 5.0.Thecorresponding valuesof *Nc,g* at
*H/B *equal to 0 and 4.2 are respectively 9.2 and 650.8, for γ*B/su0*equal to 35.0. While the increase in *Nc,g * with

*γB/su0 *is* *significant,the increase in *(H/B)cr* with γ*B/su0 *is marginal.

Figure 11:*Nc,g*versus *H/B* - Effect of γ*B/su0 *

Fig. 12 presents the variation of *Nc,r*, *evaluated from Eq. 11 with *H/B*, for a granular fill with φ of 350,ϕ*r/*ϕ of

0.75, *Lr/B* of 3.0 and ρ*B/su0*of 4, for values of γ*B/su0*equal to 5.0, 15.0 and 35.0. These results are similar to

those observed in Fig. 3.11. *Nc,r* *values increase from 9.2 at *H/B *equal to 0 to a maximum value of 93.0 at

relative granular layer thicknessequal to 3.3, for γ*B/su0*equal to 5.0.Thecorresponding valuesof *Nc,r* *at *H/B *

equal to 0 and 3.8 are respectively 9.2 and 650.8, for γ*B/su0*equal to 35.0. While the increase in *Ncr** with γ*B/su0 *

is* *significant,the increase in *(H/B)cr* with γ*B/su0 *is marginal.

### 1.00

### 1.61

### 2.23

0 4 8 12 16 20 24

**(BCR)**

**ax**

*****

**ρB/suo **

**φ****= 350**

**φ****r****/****φ****= 0.75**
**L****r****/B****= 3.0**
**H/B****= 0.5**

**γ**

**B/su0**

**= **

**35.0**

**15.0**

**5.0**

1 10 100 1000

0.00 2.50 5.00

**Nc,g**

**H/B**

**φ****= 350**

**ρ****B/s****uo ****= 4**

**γB/su0 = 35.0**

Figure 12:*Nc,r**versus *H/B *- Effect of γ*B/su0*

** **

**Conclusions **

Reclamation, the first step in improving the response of soft ground, involves laying of a dense granular layer over it. An analysis of bearing capacity of a strip footing on a reinforced granular bed over soft non-homogeneous deposit is presented considering the increase in undrained strength with depth. The results reduce to those proposed by Meyerhof (1974) for bearing capacity of a footing on granular layer overlying homogeneous clay deposit.

The *BCR* response in terms of* (BCR)u,g, (BCR)ax *&*(BCR)ax* *values show a decreasing trend with ρ*B/su0*.
*BCR* valuesdecrease for 0<ρ*B/su0*≤*4* and gradually thereafter, for 4<ρ*B/su0 *<2*4* as the rate of increase in

undrained strength with depth, i.e., the bearing capacity of soft soil alone increases with values of ρ*B/su0 *

increasingfrom 0 to 24. For 0<ρ*B/su0*≤*4,* the increase in the correction factor, *F* (Davis and Booker) increases

significantly with ρ*B/su0 *and therefore, a sharp increase in* Nc,g*values is reflected, resulting in a steep decrease in
*BCR *values*.*

The normalized bearing capacity of a two layer system with granular fill on soft soil, *Nc,g* increases

with increase in *H/B*, due to increase in undrained cohesive strength of the soft clay layer with depth. The
increase is significant upto a critical value of granular layer thickness, *(H/B)cr* as the ultimate bearing capcity

value is limited by the bearing capacity of the granular layer.* Nc,g *values are higher for higher values of γ*B/su0*

i.e., for relatively soft clays or relatively wide footings. Normalised bearing capacity values,* Nc,r** which are

over and above the *Nc,g*values are obtained due to the contribution of axial tension in reinforcement to the

ultimate bearing capacity of the reinforced two layer system.

**References **

[1] Davis, E.H. and Booker, J.R. (1973). The effect of increasing strength with depth on the bearing capacity of clays, Geotechnique, Vol. 23, No.4, 551-563.

[2] Davis, E.H. and Booker, J.R. (1985). The effect of increasing strength with depth on the bearing capacity of clays," Golden Jubilee of the International Society for Soil Mechanics and foundation Engineering: Commemorative Volume, 185-197.

[3] Davis, E.H. and Christian, J.T. (1971). Bearing Capacity of anisotropic cohesive soil, J. of Soil Mech. and Found. Div., Vol. 97, No. 5, 753-769.

[4] Mandel, J. and Salençon, J. (1969). Force portante d′ un sol sur une assise rigide". Proc. 7th IC SM & FE, Mexico, Vol. 2, 157-164. [5] Meyerhof, G.G. (1974). Ultimate bearing capacity of footings on sand layer overlying clay, Canadian Geotechnical Journal, Vol. 11,

No.2, 223-229.

[6] Salençon, J. and Matar, M. (1979). Bearing capacity of surface foundations, 3rd ASCE/EMD Spec. Conf., University of Texas, Austin, USA.

[7] Tani, K. & Craig, W. H. (1995). Bearing capacity of circular foundations on soft clay of strength increasing with depth, Soils and foundations, ISSN 0038-0806, Vol.35, no4, pp. 21-35 (41ref.), Japanese Geotechnical Society, Tokyo, JAPAN (1968) (Revue).

1.0 10.0 100.0 1000.0

0.00 2.50 5.00

**Ncr**

*****

**H/B**

**φ****= 350**

**φ****r****/****φ****= 0.75**
**L**_{r}**/B****= 3.0**

**ρ****B/s****uo ****= 4**

**γB/s _{u0 }= 35.0**