CIV-112

The 8th Symposium on Advances in Science and Technology (8thSASTech), Mashhad, Iran. 8thSASTech.khi.ac.ir

Determination of seismic bearing capacity of shallow strip footings on

slopes

Mahmoud Ghazavi1, Armin Salmani Mahali

2

1-Associate Professor, Civil Engineering Department, K. N. Toosi. University of

Technology, Tehran, Iran, [email protected]

2- Civil Engineering Department. Islamic Azad University, Arak Branch, Arak ,

[email protected]

Abstract

The seismic bearing capacity for strip footings near slopes are the aim of this paper. For this purpose, a limit equilibrium based method is used. The seismic force is considered as pseudo-static forces

acting on both footing and soil is determined. To obtain the ultimate bearing capacity, an imaginary retaining wall is assumed to pass the footing wedge and the lateral earth pressure exerted on the wall in active and passive conditions are determined. The bearing capacity factors are computed for various values of soil friction angle, seismic acceleration coefficients in horizontal and vertical directions, ground inclination, distance of the foundation from the slope edge. The effects of various parameters on seismic bearing capacity factors have been studied. The results obtained from the present method are compared with other available methods.

Key words: Limit equilibrium, seismic bearing capacity, strip footings, lateral earth pressure
mailto:[email protected]:[email protected]


1. Introduction

The determination of bearing capacity of shallow foundations basically is principle in

geotechnical engineering. Limited studies have been carried out for estimating the seismic

bearing capacity of strip footings near slopes. Most of analyses were carried out for static

situation.

Some researchers including Sarma and Iossifelis (1990), Budhu and Al-Karni (1993),

Richards et al. (1993), Dormieux and Pecker (1995), Paolucci and Pecker (1997), Soubra

(1997, 1999), Kumar and Rao (2002), Kumar (2003), and Choudhury and Subba Rao (2005)

have studied the seismic bearing capacity of shallow footings for the horizontal ground.

However, for sloping ground, data are very limited. Sawada et al. (1994), Sarma (1999) and

Askari and Farzaneh (2003) have presented solutions for seismic bearing capacity of shallow

foundations near sloping ground. Recently, Choundhury and Rao (2006) carried out the

analysis for seismic bearing capacity factors of footings construced on slopes. It is noted that

this method was initially developed by Richards et al. (1993) for footings on homogeneous

granular soil and extended to two layered granular soil by Ghazavi and Eghbali (2008), and

Ghazavi and Salmani (2012) for frictional-cohesive soil. Salmani and Ghazavi (2013) have

extended the imaginary retaining wall method for foundation base inclination.

This paper presents a simple method for determination of the seismic bearing capacity of strip

footings near the slope edge on granular soils. For this purpose, an imaginary retaining wall is

assumed the vertical direction along the edge of the footing (Fig. 1). The lateral earth

pressures exerted on the wall in active and passive conditions are determined. The

conventional bearing capacity factors are extracted and then the bearing capacity equation is

derived.

Fig. 1. Failure mechanism and wedges assumed in present model

2. Model Definition

Meyerhof (1957) proposed a method for determination of bearing capacity on the top of

slope. The ultimate bearing capacity of the foundation can be expressed by Eq. (1) and

presented design chart.


where factors are functions of the soil friction angle, D is the footing

depth, B is the footing width, and is the soil unit weight.

3. Limit equilibrium analysis

A useful simplification for determination the ultimate bearing capacity of shallow strip

footing is to imagine a retaining wall and with equal the active and passive forces, as shown

in Fig. 2. For this purpose, as shown in Fig. 1, we assume AEFC section as an equivalent

surcharge.

Fig. 2. Failure surfaces and effective forces on slip wedge in limit equilibrium condition

Pseudo-static seismic forces are considered along with other static force. Also isotropic

granular soil with equivalent surcharge is assumed in the analysis. The seismic acceleration

coefficients are denoted as kh and kv in the horizontal and vertical directions, respectively.

Note that in Fig. 2:

ae = Angle of slip surface in active zone.

pe = Angle of slip surface in passive zone.

= friction angle along surface between active and passive zone.

Pa, Pp= active and passive force.

: ground inclination angle. b: distance between foundation from the slope crest. The value of ae and pe may be given by:

*

+

[ ][ ]

[ [ ]]

*

+

[ ][

[ ]

The equivalent surcharge is given by:


(

)

(

)

: seismic inertia angle caused by the earthquake.

