project class
osama
T.12_LateralEarthPressureRetainingwalls-soil1.pdf
Conducted by: Offered to :
Riyadh, Saudi Arabia, 2019-2020
Dr. Mohamed Ezzat Assistant professor of Civil Eng.
Department of Engineering Management
College of Engineering.
Prince Sultan University
Undergraduate Students –Senior Level.
Engineering Management Department.
College of Engineering.
Prince Sultan University
2nd semester- Year 2019-2020.
EM 306 : Soil Mechanics and Foundations
Construction Management Program (CMP)
Lateral Earth Pressure & Retaining Structures
Topic No. 12
Topic (12)
❑ Page :1 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
TENTATIVE WEEKLY COURSE SCHEDULE WEEK UNIT/ TOPIC
Number of Contact
hours
1 Introduction 5
2 Soil Formation 5
3 Engineering Properties of Soil 5
4 Soil Exploration 5
5 Soil Compaction 5
6 Water in Soil 5
7 Stress in soils 5
8-9 Consolidation of soil 5
10-11 Shear Strength of soil 10
12-13 Bearing Capacity and Shallow Foundations 10
14 Deep Foundations 5
15 Lateral Earth Pressure & Retaining Structures As Scheduled
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
LATERAL EARTH PRESSURE
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :2 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
LATERAL EARTH PRESSURE
1.1 Introduction
Many theories are developed to estimate the acting lateral earth pressure, each theory has its own assumptions. So during application, it should be considered the compatibility between the theory and the retaining structure conditions.
RANKINE’S THEORY (1857)
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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A retaining wall 6.00 m high has a smooth vertical back. The backfill is sand with a horizontal surface at the top of the wall. The density of the backfill is 1.80 t/m3 , its angle of shearing resistance (angle of internal friction) is 30o. There is a ground water table located at depth 2.00 m below ground surface. Draw active pressure distribution diagram, and find its magnitude and point of application per unit length of the wall.
Example 1
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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Since the wall with smooth back
Rankine theory can be used
Soil is sand ϕ = 30 & c = zero
= 1 −sin 30
1+sin 30 = 0.33
Pa1 = (1.80 * 0) * 0.33 = Zero
Pa = (q + Σγ . H) . Ka – 2c √Ka
Ka = 𝟏−𝐬𝐢𝐧 𝝓
𝟏+𝐬𝐢𝐧 𝝓
Pressure distribution:
Pa2 = (1.80 * 2.0) * 0.33 = 1.19 t/m 2
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :5 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Pw = γw . hw
Pa3 = (1.80 * 2.0 + 0.80 * 4.0) * 0.33 = 2.24 t/m 2
= 1.00 * 4.0 = 4.00 t/m2
Magnitude of the pressure & and point of application:
Force Value Location Value
Pa1 0.50 . Pa2 . H1 = 0.50 * 1.19 * 2.0 = 1.19 y1
H1
3 + 4.00 =
2
3 + 4.00
= 4.67
Pa2 0.50 . (Pa2 – pa1) . H
0.50 * (6.89 – 0.82) * 8.0 = 24.28 y2
H
3 =
8.00
3 = 2.67
Pa3 0.50 . (pa3 – pa2) . H2
0.50 * (2.24 – 1.19) * 4.0 = 2.10 y3
H2
3 =
4.00
3 = 1.33
Pw 0.50 . pw . Hw = 0.50 * 4.0 * 4.0 = 8.00 yw H𝑤
3 =
4.00
3 = 1.33
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :6 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Pa = Pa1 + Pa2 + pa3 + pw = 1.19 + 4.76 + 2.10 + 8.00 = 16.05 t/m’
Pa . Y = Pa1 . y1 + Pa2 . y2 + pa3 . y3 + pw . yw
16.05 * Y = 1.19 * 4.67 + 4.76 * 2.00 + 2.10 * 1.33 + 8.00 * 1.33
Y = 1.78 m
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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A retaining wall 8.00 m high has a smooth vertical back, the wall supports a cohesive backfill with a horizontal surface at the top of the wall. The density of the backfill is 1.80 t/m3 , its cohesion 0.25 kg/cm2. Calculate the depth of tension cracks behind the wall, draw active pressure distribution diagram, and find its magnitude and point of application per unit length of the wall.
