Ashish Gupta and Vishwas A. Sawant · 2018-08-19 · Ashish Gupta1) and Vishwas A. Sawant2) 1),...

The 2018 World Congress on Advances in Civil, Environmental, & Materials Research (ACEM18) Songdo Convensia, Incheon, Korea, August 27 - 31, 2018

Effect of soil amplification on the seismic stability of reinforced-soil walls for c-ϕ backfill

*Ashish Gupta1) and Vishwas A. Sawant2)

1), 2) Department of Civil Engineering, Indian Institute of Technology Roorkee,

Uttara Khand 247-667, India 1) [email protected] 2) [email protected]

ABSTRACT The current practice adopted in the design of reinforced-soil wall is either based on the pseudo-static or pseudo-dynamic approach in the earthquake-prone region. Both approaches consider soil as cohessionless. Soil amplification is a very important factor for analyzing the reinforced-soil wall and should not be ignored in the design in the earthquake-prone regions. The behavior of reinforced-soil walls using the pseudo-dynamic approach is not available for c-ϕ soil backfill considering the effect of soil amplification. In this paper, the pseudo-dynamic approach has been used to find out the seismic stability of reinforced-soil wall considering the propagation of primary and shear waves under both, horizontal and vertical seismic accelerations. A numerical algorithm is proposed to obtain the required strength of reinforcements, the critical inclination of the failure angle and safety factor of reinforced-soil wall. The effects of shear strength parameters, number of reinforcement layers, length of reinforcement layers and coefficients of ground accelerations on the stability of reinforced-soil wall are critically examined. Variation in mobilized pullout resistance of reinforcement layers and factor of safety with time is considered for assessment of stability. For cohesionless backfill, numerical predictions are in good agreement when compared with available studies in literature for validation purpose. Keywords: Factor of safety; Pseudo-dynamic approach; Reinforced soil wall; Seismic stability

1) Research Scholar 2) Associate Professor


1. INTRODUCTION The study of seismic earth pressure is very essential for the design of a retaining wall in the earthquake prone regions. It can be concluded from available observed field performances that the reinforced soil walls perform well when compared to conventional retaining walls. The pioneer work for the determination of seismic earth pressure using the pseudo-static method for the design of retaining walls by Okabe (1926) and Mononobe and Matsuo (1929) and then known as Mononobe and Okabe (M-O) method (Kramer 1996). Shahgholi et al. (2001) derived an equation for the calculation of required tensile strength for the reinforced slopes using geosynthetics as reinforcement. The seismic stability analysis showing the effect of reinforcement and backfill properties of reinforced soil walls were performed using the pseudo-static method (Nouri et al. 2008; Reddy et al. 2008; Chandaluri et al. 2015). Steedman and Zeng (1990) incorporated a new technique to analyze the retaining wall under seismic loading considering time dependent approach known as a pseudo-dynamic method. The only drawback of this study was the consideration of finite shear waves in soil backfill. Nimbalkar et al. (2006) and Choudhury et al. (2007) extended this approach to analyze the seismic stability of reinforced soil wall. Soil amplification effect was introduced by Nimbalkar and Choudhury (2008) for calculating the seismic earth pressure distribution for a vertical retaining wall. Shekarian and Ghanbari (2008) analyzed the retaining walls with and without reinforcement in seismic condition using horizontal slice method for pseudo-dynamic forces. Reddy et al. (2009) studied about the seismic stability of reinforced soil wall subjected to pseudo-dynamic forces. Ghanbari and Ahmadabadi (2010) proposed a pseudo-dynamic approach for reinforced retaining walls having c-ϕ soil backfill based on the limit equilibrium method and horizontal slice method. The seismic study for the design of reinforced soil walls considering soil amplification are very limited for c-ϕ soil backfill. In the present work, a simplified limit equilibrium method is used for the analysis of reinforced soil walls using a pseudo-dynamic method. A study using various parameters, has been done to quantify the effect of c and ϕ on the required strength of total reinforcement and the factor of safety against pull out. The number of reinforcement layers used and length of reinforcement on the factor of safety due to the mobilized pull out resistance of reinforcement layers has been also presented here. 2. METHODOLOGY Present work consists of a vertical reinforced soil wall system ABC of height H retaining the soil backfill of cohesion c and soil friction angle ϕ, having unit weight γ (Fig. 1). The wall has n number of planar reinforcement of length Lr. Reinforcement layers have uniform spacing Sv=H/n. The top and bottom reinforcements are at vertical distance of 0.5Sv from top and base level. The effect of propagation of shear and primary waves is considered in the present analysis. A soil amplification effect with soil amplification factor, fa is also incorporated in the analysis assuming linear variation in input ground acceleration with


