Retaining Wall Calculation Note
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Transcript of Retaining Wall Calculation Note
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
Contents
Calculation Note for Random Stone Retaining Walls at South Marjaayoun 2 Embankment
Reservoir.......................................................................................................................................................................... 4
1. Introduction....................................................................................................................................................... 4
2. Computation Parameters.............................................................................................................................4
2.1 Wall Properties........................................................................................................................................4
2.2 Loads............................................................................................................................................................ 5
2.3 Soil Parameters....................................................................................................................................... 5
3. Random Stone Retaining Wall Design Method..................................................................................6
3.1 Calculation of Horizontal Thrust.....................................................................................................7
3.1.1 Horizontal Active Soil Thrust.......................................................................................................8
3.1.2 Horizontal Active Surcharge Thrust..........................................................................................9
3.2 Overturning Analysis............................................................................................................................9
3.3 Sliding Analysis.....................................................................................................................................10
3.4 Eccentricity of Resultant Forces Analysis.................................................................................11
3.5 Allowable Bearing Pressure Analysis.........................................................................................11
4. Random Stone Retaining Wall Calculations......................................................................................13
4.1 Constants................................................................................................................................................. 13
4.2 Geometry of the Wall......................................................................................................................... 13
4.3 Stability Check.......................................................................................................................................14
4.3.1 Combination 1.................................................................................................................................. 15
4.3.1.1 Soil Parameters........................................................................................................................... 15
4.3.1.2 Horizontal Thrust.......................................................................................................................15
4.3.1.3 Overturning Analysis................................................................................................................16
4.3.1.4 Sliding Analysis............................................................................................................................18
Page 1 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
4.3.1.5 Eccentricity of Resultant Forces Analysis........................................................................19
4.3.1.6 Allowable Bearing Pressure Analysis................................................................................19
4.3.2 Combination 2.................................................................................................................................. 21
4.3.2.1 Soil Parameters........................................................................................................................... 21
4.3.2.2 Horizontal Thrust.......................................................................................................................21
4.3.2.3 Overturning Analysis................................................................................................................22
4.3.2.4 Sliding Analysis............................................................................................................................24
4.3.2.5 Eccentricity of Resultant Forces Analysis........................................................................24
4.3.2.6 Allowable Bearing Pressure Analysis................................................................................25
4.3.3 Seismic Calculation.........................................................................................................................27
4.3.3.1 Soil Parameters........................................................................................................................... 27
4.3.3.2 Horizontal Thrust.......................................................................................................................27
4.3.3.3 Overturning Analysis................................................................................................................28
4.3.3.4 Sliding Analysis............................................................................................................................30
4.3.3.5 Eccentricity of Resultant Forces Analysis........................................................................30
4.3.3.6 Allowable Bearing Pressure Analysis................................................................................31
5. Appendixes...................................................................................................................................................... 33
5.1 Appendix I – Plan and Sections.....................................................................................................33
5.2 Appendix II – Partial Factors Applied on Actions, Soil Parameters and Resistance
34
5.3 Appendix III – Laboratory Test Results.....................................................................................36
5.3.1 Angle of Friction of Soil................................................................................................................37
5.3.2 Unit Weight of Soil..........................................................................................................................40
5.3.3 Specific Gravity of Rock................................................................................................................45
5.3.4 Field Classification and Description of Rock and Soil.....................................................52
5.4 Appendix IV - Allowable Bearing Pressure Calculation......................................................69
Page 2 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
5.5 Appendix V – Internal Stability Check........................................................................................73
5.6 Appendix VI - Stability Analysis....................................................................................................77
5.7 Appendix VII – Formulas for Seismic Calculations...............................................................81
5.7.1 Horizontal Active Soil Thrust.....................................................................................................81
5.7.2 Horizontal Active Surcharge Thrust.......................................................................................82
5.7.3 Dynamic Active Earth Pressure Coefficient for Soil.........................................................82
5.7.4 Overturning moment.....................................................................................................................83
5.7.5 Resisting Force................................................................................................................................. 84
Page 3 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
Calculation Note for Random Stone
Retaining Walls at South Marjaayoun 2
Embankment Reservoir
1. Introduction
This chapter introduces the stability design required for the random stone walls at South
Marjaayoun 2 embankment reservoir.
The design of random stone walls depends mainly on its massive weight to resist failure
from overturning and sliding forces, ensuring that this weight is uniformly distributed to the
soil beneath the wall to avoid its collapse.
The wall design was done referring to the British Standard BS EN1997-1 (Eurocode 7:
Geotechnical Design – Part I: General Rules), BS EN1998-5 (Eurocode 8: Design of Structures
for Earthquake Resistance – Part V: Foundations, Retaining Structures and Geotechnical
Aspects), the technical specification volume 2.2 section 6 and the final detailed design report
for Conveyor 800 Project, Section 5.9.
Eurocode adopt a common design philosophy based on the use of separate partial
factors rather than global factors of safety; this is a substantial departure from much
traditional geotechnical design practice as embodied in BS Codes such as BS 8004.
2. Computation Parameters
The design of earth retaining walls requires the consideration of the interaction between the
ground and the structure. To perform the design of the earth retaining walls a set of
equilibrium calculations is to be done. Wall properties, loads and soil characteristics are the
main parameters to be taken into consideration in designing the retaining walls.
2.1 Wall Properties
Random stone walls used for retaining the fill will be stone masonry walls comprised of rock
materials packed with mortar joints. According to Technical Specification Volume 2.2 Section
6, each stone shall be of minimum mass 500 kg and minimum dimension 600 mm.
The density of the designed wall was measured to be 2.4 Ton/m3 according to laboratory
test results (Appendix III).
The following figure represents the geometrical parameter of the retaining wall:
Page 4 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
Figure 01 - Geometrical Parameters of Wall
2.2 Loads
The pressures acting on the retaining wall are:
1. Uniform surcharge pressure Q acting on the entire ground surface behind the wall. Q
is assumed to be 0.5 Ton/m2.
2. At rest earth pressure exerted on the back of the wall.
3. Bearing pressure of the soil supporting the retaining wall.
2.3 Soil Parameters
According to laboratory test results (Appendix III), the soil parameters used for the design of
the retaining wall are:
1. Soil density: ɣs = 1.8 Ton/m3.
2. Friction angle of soil: = 38Φ o.
3. Allowable bearing pressure: qa = 35 Ton/m2 (Calculated in Appendix IV).
4. Water density: ɣw = 0 Ton/m3, since the wall is provided with weep
holes (4in PVC Pipes) embedded in each concrete layer and distributed at 2 meter
apart in vertical and horizontal directions, then no water is collected behind the wall.