Example 2
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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Since the wall with smooth back
Rankine theory can be used
Soil is clay ϕ = zero & c = 2.50 t/m2
= 1 −sin(𝑧𝑒𝑟𝑜)
1+sin(𝑧𝑒𝑟𝑜) = 1.00
Pa = (q + Σγ . H) . Ka – 2c √Ka
Ka = 𝟏−𝐬𝐢𝐧 𝝓
𝟏+𝐬𝐢𝐧 𝝓
Pressure distribution:
Pa1 = (1.80 * 0) * 1.00 – 2 * 2.50 * √1.00 = 5.00 t/m 2
Pa2 = (1.80 * 8) * 1.00 – 2 * 2.50 * √1.00 = 9.40 t/m 2
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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Pa = (q + Σγ . H) . Ka – 2c √Ka
0.0 = (1.80 * Zcr) * 1.00 – 2 * 2.50 * √1.00
Depth of tension Cracks (at pa = 0.0):
Zcr = 2.78 m
Magnitude of the pressure & and point of application:
Force Value Location Value
Pa 0.50 . Pa2 . (H – Zcr)
0.5 * 9.40 * (8 – 2.78) = 24.53 t/m’ y
H−Zcr
3 =
8.00 −2.78
3
= 1.74 m
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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A retaining wall 7.00 m high has a smooth vertical back, the wall supports a cohesive backfill with a horizontal surface at the top of the wall. The backfill has the following properties: for the top 3.00 m , γ = 1.75 t/m3 , ϕ = 15o and c = 0.15 kg/cm2 , and for the lower 4.00 m , γ = 1.85 t/m3 , γsub = 0.95 t/m
3 , ϕ = 20o and c = 0.10 kg/cm2 . A ground water table is located at depth 5.00 m. Determine the depth of tension cracks behind the wall, draw active pressure distribution diagram, and find its magnitude and point of application per unit length of the wall.
Example 3
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :11 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Since the wall with smooth back
Rankine theory can be used
= 1 −sin 15
1+sin 15 = 0.59Ka1 =
𝟏−𝐬𝐢𝐧 𝝓𝟏
𝟏+𝐬𝐢𝐧 𝝓𝟏
Pressure distribution:
= 1 −sin 20
1+sin 20 = 0.49Ka2 =
𝟏−𝐬𝐢𝐧 𝝓𝟐
𝟏+𝐬𝐢𝐧 𝝓𝟐
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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Pa = (q + Σγ . H) . Ka – 2c √Ka
Pa1 = (1.75 * 0) * 0.59 – 2 * 1.50 * √0.59 = 2.30 t/m 2
Pa2 = (1.75 * 3) * 0.59 – 2 * 1.50 * √0.59 = 0.79 t/m 2
Pa3 = (1.75 * 3) * 0.49 – 2 * 1.00 * √0.49 = 1.17 t/m 2
Pa4 = (1.75 * 3 + 1.85 * 2) * 0.49 – 2 * 1.00 * √0.49 = 2.99 t/m 2
Pa5 = (1.75 * 3 + 1.85 * 2 + 0.95 * 2) * 0.49 – 2 * 1.00 * √0.49 = 3.92 t/m 2
Pw = γw . hw = 1.00 * 2 = 2.00 t/m 2
Pa = (q + Σγ . H) . Ka – 2c √Ka
0.0 = (1.75 * Zcr) * 0.59 – 2 * 1.50 * √0.59
Depth of tension Cracks (at pa = 0.0):
Zcr = 2.23 m
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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Magnitude of the pressure & and point of application:
Force Value Location Value
Pa1 0.50 . Pa2 . (3 – Zcr)
0.50 * 0.79 * (3 – 2.23) = 0.30 y1
3 −Zcr
3 + 4.00 =
3 −2.23
3 +
4.00 = 4.26
Pa2 Pa3 * 2 = 1.17 * 2.0 = 2.34 y2 2