depth. The amplitudes of seismic accelerations in horizontal and vertical direction on the base of wall are ah=kh.g and av=kv.g. kh and kv are the seismic coefficients in the horizontal and vertical directions. The soil amplification effect in the seismic condition is assumed to act within the soil media. In the present analysis, AB is the failure plane making an angle, α, with the horizontal (Figure 2). Force F is the resultant force of the shear and normal force acting on the failure plane of reinforced soil. Under seismic condition the shear and primary wave velocity, Vs and Vp, are assumed to act within the reinforced soil wall. The period of lateral shaking is T = 2/, where ω is the angular frequency. Tensile force in reinforcement

For stabilizing the reinforced soil wall, 1

n

ii

T is the required sum of the tensile forces, where

Ti is the tension force generated in the ith reinforcement layer. Considering the dynamic equilibrium of forces on the reinforced soil wall system in horizontal and vertical directions:

1

sin cos 0n

h ii

Q t F C T

(1)

cos sin 0v aW Q t F C C (2)

On eliminating F, from Eqs. (1) and (2), 1

n

ii

T can be expressed as:

1

tan tan cot

tan

nv h

ii a

W Q t Q t cHT

c H

(3)

The total weight of the assumed failure wedge is W = 0.5H2cot. The required strength of reinforcement, K, can be expressed as:

2

1

0.5n

ii

K T H

2 2

tan cot0.5 0.5or,

* cot 1 tan

v h

f

Q t Q t

H HK

c a

(4)

where,

2

1

2; 0.5 and *

n

f a ii

ca c c K T H c

H


Pseudo-dynamic inertia forces The mass of a small element of thickness dz at depth z is obtained as:

( )

tan

H zm z dz

g

(5)

Soil amplification factor fz is considered to linearly vary with depth z with values unity at base and fa at the top level described as 1 1z af f H z H . At depth z and time t,

the seismic accelerations in the horizontal and vertical direction can be written as:

, sin and , sinh z h v z vs p

H z H za z t f k g t a z t f k g t

V V

(6)

The total inertia force in the horizontal and vertical direction, Qh(t) and Qv(t), can be derived as:

0 0

( ) , and ( ) ,H H

h h v vQ t m z a z t Q t m z a z t (7)

Assuming,

; ; ; ; 2

2 and 2

s ps p

t

H H t HTV t TV t

V V T

t H t

T T

2 2 2

3 3

2 cos 2 1 sin sin

4 tan 1 cos cos

a a thh

a t

H f H fkQ t

H f

(8)

2 2 2

3 3

2 cos 2 1 sin sin

4 tan 1 cos cos

a a tvv

a t

H f H fkQ t

H f

(9)

Substituting Qh(t) and Qv(t) in Eq. (4), K can be obtained as:

2 2 2

3 3 2

2 2 2

3 3 2

tan * * 1 tan tan

2 1 costan1

tan 2 2 1 sin sin 1 cos

2 1 cos

2 2 1 sin sin 1 cos

f

a av

a t a t

a ah

a t a t

c c a

f H fkK

H H f H f

f H fk

H H f H f

(10)


Factor of safety The factor of safety can be find out by assuming the full mobilization of shear resistance along the reinforcement-soil interface. The resulting axial pullout of reinforcement causes mobilization of the shear resistance over the effective length of reinforcement. Hence,

1

n

ii

t can be obtained by the following expression:

1 1

2 1 tann n

i v i i ri i

t k H L

(11a)

Using, Hi = (i – 0.5) Sv; Sv = H/n; Li = Lr – (H – Hi) cotcri and ϕr = 2ϕ/3 where, Hi = Depth of embedment Li = Effective length of ith layer of reinforcement ϕr = Interface friction angle between the soil and reinforcement ti = Tensile force mobilized due to bond resistance in the ith layer of reinforcement

3

2

1

4tan 1 cot cot

6

n

i v r v r cri cri vi

n nt S k n L H S

(11b)

The factor of safety, FS, can be expressed as:

1 1

n n

i ii i

FS t T

(12)