The seismic inertia angle is given by:

In Eq. (3):

where ah, av = seismic accelerations in horizontal and vertical directions, respectively.

g= acceleration of gravity h= failure wedge The active and passive earth forces according to the Mononobe-Okabe earth pressure theory

are given by:

( )

where:

kae , kpe =coefficient of active and passive pressure in seismic condition.

The coefficient of active and passive pressures are respectively given by:

[

]


[

]

The total active thrust and passive force are determined using:

The horizontal components of the total active and passive thrust are determined respectively

using:

The ultimate bearing capacity may be obtained by combing Eqs. (25) and (26). A comparison

with Eq. (1) leads to:

(

)

The bering capacity factors may be obtained from Eq. (27) as:

(

)

The shape of the failure surface is very simple, thus a relatively acceptable estimation of the

bearing capacity depends on the value of . In this paper, we use

4. Results

In this section, results of the above analyses are presented. Figs. 3 and 4 give the values of

seismic bearing capacity factors for various kh and kv values with a particular D and . As

seen, seismic bearing capacity factors decrease with increasing the horizontal and vertical

seismic acceleration coefficients.


Fig3. Variation of seismic bearing capacity factors with kh

(=40o, b=0.5 m, D=1 m, B=1 m, =10

o, kv=0)

Fig4. Variation of seismic bearing capacity factors with kv

(=40o, b=0.5 m, D=1 m, B=1 m, =10

o, kh=0.1)

Figs. 3 and 4 show the effect of earthquake acceleration coefficients in horizontal and vertical

directions on seismic bearing capacity factors. As observed, with increasing kh and kv , Nqe

and N e decrease. kh values are more effective in decreasing the seismic bearing capacity

coefficient than those of kv.

0

20

40

60

80

100

120

0 0.1 0.2 0.3se

ism

ic b

eari

ng

cap

acit

y fa

cto

rs

kh

Nqe

Ne

0

10

20

30

40

50

60

70

0 0.1 0.2 0.3

seis

mic

bea

rin

g ca

pac

ity

fact

ors

kv

Nqe

Ne


Fig5. Effect of kh on distance greater than that the slope does not affect on bearing capacity

( =16kN/m3, =30

o, B=1m, D=1m, =10

o)

Fig6. Effect of kv on distance greater than that the slope does not affect on bearing capacity

( =16kN/m3, =30

o, B=1m, D=1m, =10

o)

Figures 5 and 6 shows variation of seismic bearing capacity with distance greater than a

specific edge form slope edge, no more reduction in ultilmate bearing capacity occurs for

different value of kh and kv. It can be concluded that with increasing kh, the slope have less

impact on bearing capacity. For example, in the static case in 6m distance, slope does not

affect the bearing capacity, for kh = 0.1, this distance is reduced to 5.5m and for the case kh =

0.3 this distance is 5m.

5. Verification

For validation of the developed method, data presented by Chen Chang-Fu et al. (2007) are

selected for comparison with those obtained from the developed method. Figs. 7 to 10 show

this comparison. As seen, in all figures, there is generally good agreement between two

methods.

0

100

200

300

400

500

0 1 2 3 4 5 5.4 5.5 6 7

qu

lt(k

Pa)

b/B

kh=0,kv=0 kh=0.1,kv=0

kh=0.3,kv=0

0

100

200

300

400

500

0 1 2 3 4 5 5.4 5.5 6 7

qu

lt(k

Pa)

b/B

kh=0.1,kv=0kh=0.1,kv=0.1


Fig7. Variation of Nqe with soil friction angle

(kh=kv=0, b=0.5 m, D=0, B=2 m, )

Fig8. Variation of Nqe with soil friction angle

(kh=kv=0.2, b=0.5 m, D=0, B=2 m, )

Fig9. Variation of Ne with soil friction angle (kh=kv=0, b=0.5 m, D=0, B=2 m, )

0

10

20

30

40

50

60

20 25 30 35 40

Nq

e

(deg)

Present Method

Chen Chang-Fu(2007)

0

5

10

15

20

25

30

25 30 35 40

Nq

e

(deg)

Present Method

Chen Chang-Fu(2007)

0

10

20

30

40

50

60

70

80

20 25 30 35 40

Ne

(deg)

Present Method

Chen Chang-fu(2007)


Fig10. Variation of Ne with soil friction angle (kh=kv=0.2, b=0.5 m, D=0, B=2 m, )

6. Conclusions

A pseudo-static approach for the seismic forces and with the assumption the lateral earth

pressure theory determined from the well known Mononobe-Okabe method in conjunction

with simple slip surface has been used to determine the total lateral active and passive thrusts

exerted on virtual retaining wall passing vertically through the edge of the footing. The

seismic bearing capacity of strip footing on the top of slope on granular soils was derived.