2 + 2 = 3.00
Pa3 0.50 . (pa4 – pa3) . 2
0.50 * (2.99 – 1.17) * 2 = 1.82 y3
2
3 + 2 = 2.67
Pa4 Pa4 * 2 = 2.99 * 2.0 = 5.98 y4 2
2 = 1.00
Pa5 0.50 . (pa5 – pa4) * 2
0.50 * (3.92 – 2.99) * 2 = 0.93 y5
2
3 = 0.67
Pw 0.50 . pw . Hw = 0.50 * 2.0 * 2 = 2.00 yw H𝑤
3 =
2.00
3 = 0.67
Pa = Pa1 + Pa2 + pa3 + pa4 + pa5 + pw = 13.37 t/m’
Pa . Y = Pa1 . y1 + Pa2 . y2 + pa3 . y3 + pa4 . y4 + pa5 . y5 + pw . yw
Y = 1.58 m
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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A retaining wall 4.00 m high has a smooth vertical back. The backfill is sand with an inclined surface to horizontal with 15o . The density of the backfill is 1.90 t/m3 , its angle of shearing resistance (angle of internal friction) is 30o. Calculate the acting earth pressure in case of active and passive conditions.
Example 4
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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Since the wall with smooth back
Rankine theory can be used
In case of active condition:
Where: β = 15 & ϕ = 30
Ka = Cos β 𝐂𝐨𝐬 𝜷 − 𝐂𝐨𝐬𝟐𝜷 − 𝐂𝐨𝐬𝟐𝜷
𝐂𝐨𝐬 𝜷+ 𝑪𝒐𝒔𝟐𝜷 − 𝑪𝒐𝒔𝟐𝜷
= 0.373
Pa = γ . H . Ka
Pa = 1.9 * 4 * 0.373 = 2.83 t/m 2
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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Pa = 0.50 . pa . H
Pa = 0.5 * 2.834 * 4 = 5.67 t/m’
Resultant of the pressure:
In case of passive condition:
Kp = Cos β 𝐂𝐨𝐬 𝜷+ 𝐂𝐨𝐬𝟐𝜷 − 𝐂𝐨𝐬𝟐𝜷
𝐂𝐨𝐬 𝜷− 𝑪𝒐𝒔𝟐𝜷 − 𝑪𝒐𝒔𝟐𝜷
= 2.502
Pp = γ . H . Kp
Pp = 1.9 * 4 * 2.502 = 19.01 t/m 2
Pp = 0.50 . pp . H
Pp = 0.5 * 19.01 * 4 = 38.03 t/m’
Resultant of the pressure:
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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RETAINING WALLS
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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1.4 RETAINING WALLS 1.4.1 Introduction
Retaining wall are structures used to support earth or other materials, the most common types may be classified into five main types as shown in Figure 1.2 and Figure 1.3 ; Gravity walls, Semigravity walls, Cantliver walls, Counterfort walls and Buttress walls. This classification based on the method of achieving stability.
Figure 1.2: Types of retaining walls (a) Gravity wall (b) Semigravity wall
(c) Cantliver wall (d) Counterfort wall (e) Buttress wall
Figure 1.3: (a) Gravity wall in site (b) Buttress wall in site
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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1.4.2 Types of retaining walls
Gravity wall: depends upon its ownweight to resist the earth pressure, it is made of masonry or concrete and so is proportioned that no tension is developed any where and the resultant of forces fails within the middle third of the base.