Page 5 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
3. Random Stone Retaining Wall Design Method
The failure of the retaining wall is a result of the instability of the earth mass, such as
overturning or a rotational failure, a translational failure and bearing failure. Where the
distributing moments on the wall exceed the restoring moments in the rotational failure and
the distributing forces exceed the restoring forces in translational failure.
According to BS EN1997-1, two separate calculations shall, in principle, be performed:
1. Combination 1: A1 “+” M1 “+” R1
2. Combination 2: A2 “+” M2 “+” R1
Where set A includes the partial factors applied on actions or the effects of actions (Appendix
II, Table A.3), set M includes the partial factors applied for soil parameters (Appendix II,
Table A.4) and set R includes the partial resistance factors (Appendix II, Tables A.13 and
A.14).
Moreover, since the designed wall is located in an area affected by earthquakes, another
calculation must be performed to ensure the functionality of the wall during and after an
earthquake, without suffering significant structural damage. This calculation was done
according to BS EN1998-5.
The two calculations according to BS EN1997-1 are used for static conditions, whereas the
calculation according to BS EN1998-5 is used for seismic conditions.
The forces acting on the wall are mainly due to the soil retained behind the wall along with
the surcharge above it producing a horizontal thrust.
Page 6 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
3.1 Calculation of Horizontal Thrust
The total horizontal thrust exerted on the retaining wall is the summation of horizontal
active soil thrust and horizontal active surcharge thrust as shown in the following figure:
Figure 02 - Horizontal Thrust
Pha=Phs+Phq
Where:
Pha: Horizontal thrust
Phs: Horizontal active soil thrust
Phq: Horizontal active surcharge thrust
Page 7 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
3.1.1 Horizontal Active Soil Thrust
The retained soil will create earth pressure on the retaining wall that is known as the active
soil pressure resulting in a horizontal active soil thrust calculated by the following
equations:
Phs=γGKo γ dH
2
2(For Static Conditi ons)
Where
Phs: Horizontal active soil thrust [Ton/ml]
Ko: At rest earth pressure coefficient for soil Ko=1−sin∅ '
where tan ( ’) = tan ( ) / Φ Φ ɣ ’Φ , is the angle of friction of soil and Φ ɣ ’Φ is the
partial factor for angle of shear resistance (Appendix II, Table A.4)
ɣd: Design soil density = ɣɣ x ɣs [Ton/m3]
ɣɣ: Partial factor for weight density (Appendix II, Table A.4)
ɣs: Soil density [Ton/m3]
ɣG: Partial factor on permanent actions (Appendix II, Table A.3)
H: Height of Wall [m]
Phs=(1+K v )K γ sH 2
2(For SeismicConditions )(Appendix VII )
Where
K: Dynamic active earth pressure coefficient for soil
K=cos2(∅−θ)
cosθ cos(θ+δ)[1+√ sin(∅+δ)sin (∅−θ)cos (θ+δ) ]
2 where tanθ=
K h1−K v
δ : Angle of friction between the soil and the wall = 2/3 Φ
Kh: Horizontal seismic coefficient
Kv: Vertical seismic coefficient = 2/3 Kh
Page 8 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
3.1.2 Horizontal Active Surcharge Thrust
The uniform surcharge pressure acting on the entire ground surface behind the wall exerts a
horizontal active surcharge pressure calculated by the following equations:
Phq=γQK oQH (For Static Condition s)
Where
Phq: Horizontal active surcharge thrust [Ton/ml]
Q: Surcharge Pressure [Ton/m2]
ɣQ: Partial factor on variable actions (Appendix II, Table A.3)
Phq=(1+K v )KQH (For SeismicConditions)(Appendix VII )
3.2 Overturning Analysis
Overturning of the retaining wall is calculated by considering moments about the toe of the
wall (Point O, Figure 02), and shall satisfy the following:
M r>M o
Where:
Mr: Resisting moment per linear meter of wall length [Ton.m/ml]
Mo: Overturning moment per linear meter of wall length [Ton.m/ml]
The resisting moment (Mr) is calculated according to the following equations:
M r=γG×W T×xCG (For Static Conditions)
Where:
WT: Weight of the retaining wall per linear meter of wall length [Ton/ml]
W T=γGW× A
Where ɣGW is the density of the retaining wall [Ton/m3] and A is the cross
sectional area of the wall [m2]
xCG: Lateral distance from WT to the toe of the wall [m]
Page 9 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
M r=W T×xCG (For SeismicConditions)
The overturning moment (Mo) is calculated according to the following equations:
M o=M os+M oq(For Static Conditions)
Where:
Mos: Soil thrust overturning moment per linear meter of wall length [Ton.m/ml]
M os=Phs×(H3 −h) Where h is the inclination height [m]
Moq: Surcharge thrust overturning moment per linear meter of wall length
M oq=Phq×(H2 −h) [Ton.m/ml]
M o=M os+M oq+W T (K v xCG+Kh yCG) (For SeismicConditions )(Appendix VII )
Where:
YCG: Vertical distance from WT to the toe of the wall [m]
The moment due to passive pressure is neglected. The reason is because with a rotation type
failure mode, the wall may not move enough laterally to induce passive earth pressures.
3.3 Sliding Analysis
Sliding of the retaining wall occurs when the driving force (Pha) is greater than the resisting
force (Phr) according to the following equation:
Phr>Pha
Phr=μ ' γGW T (For Static Conditions)
Where:
’:μ Design friction coefficient ¿ tan∅ '
Phr=¿
Where:
Page 10 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
:μ Characteristic friction coefficient ¿ tan∅
The horizontal passive soil thrust is a favorable action since it increases the stability of the
wall against sliding. However it was neglected since there might be excavation behind the
wall.
In some situations, there may be adhesion between the bottom of the retaining wall and the
bearing soil. This adhesion is often neglected because the wall is designed for active
pressures, which is typically developed when there is wall translation. Translation of the
wall will break the adhesive forces between the bottom of the wall and the bearing soil and
therefore adhesion is often neglected.
