SUB: GEOTECHNICAL ENGINEERING
MODULE-51C
MODULE- 51C
Stability of slo pes-infinite slopes, finite slo pes. .
_____________________ ________________________________ ______________________ ______________________ ______________________ _____________________ __________ 3.
1. A deep cut of 7m has to be made in a clay with unit weight 16 kN/ and a cohesion of 25 kN/. What will be the factor of safety if one has to have a slope angle of 30 ? Stability number is given to be 0.178 (from Taylor’s chart) for a depth factor of 3.
°
(A) 0.80
(B) 1.1
(A) 10.89° (B) 11.30°
(C) 1.25
(D) 1.0
(C) 12.48° (D) 14.73°
0.178 =
F=
1.5 =
The critical slip circle for a slope is shown below along with the soil properties. The length of the arc of the slip circle is 15.6 m and the area of within the slip circle is 82 . The radius of the slip circles is 10.3 m. The factor of safety against the slip circle failure is nearly equal to
4.
Ans :
5.
1.5 =
(A) 1.05 (B) 1.22 (C) 0.78 (D) 1.28
I =
A granular soil possesses saturated density of 20 kN/m3. Its effective angle friction is 35 degrees. If the desired factor of safety is 1.5, the safe angle of slope for this soil, when seepage occurs at and parallel to the surface, will be (a) 25 (b) 23 (c) 20 (d) 13 Ans : F=
F=
Ans :
Ans :
2.
An infinite slope is to be constructed in a soil. The effective stress strength parameters of the soil are = 0 and = 30°. The saturated unit weight of the slope is 20 kN/ and the unit weight of water is 10 kN/ . Assuming that seepage is occurring parallel to the slope, the maximum slope angle for a factor of safety of 1.5 would be
I =
A canal having side slopes 1:1 is proposed to be constructed in a cohesive soil to a depth of 10 m below the ground surface. The soil properties are: u=15, =12 kPa, e = 1.0, Gs = 2.65. A) If Taylor's Stability Number, Sn is 0.08 and if the canal flows full, the factor
JH ACADEMY
1
SUB: GEOTECHNICAL ENGINEERING
of safety with respect to cohesion against failure of the canal bank slopes will be (a) 3.7 (b) 1.85 (c) 1.0 (d) None of these Ans :
=
6.
7.
=
Using N = 0 analysis and assuming planar failure as shown, the minimum factor of safety against shear failure of a vertical cut of height 4 m in a pure clay having cu=120 kN/m2 and = 20 kN/m3 is
(a) 1 Ans :
(b) 6
(c)
Failure plane angle =45+
10
(d)
The factor of safety of an infinite soil slope shown in the figure having the propertiesc = 0, c = 0, φ = 350, γdry = 16 kN/m3 and γsat = 20 kN/m3 is approximately equal to
(a) 0.70 (b) 0.80 (c) 1.00 (d) 1.20 Ans : F=
=
10. The soil profile above the rock surface for a 25oinfinite slope is shown in the figure, where is theundrained shear strength and is total unit weight. The slip will occur at a depth of
=160KN
=1.0 JH ACADEMY
9.
⁄ T=160
1.5= I =
F=
20
Weight of wedge =
For two infinite slopes (one in dry condition and other in submerged condition) in a sand deposit having the angle of shearing resistance 30 , factor of safety was determined as 1.5 (for both slopes). The slope angles would have been (a) 21.05 for dry dr y slope and 21.05 for submerged slope. (b) 19.47 for dry slope and 18.40 for submerged slope. (c) 18.4 for dry slope and 21.05 for submerged slope. (d) 22.6 for dry slope and 19.47 for submerged slope. Ans :
F =0.53
An infinite soil slope with an inclination of 35 is subjected to seepage parallel to its surface. The soil has = 100 kN/m2 = =30. Using the concept of mobilized cohesion and friction, at a factor of safety of 1.5 with respect to shear strength, the mobilized friction angle is (a) 20.02 (b) 21.05 (c) 23.33 (d) 30.00 Ans : F=
8.