Semi gravity wall: is intermediate between gravity and cantliver wall, a small amount of reinforcing steel is used to reduce the mass of concrete.
Cantliver wall: is a reinforced concrete wall in the form of an inverted T, each projection of the wall acts as a cantliver. The stability of this wall is partially provided by the weight of the soil on the heel portion of the base. It is economical for walls of heights up to 6.00 to 7.50 m.
Counterfort wall: is used when the soil be retained is of greater height. The vertical slab and the base slab tied together by counterforts placed at suitable intervals along the wall to reduce the bending moments and shears. The vertical slab and heel slab act as continuous slab. The counterfort is subjected to tensile forces.
Buttressed wall: is similar to counterfort wall except that counterforts called buttresses are provided in front of the wall and in compression instead of tension. The buttresses reduce the clearance in front of the wall and therefore their use is limited.
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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1.4.3 The common uses of retaining walls
Figure 1.4 shows the most common uses for retaining walls such as;
❖ Side hill way or rail way ❖ Elevated high way or rail way ❖ Depressed high way or rail way ❖ Canal sides ❖ Flood wall ❖ Bridge abutment ❖ Retain earth fill around a building ❖ Granular material storage ❖ Erosion protection
Figure 1.4: The common uses for retaining walls
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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1.4.4 Stability of retaining walls
Retaining walls must proved adequate stability against sliding and overturning and it should have sufficient factor of safety against bearing capacity failure. Also the retaining wall must be checked for total settlement and overall stability.
1.4.4.1 Stability against overturning
A retaining wall must be stable about the Centre of rotation (the toe) against overturning. The lateral pressure due to backfill and surcharge tends to rotate the retaining wall about its toe. This overturning moments is stabilized by the weight of the backfill above the inner base (the hell slab) plus the weight of the wall. The factor of safety against overturning is usually Taken as 1.50 for Cohesionless soil and 2.00 for cohesive soil, and calculated as;
F.S = 𝐒𝐭𝐚𝐛𝐢𝐥𝐢𝐳𝐢𝐧𝐠 𝐦𝐨𝐦𝐞𝐧𝐭
𝐨𝐯𝐞𝐫𝐭𝐮𝐫𝐧𝐢𝐧𝐠 𝐦𝐨𝐦𝐞𝐧𝐭
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :22 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
1.4.4.2 Stability against sliding The horizontal component of the lateral pressure tends to cause the wall to slide along its base. The resisting force against sliding is the friction, adhesion or combination of both which act along the bottom of the wall. The factor of safety against sliding is usually to be 1.50, and calculated as;
F.S = 𝐑𝐞𝐬𝐢𝐬𝐭𝐚𝐧𝐜𝐞 𝐟𝐨𝐫𝐜𝐞
𝐝𝐫𝐢𝐯𝐢𝐧𝐠 𝐟𝐨𝐫𝐜𝐞
When the factor of safety is difficult to be attain, a key may be constructed under the base. It is common practice to neglect the passive pressure of the soil in front of the wall unless the designer is cerain that this soil will not be removed during the service life of the wall.
1.4.4.3 Stability of the base against bearing capacity failure
The ultimate soil pressure can be computed by any theoretical method and then divided by a suitable factor of safety to obtain the allowable pressure. The factor of safety may taken as 2.00 for granular soils and 3.00 for cohesive soil. In general, the base is a footing subjected to a horizontal load from the earth pressure and eccentric vertical load. The pressure distribution below the base is obtained from Navier equation. The maximum pressure at the toe must not exceed the allowable pressure on the soil.
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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SOLVED EXAMPLES
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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Check the stability of the given retaining wall to retain earth embedment of 5.50 m high above ground level, the foundation is to be 1.00 m deep. The net safe bearing capacity is 1.20 kg/cm2 , the retained soil as shown in Figure 2.10. A ground water table is located as indicated in Figure 2.14. Note: Neglect the passive resistance.