3.4 Eccentricity of Resultant Forces Analysis
The eccentricity (e) of the resultant forces acting on the base of the wall from center of the
base must fall in the middle one third of the wall base as shown in the following equation:
−B6≤e≤
B6
Where:
B: Width at the base of the wall [m]
e: Eccentricity of resultant forces [m]
e=B2
−x where x is the difference in the opposing moments divided by WT
x=M r−M o
W T[m]
3.5 Allowable Bearing Pressure Analysis
Failure of the soil under the base of the retaining wall occurs when the bearing pressure ( )σ
under the base of the wall is greater than the design allowable bearing pressure of soil (q’a),
or when there is tension at the base.
Hence, the following equations shall be satisfied:
σ max<qa'
σ min>0
Page 11 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
Where:
qa'=qaγR
(For Static Conditions)
Where:
qa: Allowable bearing pressure of soil [Ton/m2]
γR: Partial bearing resistance factor (Appendix II, Table A.13)
qa'=qa(For SeismicConditions)
σ=γGW T
B (1± 6eB )(For Static Conditions)
σ=W T
B (1± 6eB ) (For SeismicConditions )
Page 12 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
4. Random Stone Retaining Wall Calculations
The random stone retaining wall of South Marjaayoun 2 embankment reservoir can be
divided into 5 sections according to retained fill height.
The sections named as A-A, B-B, C-C, D-D and E-E.
4.1 Constants
Density of the retaining wall: γGW = 2.40 Ton/m3
Surcharge Pressure: Q = 0.50 Ton/m2
Soil Density: γs = 1.80 Ton/m3
Angle of Friction of Soil: = 38ϕ ᵒ Allowable Bearing Pressure: qa = 35.00 Ton/m2
4.2 Geometry of the Wall
Referring to Figure 01 and Appendix I, the retaining wall geometry can be summarized in the
following table:
Page 13 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
Section A-A B-B C-C D-D E-E
Height of Wall (H) [m] 7.00 8.00 9.00 10.00 10.50
Height of the Top Section of the Wall (H') [m] 5.68 5.68 5.68 5.68 5.68
Inclination Height (h) [cm] 0.35 0.40 0.50 0.55 0.60
Width at the Middle of the Wall (W) [m] 3.50 3.50 3.50 3.50 3.50
Width at the Base of the Wall (B) [m] 3.48 4.00 5.00 5.50 6.00
Inclination Width (b) [m] 0.70 0.80 0.90 1.00 1.05
Thickness at the Top of the Wall (T) [m] 0.75 0.75 0.75 0.75 0.75
Thickness at the Base of the Wall (t) [m] 0.94 1.00 1.00 1.00 1.00
Lateral Distance from WT to the Toe of the
Wall (xCG) [m]2.43 2.82 3.56 3.92 4.28
Vertical Distance from WT to the Toe of the
Wall (yCG) [m]2.51 2.81 2.98 3.27 3.36
Cross Sectional Area of Wall (A) [m2] 16.10 20.34 26.05 31.53 35.13
4.3 Stability Check
According to BS EN1997 and BS EN1998, three separate calculations shall be performed for
checking the stability of the retaining wall:
1. Combination 1: A1 “+” M1 “+” R1
2. Combination 2: A2 “+” M2 “+” R1
3. Seismic Calculation
Page 14 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
4.3.1 Combination 1
4.3.1.1 Soil Parameters
The soil parameters integrated in all the calculations depend mainly on the combination
chosen. For combination 1, set M1, the partial factors for soil parameters are as follows
according to table A.4 (Appendix II):
Weight Density: γ γ=1
Angle of Shear Resistance: γ∅ '=1
And hence the design soil parameters are as follows:
Soil Density: γ d=γ γ×γ s=1 .80 Ton/m3
Angle of Friction of Soil: ∅ '=tan−1 tan∅ '=tan−1 tan∅γ∅ '
=¿38 .00° ¿
Friction Coefficient: μ '=tanϕ '=0 .78 At Rest Earth Pressure
Coefficient for Soil: Ko=1−sin∅'=0.38
4.3.1.2 Horizontal Thrust
The horizontal thrust exerted on the retaining wall is a combination of horizontal active soil
thrust and horizontal active surcharge thrust:
Pha=Phs+Phq
Where:
Pha: Horizontal thrust
Phs: Horizontal active soil thrust
Phq: Horizontal active surcharge thrust
Where:
Phs=γGKo γ dH
2
2
Knowing that:
ɣG = 1.35 (A lateral earth load is an unfavorable action as it
causes the wall to have a greater tendency to overturn, according to
table A.3, Appendix II)
Page 15 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
Ko = 0.38
ɣd = 1.80 Ton/m3
H = Height of Wall [m]
Phq=γQK oQH
Knowing that:
ɣQ = 1.5 (Surcharge is an unfavorable action as it increases the
tendency of the wall to overturn, according to table A.3, Appendix II)
Q = 0.5 Ton/m2
Substituting the corresponding values of each section in the above equations, the following
table provides the horizontal thrust:
Section A-A B-B C-C D-D E-E
Horizontal Active Soil Thrust
(Phs) [Ton/ml]22.88 29.89 37.82 46.70 51.48
Horizontal Active Surcharge
Thrust (Phq) [Ton/ml]2.02 2.31 2.59 2.88 3.03
Horizontal Thrust (Pha)
[Ton/ml]24.90 32.19 40.42 49.58 54.51
4.3.1.3 Overturning Analysis
Taking into consideration the moments about the toe of the retaining wall (Point O, Figure
02), the overturning moments shall satisfy the following:
M r>M o
Where:
M r=γG×W T×xCG
Knowing that:
Page 16 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
ɣG = 1 (The weight of the wall is a favorable action as
increasing the weight of the wall increases its stability, according to
table A.3, Appendix II)
W T = γGW× A [Ton/ml]
ɣGW = 2.40 Ton/m3
A = Cross sectional area of the wall [m2]
xCG = Lateral distance from WT to the toe of the wall [m]
M o=M os+M oq
Knowing that:
M os = Phs×( H3 −h) [Ton.m/ml]
M oq = Phq×(H2 −h) [Ton.m/ml]
h = Inclination height [m]
The following table represents the values of the resisting and overturning moments
corresponding to the different sections available:
Section A-A B-B C-C D-D E-E
Weight of Wall per Linear Meter
of Wall Length (WT) [Ton/ml]38.64 48.82 62.52 75.67 84.32
Soil Thrust Overturning Moment
per Linear Meter of Wall Length
(Mos) [Ton.m/ml]
45.45 67.80 94.64 130.11 149.46
Surcharge Thrust Overturning
Moment per Linear Meter of
Wall Length (Moq) [Ton.m/ml]
6.36 8.31 10.38 12.84 14.08
Overturning Moment per Linear
Meter of Wall Length (Mo)
[Ton.m/ml]
51.81 76.11 105.02 142.95 163.54
Page 17 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
Resisting Moment per Linear
Meter of Wall Length (Mr)
[Ton.m/ml]
93.88 137.47 222.84 296.54 360.63
As summarized in the above table, the resisting moment is much greater than the
overturning moment for all the sections and thus the geometry of the wall is sufficient for
resisting overturning using combination 1 calculation.