The presented method predicts reasonable results compared with an available solution in the

literature. The results show that with increasing the horizontal and vertical seismic

acceleration components, the seismic bearing capacity factors decrease drastically, as

expected..

References

1-Askari, F., and Farzaneh, O. (2003). "Upper-bound solution for seismic bearing capacity of

shallow foundations near slopes." Geotechnique, 53(8), 697702.

2-Bowles JE (1996) "Foundation Analysis and Design", 5th edn. McGraw-Hill Book

Company, New York.

3- Budhu, M., and Al-Karni, A. (1993). "Seismic bearing capacity of soils." Geotechnique,

43(), 181187.

4- Choudhury, D., and Subba Rao, K. S. (2005). "Seismic bearing capacity of shallow strip

footings." J. Manuf. Syst., 24(1), 117127.

5- Choudhury, D., and Subba Rao, K. S. (2005)." Capacity of Shallow Strip Footings

Embedded in Slope" International Journal of Geomechanics, ASCE), 1532-3641

6- Chen Chang-fu, Dong Wu-Zhong, Tang Yan-zhe, (2007)," Seismic ultimate bearing

capacity of strip footings on slope", J. Cent. South Univ. Technol., Springer, Vol. 5, 730-736.

7- Das, B.M. (2009) "Shallow foundations: Bearing capacity and settlement", 2nd ed., CRC

Press, Taylor & Francis Group, LLC.

8- Dormieux, L., and Pecker, A. (1995). "Seismic bearing capacity of foundations on

cohesionless soil." J. Geotech. Eng., 121(3), 300303.

9- Ghazavi, M. and Eghbali, A. H. (2008), "A simple limit equilibrium approach for calculation of

ultimate bearing capacity of shallow foundation on two-layered granular soils" , Geotech. & Geol.

Engrg., Vol. 26, 535-542.

0

5

10

15

20

25

30

35

25 30 35 40

Ne

(deg)

Present MethodChen Chang-Fu(2007)


10- Ghazavi, M. and Salmani, A. (2012), "A Limit equilibrium approach for determination of bearing

capacity of strip footings on frictional-cohesive soil", 9th International Congress on Civil Engineering,

Isfahan University of Technology, Isfahan, Iran

11- Salmani, A. and Ghazavi, M. (2013), "An analytical solution for determination of bearing

capacity of strip footing with inclined base", 22-23 October 2013, 1st Iranian Conference on

Geotechnical Engineering, University of Mohaghegh Ardabili, Ardabil, Iran (in Persian).

12- Kumar, J., and Rao, V. B. K. M. (2002). "Seismic bearing capacity factors for spread

foundations." Geotechnique, 52(2), 7988.

13- Meyerhof, G. G., "Some recent research on the bearing capacity of foundations",

Canadian Geotech. J., 1(1), 16, 1963.

14- Paolucci, R., and Pecker, A. (1997). "Seismic bearing capacity of shallow strip

foundations on dry soils." Soils & Founds., 37(3), 95105.

15- Richards, R., Elms, D.G. and Badhu, M, (1993), "Seismic Bearing Capacity and

Settlement of Foundations", Journal of Geotechnical Engineering Division, ASCE, 119 (4),

pp. 662-674.

16- Sarma, S. K. (1999). "Seismic bearing capacity of shallow strip footings adjacent to a

slope." Proc., 2nd Int. Conf. Earthquake Geotechnical Engineering, Lisbon, Portugal,

Balkema, Rotterdam, The Netherlands, 309313.

17- Soubra, A. H. (1999). "Upper bound solutions for bearing capacity of foundations." J.

Geotech. Geoenv. Engrg., ASCE, 125(1), 5968.

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CIV-112