Example 5
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :25 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Ka1 = 1 −sin 15
1+sin 15 = 0.59
Pa1 = 1.70 * zero * 0.59 – 2 * 4 * 0.59 = 6.14 t/m 2
Pa = γ . h . Ka – 2c √Ka
(a) Horizontal loads:
Rankine theory can be used
Assume the wall with smooth back
Ka2 = 1 −sin 32
1+sin 32 = 0.31
Pa2 = 1.70 * 3.5 * 0.59 – 2 * 4 * 0.59 = 2.53 t/m 2
Pa3 = 1.70 * 3.5 * 0.31 = 1.85 t/m 2
Pa4 = (1.70 * 3.5 + 0.95 * 3.0) * 0.31 = 2.73 t/m 2
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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= 1.85 * 3 = 5.55 t/m’
Pa1 = pa3 * 3
y1 = 1
2 * 3 = 1.50 m
= 0.5 * (2.73 – 1.85) * 3 = 1.32 t/m’
Pa2 = 0.5 * (pa4 – pa3) * 3
y2 = 1
3 * 3 = 1 m
= 1 * 3 = 3.00 t/m2
Pw1 = γw * hw1
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :27 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
= 0.5 * 3 * 3 = 4.50 t/m’
Pw1 = 0.5 * pw1 * hw1
yw1 = 1
3 * 3 = 1.00 m
= 1 * 2 = 2.00 t/m2
Pw2 = γw * hw2
= 0.5 * 2 * 2 = 2.00 t/m’
Pw2 = 0.5 * pw2 * hw2
yw2 = 1
3 * 2 = 0.67 m
u1 = pw1 = 3.00 t/m 2 u2 = pw2 = 2.00 t/m
2
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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The weights from wall, soil, uplift and moments about the toe are calculated:
W Weight Value
(ton) Arm (m)
Moment
(m.t)
W1 2.5 * (0.5 * 1.50 * 5.50) 10.31 0.50 + 2
3 * 1.50 = 1.50 15.47
W2 2.5 * (1 * 5.50) 13.75 1.50 + 1
2 = 2.0 27.50
W3 2.5 * (6.50 * 1) 16.25 4 – ( 1
2 * 2.30) = 2.85 52.81
W4 1.70 * (3.5 * 3.5) + 1.95 * (3.5 * 2) 34.48 6.50 - 3.5
2 = 4.75 163.78
U1 - 6.50 * 2 13.00 6.50
2 = 3.25 - 42.25
U2 - 0.50 * 6.50 * (3 – 2) 3.25 2
3 * 6.50 = 4.33 - 14.07
ΣW 58.54 203.24
(b) Vertical loads:
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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• Against overturning:
(c) Check stability:
Overturning moment = Pa1 . y1 + Pa2 . y2 + (Pw1 * yw1 – Pw2 * yw2)
O.T.M = 5.55 * 1.50 + 1.32 * 1 + (4.50 * 1 – 2 * 0.67) = 12.81 m.t.
Stability moment = Σmoment due to vl loads
S.M = 203.27 m.t.
F.S = 𝐒 .𝐌
𝐎.𝐓.𝐌
= 203.27
12.81 = 15.86 > 1.50 o.k.
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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• Against sliding:
Sliding force = Pa1 + Pa2 + (Pw1 – Pw2)
S.F = 5.55 + 1.32 + 4.50 – 2.00 = 9.37 t/m2
Resisting force = Resulting friction from vl loads
R.F = Σ(W – U) . tanδ
= 58.54 * tan 3
4 32 = 26.06 t/m’
F.S = 𝑹.𝑭
𝑺.𝑭
= 26.06
9.37 = 2.78 > 1.50 o.k.