4.3.1.4 Sliding Analysis
The Sliding of the retaining wall occurs when the driving force (Pha) is greater than the
resisting force (Phr) according to the following equation:
Phr>Pha
Where:
Phr=μ ' γGW T
Knowing that:
ɣG = 1 (The weight of the wall is a favorable action as
increasing the weight of the wall increases its stability, according to
table A.3, Appendix II)
’μ = 0.78
Substituting the corresponding values in the above equation, the following table is obtained:
Section A-A B-B C-C D-D E-E
Horizontal Thrust (Pha)
[Ton/ml]24.90 32.19 40.42 49.58 54.51
Resisting Sliding Force (Phr)
[Ton/ml]30.19 38.14 48.85 59.12 65.88
The resisting force is greater than the driving force for all the above sections and thus the
geometry of the wall is sufficient for resisting sliding using combination 1 calculation.
Page 18 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
4.3.1.5 Eccentricity of Resultant Forces Analysis
The eccentricity of the resultant force can be calculated as follows:
e=B2
−x [m]
Where:
B = Width at the Base of the Wall [m]
x=M r−M o
W T
The obtained eccentricity results in the following table should satisfy the following
condition:−B6≤e≤
B6
Section A-A B-B C-C D-D E-E
() [m] 1.09 1.26 1.88 2.03 2.34
Eccentricity (e) [m] 0.65 0.74 0.62 0.72 0.66
(B/6) [m] 0.58 0.67 0.83 0.92 1.00
The eccentricity for all the sections almost satisfies the above condition, thus the line of
action of forces falls within the middle third of the base as calculated for combination 1.
4.3.1.6 Allowable Bearing Pressure Analysis
The bearing pressure should satisfy the following conditions:
σ max<qa'
σ min>0
Where:
qa'=qaγR
Knowing that:
ɣR = 1 (According to table A.13, Appendix II)
Page 19 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
qa = 35 Ton/m2
σ=γGW T
B (1± 6eB )Knowing that:
ɣG = 1.35 (The weight of the wall is an unfavorable action as
increasing the weight of the wall increases the bearing pressure,
according to table A.3, Appendix II)
The table below summarizes the obtained results:
Section A-A B-B C-C D-D E-E
Minimum Bearing Pressure
(σmin) [Ton/m2.ml]-1.86 -1.89 4.41 3.98 6.40
Maximum Bearing Pressure
(σmax) [Ton/m2.ml]31.81 34.84 29.35 33.16 31.54
The bearing pressure almost satisfies the above conditions for all the sections and thus the
allowable bearing pressure of the soil beneath the wall is enough for resisting bearing
pressures using combination 1 calculation.
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
4.3.2 Combination 2
4.3.2.1 Soil Parameters
The soil parameters integrated in all the calculations depend mainly on the combination
chosen. For combination 2, set M2, the partial factors for soil parameters are as follows
according to table A.4 (Appendix II):
Weight Density: γ γ=1
Angle of Shear Resistance: γ∅ '=1.25
And hence the design soil parameters are as follows:
Soil Density: γ d=γ γ×γ s=1 .80 Ton/m3
Angle of Friction of Soil: ∅ '=tan−1 tan∅ '=tan−1 tan∅γ∅ '
=32 .01 °
Friction Coefficient: μ '=tanϕ '=0 .63 At Rest Earth Pressure
Coefficient for Soil: Ko=1−sin∅'=0.47
4.3.2.2 Horizontal Thrust
The horizontal thrust exerted on the retaining wall is a combination of horizontal active soil
thrust and horizontal active surcharge thrust:
Pha=Phs+Phq
Where:
Pha: Horizontal thrust
Phs: Horizontal active soil thrust
Phq: Horizontal active surcharge thrust
Where:
Phs=γGKo γ dH
2
2
Knowing that:
ɣG = 1 (According to table A.3, Appendix II)
Ko = 0.47
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
ɣd = 1.80 Ton/m3
H = Height of Wall [m]
Phq=γQK oQH
Knowing that:
ɣQ = 1.3 (According to table A.3, Appendix II)
Q = 0.5 Ton/m2
Substituting the corresponding values of each section in the above equations, the following
table provides the horizontal thrust:
Section A-A B-B C-C D-D E-E
Horizontal Active Soil Thrust
(Phs) [Ton/ml]20.73 27.07 34.26 42.30 46.63
Horizontal Active Surcharge
Thrust (Phq) [Ton/ml]2.14 2.44 2.75 3.05 3.21
Horizontal Thrust (Pha)
[Ton/ml]22.86 29.51 37.01 45.35 49.84
4.3.2.3 Overturning Analysis
Taking into consideration the moments about the toe of the retaining wall (Point O, Figure
02), the overturning moments shall satisfy the following:
M r>M o
Where:
M r=γG×W T×xCG
Knowing that:
ɣG = 1 (According to table A.3, Appendix II)
W T = γGW× A [Ton/ml]
ɣGW = 2.40 Ton/m3
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
A = Cross sectional area of the wall [m2]
xCG = Lateral distance from WT to the toe of the wall [m]
M o=M os+M oq
Knowing that:
M os = Phs×( H3 −h) [Ton.m/ml]
M oq = Phq×(H2 −h) [Ton.m/ml]
h = Inclination height [m]
The following table represents the values of the resisting and overturning moments
corresponding to the different sections available:
Section A-A B-B C-C D-D E-E
Weight of Wall per Linear Meter
of Wall Length (WT) [Ton/ml]38.64 48.82 62.52 75.67 84.32
Soil Thrust Overturning Moment
per Linear Meter of Wall Length
(Mos) [Ton.m/ml]
41.17 61.42 85.72 117.86 135.38
Surcharge Thrust Overturning
Moment per Linear Meter of
Wall Length (Moq) [Ton.m/ml]
6.74 8.80 11.00 13.60 14.93
Overturning Moment per Linear
Meter of Wall Length (Mo)
[Ton.m/ml]
47.91 70.22 96.73 131.46 150.30
Resisting Moment per Linear
Meter of Wall Length (Mr)
[Ton.m/ml]
93.88 137.47 222.84 296.54 360.63
As summarized in the above table, the resisting moment is much greater than the
overturning moment for all the sections and thus the geometry of the wall is sufficient for
resisting overturning using combination 2 calculation.