3. RESULTS AND DISCUSSION A parametric study is implemented to enumerate the effect of c and ϕ on the required strength of total reinforcement and the factor of safety against pull out. Three cases are considered in the present study to observe the effect of c and fa as (case-1 c=0, fa=1.0; case-2 c=10kpa, fa=1.0; case-3 c=10kPa, fa=1.2). Variation of other parameters considered are reported in Table 1. Effect of c and ϕ in Kmax Figs. (3a-3c) show the variation between required maximum strength of reinforcement, Kmax, and ϕ, for different values of kh for three cases. It is clearly shown in Figs. (3a-3c) that with increase in the value of c and ϕ, the values of Kmax decreases substantially. For any value of ϕ, Kmax is greater for the higher values of kh. For example, at ϕ=30º on increasing the kh from static (kh=0) to dynamic case (kh=0.1, 0.2 and 0.3); percentage increase in Kmax is 18.2, 42.4 and 69.7% for case-1. The percentage increase is 75, 150 and 250% (case-2) and 75, 175 and 300% (case-3), when kh increases from static value to dynamic value (kh=0.1, 0.2 and 0.3). For ϕ=40º, kh=0.3 and fa=1.0, increase in cohesion


from 0 (case-1) to 10kPa (case-2) results 53.9% decrease in Kmax highlighting effect of cohesion. On considering the effect of soil amplification for the same cohesive soil backfill, Kmax increases significantly. For change in soil amplification fa from 1.0 to 1.2, percentage increase in Kmax is 11.1%. This example quantifies the effect of soil cohesion along with the effect of soil amplification and kh. It can be also observed that the Kmax value increases substantially for ϕ < 30º and for kh ≥ 0.2. Effect of c and ϕ in FS Figs. (4a-4c) show the variation in FS with ϕ for different values of kh for three cases for n=5, Lr/H=0.8. In Figs. (4a-4c), FS increases nonlinearly with an increase in the value of c and ϕ both. For the same value of soil cohesion, considering the soil amplification, the FS value decreases. For example, at kh=0.3 and ϕ=30º, FS is 2.85 (case-1), 6.49 (case-2) and 5.54 (case-3). This example concludes the effect of c with increase in FS as 127.8%, when compare with c=0. The effect of fa is observed as decrease in FS by 14.6% when compared with c=10kPa and fa=1.0. From the reported results, it can be concluded that FS increases with a very high amount for ϕ > 25º and for kh < 0.1. Effect of n and Lr/H in FS Figs. (5a-5c and 6a-6c) show the variation of FS with n and Lr/H taken for different values of kh and ϕ=30º in the reinforced soil wall for three cases. From both set of Figs. (5a-5c and 6a-6c), it can be clearly observed that the value of FS increases significantly on increasing the value of n and Lr/H both. Increase in FS is due to the bond resistance between the soil and reinforcement. Using kh=0.3, ϕ=30º and n=3, FS is 1.66, 3.82 and 3.25 for the three respective cases. The value of FS for n=7 is 4.03, 9.14 and 7.81 for the same. From this example for n=7, the effect of c (126% increase when compared with c=0) and effect of fa is shown (17% decrease when compared with c=10kPa and fa increases from 1.0 to 1.2). For this case, on increasing n=3 to 7, FS increases 143, 139 and 140%. Similarly when Lr/H is 1.0, the effect of c (118% increase when compared with c=0). It can be also observed that FS value increases about 45% with increase in Lr/H=0.8 to 1.0 for c=0 and fa=1.0. 4. VALIDATION OF THE PRESENT WORK The maximum total tensile forces, generated in the reinforcement layers has been compared with those obtained by Shahgholi et al. (2001) and Tafreshi and Rahimi (2012), as shown in Table 2. The maximum total tensile force values obtained in the present work show a very good agreement with maximum difference < 9%. Kmax and critical inclination of the failure plane (cri) has been compared with Ghanbari and Ahmadabadi (2010) and Azad et al. (2008) as shown in Table 3. For a set of parameters (kv=0, kh=0.2, δ=0, c=0, ϕ=30º, =20kN/m3, T=0.2s, Vs=150m/s and Vp=1.87Vs), K and cri


show a good agreement as the maximum difference in the values of Kmax and cri is less than 9%. 5. CONCLUSIONS The simplified solution presented to quantify the required strength of total reinforcement and the factor of safety against pull out for c-ϕ soil backfill considering the effect of soil amplification. The main conclusions of the present study are as follows: The required maximum strength of reinforcement Kmax decreases with increase in ϕ value and increases on increase in kh values. The value of required strength of reinforcement decreases considerably when c value increases. It is also noticed that Kmax value increases with higher rate for the values of ϕ < 30º and kh ≥ 0.2. Factor of safety increases effectively with an increase in the value of soil cohesion and soil friction angle. The effect is more for ϕ > 25º. The effect of cohesion is considerable and the soil amplification effect is significant for the design of reinforced soil wall, which is clearly perceptible in the present work. Factor of safety increases in linear manner with considerable rate on increasing n and Lr/H, increases from lower value to higher value.