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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Eccentricity from base mid:
The total net moment = (S.M – O.T.M)
= 203.24 – 12.81= 190.43 m.t
The total vertical load = 58.54 ton
Distance of resultant ത𝐱 from toe is:
ത𝐱 = 𝟏𝟗𝟎.𝟒𝟑
𝟓𝟖.𝟓𝟒 = 3.24 m
e = 𝐁
𝟐 - ത𝐱
• Against bearing capacity failure:
= 6.5
2 - 3.24 = 0.01 < B/6 in the middle third
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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qtoe = 𝚺𝐰
𝐁𝐋 𝟏 +
𝟔 𝐞
𝐁
= 58.54
6.5 ∗1 1 +
6 ∗0.01
6.5 = 9.09 t/m2 < qall.
qheel = 𝚺𝐰
𝐁𝐋 𝟏 −
𝟔 𝐞
𝐁
= 58.54
6.5 ∗1 1 −
6 ∗0.01
6.5 = 8.92 t/m2 < qall.
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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Design a cantilever wall to retain a bank of earth 4.8 m high above ground level. The bottom of the base is 1.2 m below ground level. The soil has a density of 1.8 t/m3 and angle of internal friction of 30o. The surface of the bank is horizontal and is subjected to surcharge of 1.5 t/m2. Check stability and calculate straining actions only for concrete design.
Example 6
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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= 1 −sin 30
1+sin 30 = 0.33
(a) Horizontal loads:
Rankine theory can be used
Assume the wall with smooth back
Ka = 𝟏 −𝐬𝐢𝐧 𝝓
𝟏−𝐬𝐢𝐧 𝝓
Kp = 1
ka = 3.00
Pa = (q + γ . h) Ka
Pa1 = (1.5 + 1.80 * 0) * 0.33 = 0.50 t/m 2
Pa2 = (1.5 + 1.80 * 6) * 0.33 = 4.10 t/m 2
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :35 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
= 0.50 * 6 = 3 t/m’
Pa1 = pa1 . H
y1 = 1
2 * 6 = 3 m
= 0.50 * (4.10 – 0.50) * 6 = 10.80 t/m’
Pa2 = 0.50 . (pa2 – pa1) . H
y2 = 1
3 * 6 = 2 m
Pp = γ . h . Kp
= 1.80 * 1.2 * 3 = 6.48 t/m2
Pp = 0.50 . pp . h
= 0.50 * 6.48 * 1.2 = 3.89 t/m’
yp = 1
3 * 1.2 = 0.40 m
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :36 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
The weights from wall, soil, surcharge and moments about the toe are calculated:
W Weight Value
(ton) Arm (m)
Moment
(m.t)
W1 2.5 * (0.5 * 0.25 * 5.5) 1.720 1.4 + ( 2
3 * 0.25) = 1.57 2.70
W2 2.5 * (0.3 * 5.5) 4.125 1.4 + 0.25 + (
1
2 * 0.30)
= 1.80 7.43
W3 2.5 * (0.5 * 4) 5.000 1
2 * 4.00 = 2.00 10.0
W4 1.8 * (2.05 * 5.5) 20.440 4 – ( 1
2 * 2.05) = 2.975 60.80
W5 1.5 * 2.05 3.075 2.975 9.15
ΣW 34.36 90.08
(b) Vertical loads:
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :37 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
• Against overturning:
(c) Check stability:
Overturning moment = Pa1 . y1 + Pa2 . y2
O.T.M = 3.00 * 3 + 10.8 * 2 = 30.6 m.t.
Stability moment = Σmoment due to vl loads + Σmoment due to passive (neglected)
S.M = 90.08 – 9.15 = 80.93 m.t.
F.S = 𝐒 .𝐌
𝐎.𝐓.𝐌
= 80.93
30.60 = 2.64 > 1.50 o.k.
Note: the surcharge load must not considered in any stabilizing computations.