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
4.3.2.4 Sliding Analysis
The Sliding of the retaining wall occurs when the driving force (Pha) is greater than the
resisting force (Phr) according to the following equation:
Phr>Pha
Where:
Phr=μ ' γGW T
Knowing that:
ɣG = 1 (According to table A.3, Appendix II)
’μ = 0.63
Substituting the corresponding values in the above equation, the following table is obtained:
Section A-A B-B C-C D-D E-E
Horizontal Thrust (Pha)
[Ton/ml]22.86 29.51 37.01 45.35 49.84
Resisting Sliding Force (Phr)
[Ton/ml]24.15 30.51 39.08 47.29 52.70
The resisting force is greater than the driving force for all the above sections and thus the
geometry of the wall is sufficient for resisting sliding using combination 2 calculation.
4.3.2.5 Eccentricity of Resultant Forces Analysis
The eccentricity of the resultant force can be calculated as follows:
e=B2
−x [m]
Where:
B = Width at the Base of the Wall [m]
x=M r−M o
W T
The obtained eccentricity results in the following table should satisfy the following
condition:−B6≤e≤
B6
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
Section A-A B-B C-C D-D E-E
() [m] 1.19 1.38 2.02 2.18 2.49
Eccentricity (e) [m] 0.55 0.62 0.48 0.57 0.51
(B/6) [m] 0.58 0.67 0.83 0.92 1.00
The eccentricity for all the sections satisfies the above condition, thus the line of action of
forces falls within the middle third of the base as calculated for combination 2.
4.3.2.6 Allowable Bearing Pressure Analysis
The bearing pressure should satisfy the following conditions:
σ max<qa'
σ min>0
Where:
qa'=qaγR
Knowing that:
ɣR = 1 (According to table A.13, Appendix II)
qa = 35 Ton/m2
σ=γGW T
B (1± 6eB )Knowing that:
ɣG = 1 (According to table A.3, Appendix II)
The table below summarizes the obtained results:
Section A-A B-B C-C D-D E-E
Minimum Bearing Pressure
(σmin) [Ton/m2.ml]0.55 0.81 5.26 5.23 6.95
Maximum Bearing Pressure 21.63 23.60 19.75 22.29 21.16
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
(σmax) [Ton/m2.ml]
The bearing pressure satisfies the above conditions for all the sections and thus the
allowable bearing pressure of the soil beneath the wall is enough for resisting bearing
pressures using combination 2 calculation.
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
4.3.3 Seismic Calculation
4.3.3.1 Soil Parameters
The soil parameters integrated in all seismic calculations are used by their characteristic
values as described in section 4.1 of this calculation note. Moreover, seismic coefficients will
be used in the below calculations. These coefficients are as follows according to the final
detailed design report for Conveyor 800 Project, Section 5.9:
Horizontal seismic coefficient: Kh=0.13
Vertical seismic coefficient: K v=23Kh=0.09
And hence the remaining soil parameters are as follows:
Characteristic Friction
Coefficient: μ=tanϕ=0.78
Angle of friction between
the soil and the wall: δ=23∅=25.33 °
Angle Used for Computing K: θ=tan−1( Kh1−K v )=8 .10 °
Dynamic Active Earth
Pressure Coefficient for Soil:
K=cos2(∅−θ)
cosθ cos(θ+δ)[1+√ sin(∅+δ)sin (∅−θ)cos (θ+δ) ]
2=0.30
4.3.3.2 Horizontal Thrust
The horizontal thrust exerted on the retaining wall is a combination of horizontal active soil
thrust and horizontal active surcharge thrust:
Pha=Phs+Phq
Where:
Pha: Horizontal thrust
Phs: Horizontal active soil thrust
Page 27 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
Phq: Horizontal active surcharge thrust
Where:
Phs=(1+K v )K γ sH2
2
Knowing that:
Kv = 0.09
K = 0.30
ɣs = 1.80 Ton/m3
H = Height of Wall [m]
Phq=(1+K v )KQH
Knowing that:
Q = 0.5 Ton/m2
Substituting the corresponding values of each section in the above equations, the following
table provides the horizontal thrust:
Section A-A B-B C-C D-D E-E
Horizontal Active Soil Thrust
(Phs) [Ton/ml]14.55 19.01 24.06 29.70 32.75
Horizontal Active Surcharge
Thrust (Phq) [Ton/ml]1.16 1.32 1.49 1.65 1.73
Horizontal Thrust (Pha)
[Ton/ml]15.71 20.33 25.54 31.35 34.48
4.3.3.3 Overturning Analysis
Taking into consideration the moments about the toe of the retaining wall (Point O, Figure
02), the overturning moments shall satisfy the following:
M r>M o
Where:
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
M r=W T×xCG
Knowing that:
W T = γGW× A [Ton/ml]
ɣGW = 2.40 Ton/m3
A = Cross sectional area of the wall [m2]
xCG = Lateral distance from WT to the toe of the wall [m]
M o=M os+M oq+W T (K v xCG+Kh yCG)
Knowing that:
M os = Phs×(H3 −h) [Ton.m/ml]
M oq = Phq×( H2 −h) [Ton.m/ml]
h = Inclination height [m]
Kh = 0.13
yCG = Vertical distance from WT to the toe of the wall [m]
The following table represents the values of the resisting and overturning moments
corresponding to the different sections available:
Section A-A B-B C-C D-D E-E
Weight of Wall per Linear Meter
of Wall Length (WT) [Ton/ml]38.64 48.82 62.52 75.67 84.32
Soil Thrust Overturning Moment
per Linear Meter of Wall Length
(Mos) [Ton.m/ml]
28.91 43.13 60.20 82.76 95.07
Surcharge Thrust Overturning
Moment per Linear Meter of
Wall Length (Moq) [Ton.m/ml]
3.64 4.76 5.94 7.35 8.06
Overturning Moment per Linear 53.30 77.63 109.68 147.98 171.21
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
Meter of Wall Length (Mo)
[Ton.m/ml]
Resisting Moment per Linear
Meter of Wall Length (Mr)
[Ton.m/ml]
93.88 137.47 222.84 296.54 360.63
As summarized in the above table, the resisting moment is much greater than the
overturning moment for all the sections and thus the geometry of the wall is sufficient for
resisting overturning under seismic conditions.