LIST OF NOTATIONS

1

n

ii

T Total required sum of tensile forces for n number of reinforcement (kN/m)

1

n

ii

t Total tensile force mobilized in the n number of reinforcement (kN/m)

Unit weight of soil (kN/m3) Angular frequency (rad/s) Assumed failure plane making an angle with the horizontal (º) Time for propagating primary wave (s) Time for propagating shear wave (s) Wavelength of the vertically propagating primary wave (m) cri Critical inclination of the failure plane (º) af Adhesion factor ah Horizontal seismic acceleration av Vertical seismic acceleration c Soil cohesion (kN/m2) C Total cohesive force (kN/m) c* Normalized cohesion of soil (dimensionless) ca Soil-wall adhesion (kN/m2) Ca Total adhesive force (kN/m) F Resultant of shear and normal forces (kN/m) fa Soil amplification factor at top level fz Soil amplification factor at depth z g Acceleration due to gravity force H Height of wall (m) Hi Depth of embedment K Required strength of reinforcement (dimensionless) kh Horizontal seismic coefficient Kmax Required maximum strength of reinforcement (dimensionless) kv Vertical seismic coefficient Li Effective length of ith layer of reinforcement Lr Length of reinforcement layer n Total number of planar reinforcement Qh(t) Total inertia force in horizontal direction (kN/m) Qv(t) Total inertia force in vertical direction (kN/m) Sv Reinforcement layer spacing T Period of lateral shaking (s) ti Tensile force mobilized in the ith layer of reinforcement (kN/m) Ti Tension force generated in the ith layer of reinforcement (kN/m) Vp Primary wave velocity (m/s) Vs Shear wave velocity (m/s)


W Weight of soil backfill (kN/m) λ Wavelength of the vertically propagating shear wave (m) ϕ Soil friction angle (º) ϕr Interface friction angle between the soil and reinforcement


REFERENCES Chandaluri, V.K., Sawant, V.A. and Shukla, S.K. (2015), “Seismic stability analysis of

reinforced soil wall using Horizontal Slice method”, Int. J. Geosynthetics and Ground Eng., 1:23(3), 1-10.

Choudhury, D., Nimbalkar, S.S. and Mandal, J.N. (2007), “External stability of reinforced soil walls under seismic conditions”, Geosynthetics Int., 14(4), 211-218.

Ghanbari, A. and Ahmadabadi, M. (2010), “New analytical procedure for seismic analysis of reinforced retaining wall with cohesive-frictional backfill”, Geosynthetics Int., 17(6), 364-379.

Kramer, S.L. (1996), “Geotechnical Earthquake Engineering”, Prentice-Hall, Englewood Cliffs.

Mononobe, N. and Matsuo, H. (1929), “The determination of earth pressures during earthquakes”, In Proc. World Eng. Congress, Tokyo, Japan, 9, 177-185.

Nimbalkar, S.S. and Choudhury, D. (2008), “Effects of body waves and soil amplification on seismic earth pressures”, J. Earthquake and Tsunami, 2(1), 33-52.

Nimbalkar, S.S., Choudhury, D. and Mandal, J.N. (2006), “Seismic stability of reinforced soil wall by Pseudo-dynamic method”, Geosynthetics Int., 13(3), 111-119.

Nouri, H., Fakher, A. and Jones, C.J.F.P. (2008), “Evaluating the effects of the magnitude and amplification of pseudo-static acceleration on reinforced soil slopes and walls using the limit equilibrium Horizontal Slices method”, Geotextiles and Geomembranes, 26(3), 263-278.

Okabe, S. (1926), “General theory of earth pressure”, J. Japanese Soc. Civil Eng., 12(1), 1277-1323

Reddy, G.V.N., Choudhury, D., Madhav, M.R. (2009), “Pseudo-dynamic analysis of reinforced soil wall subjected to oblique displacement”, Geosynthetics Int., 16(2), 61-70.

Reddy, G.V.N., Madhav, M.R. and Saibaba, R.E. (2008), “Pseudo-static seismic analysis of reinforced soil wall-Effect of oblique displacement”, Geotextiles and Geomembranes, 26(5), 393-403.