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :38 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
R.F = Σ(W – W5) . tanδ + Pp
= (34.36 – 3.075) * tan 2
3 30 + 3.888 = 15.28 t/m’
F.S = 𝑹.𝑭
𝑺.𝑭
= 15.28
13.80 = 1.11 > 1.50 Not satisfied
• Against sliding:
Sliding force = Pa1 + Pa2
S.F = 3.00 + 10.80 = 13.80 t/m’
Resisting force = Resulting friction from vl loads + Pp
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :39 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
RECIPE FOR SUCCESS,
As long as you live, Just Keep
L e a r n i n g …
References
• Das, B., M. (2014), “ Principles of geotechnical Engineering ” Eighth Edition, CENGAGE Learning, ISBN-
13: 978-1-133-10867-2.
• Knappett, J. A. and Craig R. F. (2012), “ Craig’s Soil Mechanics” Eighth Edition, Spon Press, ISBN: 978-0-
415-56125-9.
• Orabi, A. (2015),Soil Mechanics, “Introduction &Properties of Soil lecture notes”, International university of
sciences and technology.
• Terzaghi, K. (1936) "Stress Distribution in Dry and in Saturated Sand Above a Yielding Trap-Door",
Proceedings. First International Conference on Soil Mechanics and Foundation Engineering, Cambridge,
Massachusetts, pp. 307-311.
• Terzaghi, K. (1943). “Theoretical Soil Mechanics”. John Wiley & Sons, New York.
• Meyerhof, G. G. (1951). “The Bearing Capacity of Foundations”. In Géotechnique, vol. 2, no. 4, pp. 301-
332.
• Radwan, A. (2013), “fundamentals of Soil Mechanics”. Helwan university, Faculty of engineering. Civil
Department library.
• El-Kadi, F. (2002), “Principles of Soil Mechanics”. Ain shams university, Faculty of engineering. Civil
Department library.
• Vesic, A. S. (1975). Principle of pile foundation design. Soil Mechanics Series No 38, School of
Engineering, Duke University.
• Joseph E. Bowels, (1999), "Physical and Geotechnical Properties of Soils"; McGraw Hill Book.
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :40 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
• Presentation of the theories and principles of soil mechanics
and foundation engineering.
• Explore the equipment's and instrumentations used for in-situ
and laboratory testing of soil.
• Outline the design standards of different types of foundation,
soil support systems according to several international codes.
• Provide sufficient field case studies and solved examples so that
students can make judgements as to the credibility of results
that they may obtain, or review, in the future.
Soil is a complex multiphase material. A sound understanding of
the fundamental principles and design applications of soil
mechanics is needed to predict the behavior and performance of
soil as a construction material or as a supporting medium for
engineering structures.
The main objective of this course is to provide the undergraduate
student with an insight into the theories and principles of soil
mechanics and foundation engineering, and its applications in
practical problems. The methodology that will be followed in this
course to achieve its objectives are directed towards the following
points:
Preface
Course Instructor
Dr. Mohamed Ezzat Al-Atroush
Dr. Mohamed Ezzat obtained his Ph.D. Degree from Ain Shams University, Egypt, in 2018. He joined the Prince Sultan University (PSU) in 2019 as an Assistant Professor in the area of Civil Engineering. He has broad experience in the field of geotechnical engineering on academic and professional works. Also, he has published many international journal and conference publications in the area of Geotechnical Engineering. He is a member of several international technical committees, such as the American society of civil engineers (ASCE).
On the other hand, Dr. Ezzat participated in many consultancy projects involving site investigations, problematic soils, evaluation of stability of slopes and escarpments, construction and permanent dewatering, design of deep excavation support, traditional and specialized lab testing, field monitoring, geophysical studies, foundation and bridge design, effect of tunnel induced ground deformations on adjacent surface and underground structures. His main research interests are in the Large Diameter bored piles, tunneling and deep excavations, Dynamic soil-structure interaction, Ground Improvement, and Energy and Sustainable Geotechnics.
Prince Sultan University, Riyadh, Saudi Arabia, 2019-2020