4.3.3.4 Sliding Analysis
The Sliding of the retaining wall occurs when the driving force (Pha) is greater than the
resisting force (Phr) according to the following equation:
Phr>Pha
Where:
Phr=¿
Knowing that:
μ = 0.78
Substituting the corresponding values in the above equation, the following table is obtained:
Section A-A B-B C-C D-D E-E
Horizontal Thrust (Pha)
[Ton/ml]15.71 20.33 25.54 31.35 34.48
Resisting Sliding Force (Phr)
[Ton/ml]22.55 28.49 36.49 44.16 49.21
The resisting force is greater than the driving force for all the above sections and thus the
geometry of the wall is sufficient for resisting sliding under seismic conditions.
4.3.3.5 Eccentricity of Resultant Forces Analysis
The eccentricity of the resultant force can be calculated as follows:
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
e=B2
−x [m]
Where:
B = Width at the Base of the Wall [m]
x=M r−M o
W T
The obtained eccentricity results in the following table should satisfy the following
condition:−B6≤e≤
B6
Section A-A B-B C-C D-D E-E
() [m] 1.05 1.23 1.81 1.96 2.25
Eccentricity (e) [m] 0.69 0.77 0.69 0.79 0.75
(B/6) [m] 0.58 0.67 0.83 0.92 1.00
The eccentricity for all the sections almost satisfies the above condition, thus the line of
action of forces falls within the middle third of the base as calculated under seismic
conditions.
4.3.3.6 Allowable Bearing Pressure Analysis
The bearing pressure should satisfy the following conditions:
σ max<qa'
σ min>0
Where:
qa'=qa
Knowing that:
qa = 35 Ton/m2
σ=W T
B (1± 6eB )The table below summarizes the obtained results:
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
Section A-A B-B C-C D-D E-E
Minimum Bearing Pressure
(σmin) [Ton/m2.ml]-2.11 -1.97 2.15 1.95 3.46
Maximum Bearing Pressure
(σmax) [Ton/m2.ml]24.30 26.38 22.86 25.56 24.64
The bearing pressure almost satisfies the above conditions for all the sections and thus the
allowable bearing pressure of the soil beneath the wall is enough for resisting bearing
pressures under seismic conditions.
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
5. Appendixes
5.1 Appendix I – Plan and Sections
The following figures show the plan layout and the different sections of the retaining wall:
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
5.2 Appendix II – Partial Factors Applied on Actions, Soil Parameters
and Resistance
The following tables represent the partial factors on actions or the effects of actions (Table
A.3), the partial factors for soil parameters (Table A.4), the partial resistance factors for
retaining structures (Table A.13) and the partial resistance factors for slopes and overall
stability (Table A.14).
The tables are presented in Annex A of BS EN1997.
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
5.3 Appendix III – Laboratory Test Results
The values of the angle of friction of soil and the unit weight of the retaining wall and of the
retained soil were computed according to tests done in our laboratory.
The test results are listed below:
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
5.3.1 Angle of Friction of Soil
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
5.3.2 Unit Weight of Soil
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CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
5.3.3 Specific Gravity of Rock
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
5.3.4 Field Classification and Description of Rock and Soil
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
5.4 Appendix IV - Allowable Bearing Pressure Calculation
The allowable bearing pressure (qa) was calculated according to the following equation of BS
EN1997:
qa=c ' N c bc sc ic+q'N qbq sq iq+0.5 γ dB
'N γ bγ sγ iγ
Since the cohesion of soil (c’) is equal to 0, the equation of qa will be:
qa=q'Nqbq sqiq+0.5 γ dB
' N γbγ sγ iγ
Where:
ɣd: Design soil density = 1.80 Ton/m3
’:φ Design angle of friction of soil = 38˚
q’: Design effective overburden pressure at the level of wall base [Ton/m2]
q '=γ d×t where t is the thickness of buried soil at the wall base
[m]
Nq,ɣ: Bearing capacity factors
Nq=eπ tan∅ ' tan2(45+∅ '
2)
N γ=2(N q−1) tan∅'
bq,ɣ: Inclination of base factors
bq=bγ ¿(1−α tan∅ ')2 where is the inclination of the wallα [m]
sq,ɣ: Shape factors
sq=sγ=1 (For foundations where the length is much greater than the width)
iq,ɣ: Load inclination factors
iq=(1−FHFV
)2
iγ=(1−F HFV
)3
Where FH/FV is the ratio of horizontal forces to vertical forces
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
FH=Fhs+Fhq [Ton/ml]
Fhs=K o γdH
2
2[Ton/ml]
Fhq=KoQH [Ton/ml]
Ko: At Rest Earth Pressure Coefficient for Soil = 0.38
Q: Surcharge Pressure = 0.5 Ton/m2
H: Height of Wall [m]
FV=W T=γGW× A [Ton/ml]
WT: Weight of the retaining wall per linear meterof wall length [Ton/ml]
ɣGW: Density of the retaining wall = 2.40 Ton/m3
A: Cross sectional area of the wall [m2]
B’: Effective foundation width [m]
B'=B−2e
B: Width at the base of the wall [m]
e: Eccentricity of resultant forces [m]
e=B2
−x where x=MFr−MFo
W T is the difference in the opposing
moments divided by WT [m]
MFr=FV× xCG [Ton.m/ml]
MFo=Fhs×(H3 −h)+Fhq×( H2 −h) [Ton.m/ml]
xCG: Lateral distance from WT to the toe of the wall [m]
h: Inclination height [m]
Substituting the above values, the following table summarizes the results of the allowable
bearing pressure (qa) for each different wall section:
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
Section A-A B-B C-C D-D E-E
Design Effective Overburden Pressure
Design Effective Overburden Pressure (q') [Ton/m2] 1.69 1.8 1.8 1.8 1.8
Horizontal and Vertical Forces
Horizontal Active Soil Force (Fhs) [Ton/ml] 16.95 22.14 28.02 34.59 38.14
Horizontal Active Surcharge Force (Fhq) [Ton/ml] 1.35 1.54 1.73 1.92 2.02
Horizontal Force (FH) [Ton/ml] 18.29 23.68 29.75 36.51 40.15
Vertical Force (FV) [Ton/ml] 38.64 48.82 62.52 75.67 84.32
Factors
Bearing Capacity Factor (Nq) 48.93 48.93 48.93 48.93 48.93
Bearing Capacity Factor (Nɣ) 74.90 74.90 74.90 74.90 74.90
Inclination of Base Factor (bq) 0.85 0.85 0.85 0.85 0.85
Inclination of Base Factor (bɣ) 0.85 0.85 0.85 0.85 0.85
Shape Factor (sq) 1.00 1.00 1.00 1.00 1.00
Shape Factor (sɣ) 1.00 1.00 1.00 1.00 1.00
Load Inclination Factor (iq) 0.28 0.27 0.27 0.27 0.27
Load Inclination Factor (iɣ) 0.15 0.14 0.14 0.14 0.14
Effective Foundation Width
Overturning Moment per Linear Meter of Wall
Length (MFo) [Ton.m/ml]37.91 55.76 77.02 104.94 120.10
Resisting Moment per Linear Meter of Wall Length
(MFr) [Ton.m/ml]93.88 137.47 222.84 296.54 360.63
( ) [m]ẍ 1.45 1.67 2.33 2.53 2.85
Eccentricity (e) [m] 0.29 0.33 0.17 0.22 0.15
Effective Foundation Width (B') [m] 2.90 3.35 4.66 5.06 5.71
Allowable Bearing Pressure
Allowable Bearing Pressure (qa) [Ton/m2] 43.73 46.08 59.10 60.28 67.54
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
As a result, a minimum value for the allowable bearing pressure was assumed to be 35
Ton/m2.