Shahgholi, M., Fakher, A. and Jones, C.J.F.P. (2001), “Horizontal Slice method of analysis”, Geotechnique, 51(10), 881-885.

Shekarian, S. and Ghanbari, A. (2008), “A Pseudo-dynamic method to analyze retaining wall with reinforced and unreinforced backfill”, J. Seismology and Earthquake Eng., Iran: Spring 10(1), 41-47.

Steedman, R.S. and Zeng, X. (1990), “The influence of phase on the calculation of pseudo-static earth pressure on a retaining wall”, Geotechnique, 40(1), 103-112.

Tafreshi, S.N.M. and Rahimi, M. (2012), “A simplified Pseudo-dynamic method of reinforced retaining-wall subjected to seismic loads”, In Proc. 15th World Conf. Earthquake Eng. (15WCEE). Lisbon, Portugal, Volume 27.


Table 1. Variation of parameters considered in the present study

S. No. Description Values are taken 1. Unit weight of soil backfill () 18 kN/m3 2. The height of retaining wall (H) 5 m 3. 4.

Shear wave velocity (VS) Ratio of VP/VS

100 m/s 1.87

5. Primary wave velocity (VP) 187 m/s 6. The time period of lateral shaking (T) 0.3 s 7. Soil friction angle (ϕ) 10º, 15º, 20º, 25º, 30º, 35º, 40º & 45º8. Horizontal seismic coefficient (kh) 0.0, 0.1, 0.2 & 0.3 9. Soil amplification factor (fa) 1.0 & 1.2 10. Number of reinforcement layer (n) 3, 5 & 7 11. Length of reinforcement layer (Lr/H) 0.6, 0.7, 0.8, 0.9, 1.0, 1.1 & 1.2


Table 2. Comparison of maximum total tensile forces calculated by Shahgholi et al. (2001), Tafreshi and Rahimi (2012) and present work for different values of horizontal seismic

acceleration with kv = 0

kh Shahgholi et al. (2001) Tafreshi and Rahimi (2012) Present Study ϕ (º)

20 25 30 20 25 30 20 25 30 0.0 110 91 75 110 91 75 110.3 91.3 75 0.1 137 113 93 127 107 89 127.4 106.6 88.8 0.2 164 135 105 150 126 105 149.6 125.6 105.30.3 196 160 130 183 150 126 182.7 150.4 125.9


Table 3. Comparison between results obtained from the present study by Ghanbari and Ahmadabadi (2010) and Azad et al. (2008) in the case of (kv = 0, kh = 0.2, δ = 0º, c = 0, ϕ =

30º, = 20 kN/m3, T = 0.2 s, Vs = 150 m/s and Vp = 1.87 Vs)

H (m) t = 0.0 t = 0.02 t = 0.04 t = 0.08 t = 0.10 t = 0.12 K cri K cri K cri K cri K cri K cri

Present method 3 m 0.29 63.2 0.36 58.2 0.43 52.8 0.45 51.4 0.38 56.3 0.31 61.7

Ghanbari and Ahmadabadi (2010) 3 m 0.29 62.5 0.36 58.2 0.43 54 0.45 53 0.38 57 0.31 61.8

Azad et al. (2008) 3 m 0.33 60.5 0.36 58 0.43 53 0.45 51 0.37 57 0.33 60 H (m) t = 0.0 t = 0.04 t = 0.08 t = 0.12 t = 0.16 t = 0.20

K cri K cri K cri K cri K cri K cri

Present method 15 m 0.27 64.9 0.27 64.6 0.37 57.5 0.43 52.6 0.36 58.3 0.27 64.9

Ghanbari and Ahmadabadi (2010) 15 m 0.27 64.5 0.28 63 0.37 57 0.44 54 0.36 59.5 0.27 64.5

Azad et al. (2008) 15 m 0.33 60.5 0.34 59 0.38 56 0.48 52 0.39 57 0.33 60.5


Fig. 1 Reinforced soil wall system


Fig. 2 Forces acting on the reinforced soil wall system in seismic condition


0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

10 15 20 25 30 35 40 45

Km

ax

ϕ (º)

c = 0 and fa = 1.0

kh = 0.0

kh = 0.10

kh = 0.20

kh = 0.30

Fig. 3a Kmax with ϕ for c = 0 and fa = 1.0


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10 15 20 25 30 35 40 45

Km

ax

ϕ (º)