⁄
B) If there is a sudden drawdown drawdown of water in the canal and if Taylor's Stability Number for the reduced value of vis 0.126, the factor of safety with respect to cohesion against the failure of bank slopes will be (a) 1.85 (b) 1.18 (c) 0.84 (d) 0.53 Ans : 0.126 =
MODULE-51C
(A) 8.83 m (B) 9.79 m (C) 7.83 m (D) 6.53 m Ans : If the failure occurs in top layer, T = h S =40 2
SUB: GEOTECHNICAL ENGINEERING
T>S h
but h is maximum 5m only
T =[ =[ ]] S =60 T=S ] [ H =3.83 m
From top the depth is 5+3.83=8.83 m
11. Consider the following assumptions for slope stability analysis: 1. Friction is fully mobilized 2. Effective stress analysis is adopted 3. Total stress analysis is used 4. Resultant ‘R’ passes through the centre of the circle. 5. Resultant ‘R’ is tangential to the friction circle. The assumptions necessary for friction circle method of analysis would include (a)1, 3 and 4(b)1, 3 and 5 (c) 2 and 4 (d) 2 and 5 12. Consider the following statements associated with stability of slope: 1. Stability number is inversely proportional to cohesion and directly proportional to height. 2. Swedish method of analysis is based on circular failure surface. 3. The Cullman method assumes that rupture will occur in a plane. Which of these statements are correct? (a)2 and 3 (b)1 and 3 (c)1 and 2
(d)1, 2 and 3
Ans : ( C )
13. Taylor’s stability number S n is given by which one of the following expressions? (c is cohesion, F c is factor of safety, is density of soil and H, the height of the slope).
(a)
(b)
JH ACADEMY
MODULE-51C
(d) () )
(c)
Ans : ( B ) 14. Consider the following statements: Dewatering increases the slope stability of cohesion less soil mainly because 1.It causes change in pH 2.It reduces pore water pressure which of the statements is/are correct? (a)1 only (b)2 only (c)Both 1 and 2
(d) neither 1 nor 2
15. Determine the factor of safety with respect to cohesion only for a submerged embankment 25m high whose upstream face has an inclination of . The soil has the following properties; c=40KN/ , =, . The relavant stability number is equal to 0.108. what is the factor of safety if the embankment experience the effect of sudden drawdown? For = and , the value of stability number is 0.136 Ans: 1.85,0.65 Ans : 0.136 =
0.108 =
16. What inclination is required where a filling 12m high is to be constructed having a factor of safety of 1.25? the soil has c= 20KN/ , = , =17.0KN/ the stability number for = is equal to 0.63 when the slope is and 0.098 when the slope is . Ans: F =1.25
For
3
SUB: GEOTECHNICAL ENGINEERING
17. A cutting of depth of 10m is to be made in soil which has c= 30KN/ =19KN/ and=0. There is a hard stratum below the original soil surface at a depth of 12m. Find the safe of cutting if the factor of safety is 1.50. For =1.20,
= 0.143 for and, = 0.101 for . Ans:
X =
=
18. A vertical cut is to be made in clayey soil for which tests gave c=30KN/ , =16KN/ and =0. Find the maximum height for which the cut may be temporarily unsupported. For =0, and , the value of stability number is 0.261 Ans: 7.18m 0.261=
19. When is the factor of safety for a slope 12m high in a clay (c=50KN/ , =18KN/ and =0) having a rock stratum at a depth of 12m below the toe? =2.0 and , the value of is equal to 0.177. Ans: 1.3 0.177=
20. A long natural slope in an over consolidated clay ( , ) is inclined at to the horizontal. The water table is at the surface and the seepage is parallel to the slope. If a plane slip had developed at a depth of 5m below the surface, determine the factor of safety. Take
Ans: 1.90 = =1.90
F=
JH ACADEMY
MODULE-51C
21. A vertical cut is made in a clay deposit (c=30KN/ , =16KN/ ). Find the maximum height of the cut which can be temporarily supported. Ans: 7.18m 22. A cut of depth 10m is made in a cohesive soil deposit (c=30KN/ , =19KN/ ). There is a hard stratum under the cohesive soil at a depth of 12m below the original ground surface. If the required factor of safety is 1.50, determine the safe slope. Ans: 0.105
23. Determine the factor of safety with respect to cohesion if an embankment 25m high and having a slope of and (c=40KN/ , =18KN/ = ). Ans: 2.01 0.097 =
24. Determine the factor of safety with respect to cohesion if an embankment 25m high and having a slope of is subjected to sudden drawdown ( c= 40KN/ , and =18KN/ .) Ans:
25. A soil mass is resting on an inclined impermeable clay layer, as shown in fig. Determine the factor of safety against wedge failure along the interface. The soil has c= 6KN/ , and =17KN/ Ans: 2.16