Moreover, as recommended by the Engineer, the wall is laid on soil replacement fill with an
average of depth 3.5 meters beneath heel of wall, and thus the allowable bearing pressure is
achieved.
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
5.5 Appendix V – Internal Stability Check
Internal stability check should be studied to avoid the failure of the retaining wall and to
ensure that all the stones comprising the wall are acting together. Knowing that the
minimum thickness of the stones used in the construction of the retaining wall is 60cm, it is
enough to study the stability of the retaining wall against sliding across the joints, i.e. every
60cm. Moreover, since the stones in each row are of variable thicknesses, this will create
keys between rows that will produce additional sliding resistance.
Referring to this calculation note, combination 1 has shown to be the most critical regarding
stability against sliding, so the internal stability checks against sliding can be performed only
on this combination.
Considering (i) to be the height from the top of the wall, the resisting force against sliding at
height (i), (Phr(i)), must be greater than the sliding force at the same height, (Pha(i)), according
to the following equation:
Phr (i )>Pha(i)
Where:
Phr (i )=μ ' γGW T (i)
Knowing that:
ɣG = 1 (The weight of the wall is a favorable action as
increasing the weight of the wall increases its stability, according to
table A.3, Appendix II)
W T (i) = γGW× A(i) [Ton/ml]
ɣGW = 2.40 Ton/m3
A(i) = Cross sectional area from the top of the wall to height i
from top of wall [m2]
’μ = 0.78
Pha (i)=Phs(i)+Phq (i)
Phs (i)=γGKo γ d i
2
2
Knowing that:
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
ɣG = 1.35 (A lateral earth load is an unfavorable action as it
causes the wall to have a greater tendency to overturn, according to
table A.3, Appendix II)
Ko = 0.38
ɣd = 1.80 Ton/m3
Phq (i)=γQKoQi
Knowing that:
ɣQ = 1.5 (Surcharge is an unfavorable action as it increases the
tendency of the wall to overturn, according to table A.3, Appendix II)
Q = 0.5 Ton/m2
The sliding force is independent of the geometry of the section but yet depends on the height
at which the force is calculated. Consequently the sliding force results are the same for all
sections at each height.
Whereas the resisting force depends on the area of section from top of wall to height i, and
for simplicity the calculation will be applied only for the smallest area.
Substituting the corresponding values in the above equations, the following table is
obtained:
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
Sections A-A,
B-B, C-C, D-D &
E-E
A(i)
[m2]
WT(i)
[Ton/ml]
Phr(i)
[Ton/ml]
Phs(i)
[Ton/ml]
Phq(i)
[Ton/ml]
Pha(i)
[Ton/ml]
i = 0.6 m 0.59 1.41 1.10 0.17 0.17 0.34
i = 1.2 m 1.31 3.15 2.46 0.67 0.35 1.02
i = 1.8 m 2.21 5.30 4.14 1.51 0.52 2.03
i = 2.4 m 3.27 7.86 6.14 2.69 0.69 3.38
i = 3.0 m 4.51 10.82 8.46 4.20 0.86 5.07
i = 3.6 m 5.92 14.20 11.09 6.05 1.04 7.09
i = 4.2 m 7.49 17.98 14.05 8.24 1.21 9.45
i = 4.8 m 9.24 22.17 17.32 10.76 1.38 12.14
i = 5.4 m 11.15 26.77 20.91 13.62 1.56 15.17
i = 6.0 m 13.22 31.73 24.79 16.81 1.73 18.54
i = 6.6 m 15.31 36.75 28.71 20.34 1.90 22.24
i = 7.2 m 17.71 42.51 33.21 24.21 2.08 26.28
i = 7.8 m 20.59 49.42 38.61 28.41 2.25 30.66
i = 8.4 m 23.59 56.62 44.24 32.95 2.42 35.37
i = 9.0 m 26.89 64.54 50.42 37.82 2.59 40.42
i = 9.6 m 30.49 73.18 57.17 43.04 2.77 45.80
The resisting force is greater than the driving force at all the heights, thus the internal
stability of the wall is sufficient for resisting sliding.
As mentioned in the method statement of the earth embankment reservoirs, the
construction of the wall must be followed by successive backfilling behind the rock layers,
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CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
and thus precautions must be taken into consideration so that the compaction
procedure does not affect the internal stability of the wall. To ensure that, roller must
be kept at a distance “d” from the back of the wall, where d is calculated as per the
following equation (According to Reinforced Concrete Designers Handbook, 10th
Edition, By Reynolds and Steedman):
F s=KoN
d+0.5b
Knowing that:
F s = Sliding Force due to Roller [Ton/ml]
N = Weight of Roller [Ton]
Ko = Active Earth Pressure Coefficient for Soil
b = Width of Roller [m]
The roller to be used during compaction will be of maximum weight of 9 Ton, and a width of
2 m, and thus (N) will be taken as 9 Ton and (b) as 2 m.
According to the above table, the minimum difference between the resisting sliding force
(Phr) and the sliding force (Pha) is found to be 1.44 Ton/ml (Excluding the last layer which
will be compacted using plate compactor only), and thus (Fs) will be taken as 1.44 Ton/ml.