c = 10 kPa and fa = 1.0

kh = 0.0

kh = 0.10

kh = 0.20

kh = 0.30

Fig. 3b Kmax with ϕ for c = 10 kPa and fa = 1.0


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10 15 20 25 30 35 40 45

Km

ax

ϕ (º)

c = 10 kPa and fa = 1.2

kh = 0.0

kh = 0.10

kh = 0.20

kh = 0.30

Fig. 3c Kmax with ϕ for c = 10 kPa and fa = 1.2


0

3

6

9

12

15

10 15 20 25 30 35 40

Fac

tor

of S

afet

y, F

S

ϕ (º)

c = 0, fa = 1.0, Sv = 1, n = 5 and Lr/H = 0.8

kh = 0.0

kh = 0.10

kh = 0.20

kh = 0.30

Fig. 4a FS with ϕ for c = 0 and fa = 1.0


0

5

10

15

20

25

30

10 15 20 25 30

Fac

tor

of S

afet

y, F

S

ϕ (º)

c = 10 kPa, fa = 1.0, Sv = 1, n = 5 and Lr/H = 0.8

kh = 0.0

kh = 0.10

kh = 0.20

kh = 0.30

Fig. 4b FS with ϕ for c = 10 kPa and fa = 1.0


0

5

10

15

20

25

30

10 15 20 25 30

Fac

tor

of S

afet

y, F

S

ϕ (º)

c = 10 kPa, fa = 1.2, Sv = 1, n = 5 and Lr/H = 0.8

kh = 0.0

kh = 0.10

kh = 0.20

kh = 0.30

Fig. 4c FS with ϕ for c = 10 kPa and fa = 1.2


1

2

3

4

5

6

7

8

9

10

3 4 5 6 7

Fac

tor

of S

afet

y, F

S

Number of Reinforcement Layer, n

c = 0, fa = 1.0, ϕ = 30º and Lr/H = 0.8

kh = 0.0

kh = 0.10

kh = 0.20

kh = 0.30

Fig. 5a FS with n for c = 0 and fa = 1.0


0

5

10

15

20

25

30

35

40

45

3 4 5 6 7

Fac

tor

of S

afet

y, F

S


c = 10 kPa, fa = 1.0, ϕ = 300 and Lr/H = 0.8

kh = 0.0

kh = 0.10

kh = 0.20

kh = 0.30

Fig. 5b FS with n for c = 10 kPa and fa = 1.0


0

5

10

15

20

25

30

35

40

45

3 4 5 6 7

Fac

tor

of S

afet

y, F

S


c = 10 kPa, fa = 1.2, ϕ = 30º and Lr/H = 0.8

kh = 0.0kh = 0.10kh = 0.20kh = 0.30

Fig. 5c FS with n for c = 10 kPa and fa = 1.2


1

2

3

4

5

6

7

8

9

10

11

12

0.6 0.7 0.8 0.9 1 1.1 1.2

Fac

tor

of S

afet

y, F

S

Length of Reinforcement Layer, Lr/H

c = 0, fa = 1.0, ϕ = 30º, Sv = 1 and n = 5

kh = 0.0

kh = 0.10

kh = 0.20

kh = 0.30

Fig. 6a FS with Lr/H for c = 0 and fa = 1.0


0

5

10

15

20

25

30

35

40

45

50

0.6 0.7 0.8 0.9 1 1.1 1.2

Fac

tor

of S

afet

y, F

S


c = 10 kPa, fa = 1.0, ϕ = 30º, Sv = 1 and n = 5

kh = 0.0

kh = 0.10

kh = 0.20

kh = 0.30

Fig. 6b FS with Lr/H for c = 10 kPa and fa = 1.0


0

5

10

15

20

25

30

35

40

45

50

0.6 0.7 0.8 0.9 1 1.1 1.2

Fac

tor

of S

afet

y, F

S


c = 10 kPa, fa = 1.2, ϕ = 30º, Sv = 1 and n = 5

kh = 0.0

kh = 0.10

kh = 0.20

kh = 0.30

Fig. 6c FS with Lr/H for c = 10 kPa and fa = 1.2

Ashish Gupta and Vishwas A. Sawant · 2018-08-19 · Ashish Gupta1) and Vishwas A. Sawant2) 1),...

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*Ashish Gupta and Vishwas A. Sawant · 2018-08-19 · *Ashish Gupta1) and Vishwas A. Sawant2) 1),...

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Ashish Gupta and Vishwas A. Sawant · 2018-08-19 · Ashish Gupta1) and Vishwas A. Sawant2) 1),...

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