4
SUB: GEOTECHNICAL ENGINEERING
26. An embankment is to be made of a soil which has the following shear strength parameters under the existing conditions: conditions: , If It is assumed that different margins of safety are available for cohesion component and friction component of shearing strength and the mobilized values of cohesion and friction are: = 22KN/ , =, what is the factor of safety with respect to (a) cohesion and (b) friction? If the average value of normal effective stress on the failure surface is 120KN/ , what is the value of (a) true factor of safety, () when =1 and (c) and when =1? Ans: 1.31, 1.95
W=
=60.8 KN
Length of sliding plane x =
S=Shearstrength=
=55.51 KN 5.91 KN T = sliding force = 60.8
F= =
,
27. A granular soil has . A slope has to be made of this material. If a factor of safety of 1.3 is needed against slope failure, determine the safe angle of the slope (a) when the slope is dry or submerged without seepage, (b) if seepage occurs at and parallel to the surface of the slope. If seepage occurs parallel to the slope with the water table at a depth of 1.5m, what is the factor of safety available on a slip plane parallel to the ground surface at a depth of 4m? assume Ans: 0.5326, 14.6 0, 0.426 a) b)
When a)
⁄
b) =
JH ACADEMY
=
=
28. A canal having side slopes 1 to 1 is proposed to be constructed in a cohesive soil to a depth of 5m below ground surface. The soil properties are given below: = =12KN/ =1.0 =2.65 Using Taylor’s stability number, find the factor of safety with respect to cohesion against failure of the bank slopes, (a) When the canal is full of water and (b) When there is a sudden drawdown of water in the canal. Ans: 8.1KN/ , a=3.7, b=1.06 1.3 = i=
a)
F=
It is same for dry and submerged case
( )) 1.3 =
b)
F=
c) W= [(
)]
S=
=
28.11KN
MODULE-51C
T = 45.47 = 31.51
F = =
29. An infinite slope in a sandy soil is inclined at to the horizontal. The properties of the soil are: =0, =17KN/ =21KN/ .
5
SUB: GEOTECHNICAL ENGINEERING
A hard layer exists 5m below and parallel to the surface. What is the factor of safety against slip when (a) the slope has negligible water in it, (b) the slope is completely submerged with seepage parallel to the surface and (c) the water table level is parallel to the ground surface at 2.5m depth, seepage being parallel? Ans :
⁄ = 17.9-9.81 =8.1 ⁄ ) )
c)
When there is a sudden draw down
30. An infinite slope is to be constructed of a clay soil. The ground water level is at the ground surface itself, with seepage parallel to the ground. The soil properties are: =15KN/ , , =20KN/ What is the factor of safety against movement along a plane to the ground surface at depths of 4m and 5.5m? Ans : a) b)
= F= ( )) = =0.987
F=
c)
F= 31. Find the critical angle of an infinite slope in a clay soil having =20KN/ , , =2.72 and e=0.9 for the following cases: (a) Soil is dry, (b) The slope is submerged with seepage parallel to the surface.
JH ACADEMY
MODULE-51C
32. A cutting is to be made in a soil deposit for a depth of 15m in a homogeneous soil with the following properties: =25KN/ and = ,
(a) If a true factor of safety of 1.5 is needed against slope failure, what is the steepest slope angle that can be provided? (b) For this slope, what would be the factor of safety with respect to cohesion? 33. An embankment is to be made from a soil with =20KN/ and = , . If a factor of safety of 1.5 with respect to shear strength is required for the embankment slope, determine (a) The limiting height of the slope if built at a slope angle of and (b) The steepest angle of the slope if the embankment height is to be kept at 18m. 34. A cutting 8m deep is to be made in a saturated clay soil with =20KN/ , =28KN/ and =0. A hard stratum exists at a depth of 12m below ground level. Determine the angle of the slope at which failure would occur. If a factor of safety of 1.4 is required, what maximum slope angle can be permitted? 35. An embankmentof 12m height with side slopes of 1:1 is to be built of a saturated clay, whose properties are as follows: =20KN/ , =28KN/ and The slope is presently completely submerged, but it is anticipated that a ‘sudden complete drawdown’ may occur in future and the water table may may reach below the toe of the slope. Determine Determine (a) The factor of safety with respect to height corresponding to the submerged and sudden drawdown cases, and (b) The factor of safety with respect to shear strength corresponding to the submerged and sudden drawdown cases.
6