Substituting the values of Fs, Ka, N and b in the above equation we obtain d equal to 1.38m.
Thus by maintaining the compactor at a distance of 1.5m behind the back of the wall, its
internal stability will be ensured during construction phase, where the rest of the material
will be compacted with plate compactor.
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
5.6 Appendix VI - Stability Analysis
Stability analysis was performed using the software TALREN 4 in compliance with the
European code.
The factor of safety obtained is 1.80 which is higher than the required factor of 1.5 for
overall stability.
The results of the analysis are shown below:
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
5.7 Appendix VII – Formulas for Seismic Calculations
According to BS EN1998-5 (Eurocode 8: Design of Structures for Earthquake Resistance –
Part V: Foundations, Retaining Structures and Geotechnical Aspects), chapter 7, paragraph
7.3.2.2 (Pages below), the seismic action is represented by a set of horizontal and vertical
static forces equal to the product of the gravity forces and a seismic coefficient, where these
forces are considered as acting upward or downward so as to produce the most unfavorable
effect.
The gravity forces acting on the retaining wall are the surcharge (Q) and the weight of the
wall (WT), as a result, the horizontal force representing the seismic action is Kh WT and the
vertical forces are Kv Q and Kv WT.
Knowing that the design of the wall was performed according to combination 1 and 2 and
then checked for seismic calculations, then increasing any of the unfavorable actions and
coefficients used in seismic calculations will not affect the design of the wall.
5.7.1 Horizontal Active Soil Thrust
According to BS EN1998-5 (Eurocode 8: Design of Structures for Earthquake Resistance –
Part V: Foundations, Retaining Structures and Geotechnical Aspects), the total design force
acting on the retaining structure (Ed) is given by:
Ed=12γ ¿ (1∓K v )K H
2(Defined below in Equation E.1, Annex E)
Where:
H: Wall height [m]
γ ¿: Soil unit weight [Ton/m3] (Defined below in
Equation E.5, Annex E)
Kv: Vertical seismic coefficient
K: Earth pressure coefficient (static + dynamic) (Defined below in section 5.6.3)
Since the horizontal active soil thrust is considered as unfavorable action, then despite the
direction of the vectors of seismic acceleration coefficients, using the formula
Phs=(1+K v )K γ sH2
2
(Defined above in section 3.1.1), will ensure a safe design as the value of the unfavorable
action is being increased.
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CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
5.7.2 Horizontal Active Surcharge Thrust
The vertical force representing the seismic action (Kv Q) is considered acting downward so
as to increase the unfavorable horizontal active surcharge thrust, thus the total surcharge
load is (1+Kv)Q and the horizontal active surcharge thrust defined in section 3.1.2 was
calculated according to the following formula:
Phq=(1+K v )KQH
5.7.3 Dynamic Active Earth Pressure Coefficient for Soil
According to BS EN1998-5 (Eurocode 8: Design of Structures for Earthquake Resistance –
Part V: Foundations, Retaining Structures and Geotechnical Aspects), Annex E, Equation E.2
(Pages below), the dynamic active earth pressure coefficient for soil may be computed from
the Mononobe and Okabe formula as follows:
K=sin2(ѱ+∅ d
' −θ)
cosθ sin2ѱ sin (ѱ−θ−δ d)[1+√ sin(∅ d' +δ d)sin(∅ d
' −β−θ)sin(ѱ−θ−δ d)sin (ѱ+β) ]
2
Where:
∅ d' : Design value of the angle of shearing resistance of soil
∅ d' =tan−1( tan∅ 'γ∅ ' )
∅ ' : Angle of Shearing Resistance
γ∅ ': Partial Factor for the Angle of Shearing Resistance
δ d: Design Value of the Friction Angle between the soil and the wall
δ d=tan−1( tan δγ∅ ' )
δ : Friction Angle between the Ground and the Retaining Wall
θ: Angle defined as tanθ=Kh1± K v
(Since increasing θ increases the value of K, then
for more safety we used the value of the maximum θ resulting from a
maximum tan θ, and thus we defined tanθ=K h1−K v
)
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CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
Kh: Horizontal seismic coefficient
Kv: Vertical seismic coefficient
Ѱ : Inclination Angle of the Back of the Wall from the Horizontal Line
β: Inclination Angle of the Backfill Surface from the Horizontal Line
Substituting the following values:
∅ '=∅γ∅ '=1}∅ d
' =∅∧δ d=δ
Ѱ=90 ° (In our case Ѱ is slightly greater than 90 , but since increasing ⁰ Ѱ
decreases the value of K, then using a value of Ѱ= 90 will be more safe)⁰
β=0 °
The above formula may be written as:
K=sin2(90 °+∅−θ)
cosθ sin290 ° sin(90°−θ−δ)[1+√ sin (∅+δ)sin (∅−0 °−θ)sin(90°−θ−δ)sin (90 °+0 °) ]
2
Knowing that sin (90 °−x )=cos x, then the latter formula is simplified to:
K=cos2(∅−θ)
cosθ cos(θ+δ)[1+√ sin(∅+δ)sin (∅−θ)cos (θ+δ) ]
2
5.7.4 Overturning moment
The overturning moment is the sum of the moments due to the horizontal active soil thrust,
horizontal active surcharge thrust and horizontal and vertical seismic forces resulting from
the weight of the wall.
Since the overturning moment is unfavorable action, then the moments due to the seismic
forces are taken positive, thus the vertical force (Kv WT) is considered acting downward,
whereas the horizontal force (Kh WT) is considered acting opposing the toe of the wall.
As a result, the overturning moment (Mo) defined in section 3.2 above is:
M o=M os+M oq+W T (K v xCG+Kh yCG)
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CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
5.7.5 Resisting Force
The force resisting sliding is equal to the product of the gravity force due to the weight of the
wall and a friction coefficient for soil. Under seismic state, the weight of the wall produces
additional vertical force (Kv WT) and horizontal force (Kh WT). In this case, the vertical
seismic force was considered acting upward and the horizontal force acting toward the toe
of the wall since the resisting force is a favorable action.
As a result, the resisting force (Phr) defined in section 3.3 above is:
Phr=¿
Page 86 of 88
CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CDR Contract No. 4354: HYDRO AGRICULTURAL DEVELOPMENT OF SOUTH LEBANON IRRIGATION AND WATER SUPPLY SCHEME – CONVEYOR 800
CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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CALCULATION NOTE: RANDOM STONE RETAINING WALLS AT SM2 EMBANKMENT RESERVOIR
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