Stability calculation

Stability calculation

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Forces working on wall

Forces		X	Y
F_d	Self weight (dead load) of wall	x_d	y_d
F_ds1	Self weight of soil above ground water table	x_ds1	y_ds1
F_ds2	Self weight of soil below ground water table	x_ds2	y_ds2
F_sx,F_sy	Horizontal and vertical soil pressures	x_s	y_s
F_w1	Ground water pressure		y_w1
F_w2	Free water pressure		y_w2
F_de	Seismic load of wall		y_d
F_dse1	Seismic load of soil above ground water table		y_ds1
F_dse2	Seismic load of soil below ground water table		y_ds2
F_sex,F_sey	Horizontal and vertical seismic soil pressures	x_se	y_se
F_we	Free standing water seismic pressure		y_we
F_ax,F_ay	Horizontal and vertical additional loads	x_a	y_a

Driving forces and moments

Vertical force		Horizontal force		Moment
V	x	H	y	M_o
F_d	x_d			F_dx_d
F_ds1	x_ds1			F_ds1x_ds1
F_ds2	x_ds2			F_ds2x_ds2
F_sy	x_s			F_syx_s
		F_sx	y_s	F_syy_s
		F_w1	y_w1	F_w1y_w1
		F_w2	y_w2	F_w2y_w2
		F_de	y_d	F_dey_d
		F_dse1	y_ds1	F_dse1y_ds1
		F_dse2	y_ds2	F_dse2y_ds2
F_sey	x_se			F_seyx_se
		F_sex	y_se	F_sexy_se
		F_we	y_we	F_wey_we
F_ay	x_a			F_ayx_a
		F_ax	y_a
SV		SH		SM

Signs:

1. Downward vertical force is positive.

2. Rightward horizontal force is positive

3. Clockwise moment is positive

Resultant force

The resultant forces working on the wall are SV (vertical) and SH (horizontal). Location of resultant force on the wall base, x_R = SM/SV.

There are cases of location of resultant force, as follows.

1. B/3 < x_R < 2B/3 - Whole base is in compression.

2. 0 < x_R < B/3 - Left base in compression, right base in tension.

3. 2B/3 < x_R < B - Right base in compression, left base in tension.

4. x_R < 0, x_R > B - Wall is not stable (overturned).

Base pressure

Case	B_P	s₁	s₂
B/3 < x_R < 2B/3	B
0 < x_R < B/3	3x_R		0
2B/3 < x_R < B	3(B-x_R)	0
x_R < 0, x_R > B	N/A	N/A	N/A

Sliding

The sliding force of the wall is SH. This force can be restrained by among other things as follows.

1. Base friction = SV tan f, where f is the internal friction angle of the base earth.

2. Base cohesion = B_P c, where c is the cohesion of the base earth.

3. Toe passive pressure. Restraining capacity is the passive soil pressure on the toe. See Soil pressures.

4. Adjacent structure, anchors or piles. Restraining capacity determined by maximum horizontal load of structure, anchors or piles.

5. A shear key. Restraining capacity is the passive soil pressure on the key. See Soil pressures.

Requirements

The followings are requirements for resultant location, bearing capacity safety factor and sliding safety factor.

1. Load conditions

Load condition	Annual probability	Return period
Usual	Greater or equal to 0.10	Less than or equal to 10 years
Unusual	Less than 0.10 but greater than or equal to 0.0033	Greater than 10 years but less than or equal to 300 years
Extreme	Less than 0.0033	Greater than 300 years

2. Resultant location

Usual: 100% of base in compression

Unusual: 75% of base in compression

Extreme: Resultant within base

3. Bearing capacity safety factor

Usual: 3

Unusual: 2

Extreme: >1

4. Sliding safety factor

Normal structures

Site information category	Usual	Unusual	Extreme
Well defined	1.4	1.2	1.1
Ordinary	1.5	1.3	1.1
Limited	3.0	2.6	2.2

Critical structures

Site information category	Usual	Unusual	Extreme
Well defined	1.7	1.3	1.1
Ordinary	2.0	1.5*	1.1*
Limited**	-	-	-

* For preliminary seismic analysis without detailed site-specific ground motion, use FS = 1.7 for unusual and FS = 1.3 for extreme.

** Limited site information is not permitted for critical structures.

Sources:

1. United States Army Corps of Engineers, EM 1100-2-2100 Stability Analysis of Concrete Structures, 2005

2. United States Army Corps of Engineers, EM 1110-2-2502 Retaining and Flood Walls, 1989

See also:

1. Soil pressures.

2. Water pressures.

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