H = 5.8 m l1 = 0.0 m 0

0 deg l2 l3 h1 l4 A q L

0 deg (deg) (m) (m) (m) (m) (kN/m) (m)

l = 20 m 75 1.6 1.6 0.0 1.6 4.51 7.8 6.0h = 5.8 m 70 2.1 2.1 0.0 2.1 6.12 10.6 6.2

65 2.7 2.7 0.0 2.7 7.84 13.5 6.4q1 = 5 kPa 60 3.3 3.3 0.0 3.3 9.71 16.7 6.7from 0 m to 20 m 55 4.1 4.1 0.0 4.1 11.78 20.3 7.1

50 4.9 4.9 0.0 4.9 14.11 24.3 7.6q2 = 5 kPa 45 5.8 5.8 0.0 5.8 16.82 29.0 8.2

40 6.9 6.9 0.0 6.9 20.05 34.6 9.035 8.3 8.3 0.0 8.3 24.02 41.4 10.1

H = 3.7 m h2 = 5.952 m 25.295

0 deg l1 h3 l2 A q L

35 deg (deg) (m) (m) (m) (kN/m) (m)

la = 8.5 m 75 1.0 0.0 1.0 1.83 29.7 3.8lb = 2.50 m 1.86 70 1.3 0.0 1.3 2.49 40.4 3.9h1 = 5 m 5.45 65 1.7 0.0 1.7 3.19 51.8 4.1

60 2.1 0.0 2.1 3.95 64.1 4.3q1 = 30 kPa 55 2.6 0.0 2.6 4.79 77.7 4.5

50 3.1 0.0 3.1 5.74 93.1 4.8q2 = 30 kPa 45 3.7 0.0 3.7 6.85 111.0 5.2

40 4.4 0.0 4.4 8.16 132.3 5.835 5.3 0.0 5.3 9.78 158.5 6.5

Asoil

=

=

= (m2)

A1 =

=

= (m2)

AH

q1

q2

l

h

h1

l1 l2Bl3

l4

Asoil

AH

q1

q2lb

h1

h3

l1

l2

la

h2A1

Date: Mar-16Existing Condition

Type of Wall = virtual back' of R.C. inverted T-shaped cantilever= 34 deg The backfill slope angle = 35 deg

= 1/2 or the backfill slope, whichever is smaller(GEOGUIDE 1, Table 14) = 17.0 deg

Trial Wedge Analysis

wedge A W q c1' L1 c2' L2 c.L Hgw

(deg) (m2) (kN/m) (kN/m) (m) (m) (kN/m) (deg) (deg) (deg) (deg) (m) (m) (kN/m) (kN/m)

1 85 3.48 19 66.2 3.965 4 6.789 5 2.687 41 34 5 39 17.0 0 5.50 5.50 0 02 80 9.94 19 188.8 11.03 4 9.669 5 3.000 54 34 10 44 17.0 0 5.50 5.50 0 03 75 14.62 19 277.8 11.03 4 5.074 5 3.426 37 34 15 49 17.0 0 5.50 5.50 0 04 70 17.01 19 323.3 11.03 4 2.403 5 4.029 30 34 20 54 17.0 0 5.50 5.50 0 05 65 18.50 19 351.5 11.03 4 0.270 5 4.935 26 34 25 59 17.0 0 5.50 5.50 0 06 60 19.54 19 371.2 11.03 4 0.000 5 4.400 22 34 30 64 17.0 0 5.50 5.50 0 07 55 20.24 19 384.6 11.03 4 0.000 5 3.836 19 34 35 69 17.0 0 5.50 5.50 0 08 50 20.79 19 395.0 11.03 4 0.000 5 3.423 17 34 40 74 17.0 0 5.50 5.50 0 09 45 21.09 19 400.7 11.03 4 0.000 5 3.111 16 34 45 79 17.0 0 5.50 5.50 0 0

wedge W+q Ra Pa Maximum1 70.2 148.4 148.4 0.0 13.0 4 40 16 13 21 12 4 13.0 (from graph)

2 199.9 148.4 148.4 0.0 26.2 9 53 97 94 135 88 27 92.0 148.2

3 288.9 148.4 148.4 0.0 39.8 10 36 148 171 226 139 42 144.9 141.7

4 334.3 148.4 148.4 0.0 54.0 10 28 152 209 258 142 43 148.2 43.35 362.5 148.4 148.4 0.0 69.2 11 23 139 231 269 128 39 133.76 382.2 148.4 148.4 0.0 85.7 11 19 119 244 272 108 33 113.27 395.6 148.4 148.4 0.0 103.9 11 16 96 250 268 85 26 88.98 406.0 148.4 148.4 0.0 124.5 11 13 72 250 260 61 19 63.49 411.7 148.4 148.4 0.0 148.4 11 11 47 241 246 36 11 37.6

Angle of friction, 'Mobilised angle of wall friction, '

' '

(kN/m3) (kN/m2) (kN/m2) (kN/m2)

u1h

u2h

u1v

u2v

c∙Lh

c∙Lv

Rah

Rav

Pah

Pav

Pamax

Pahmax

Pavmax

4045505560657075808590

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

13.0

92.0

144.9 148.2

133.7

113.2

88.9

63.4

37.6

Determination of maximum Pa

Pa

TRIAL WEDGE SPREADSHEET EXPLANATION

Initial Input

The required input for this spreadsheet is as follows:

- angle to the horizontal of the chosen trial failure surface,A -

- unit weight of soil,q - surcharge experienced by the wedge of soil,c' - effective cohesion of the soil,L - length of chosen trial failure surface,

- effective angle of shearing resistance of the soil -

- angle to the vertical of the plane upon which the active pressure of the retained soil acts,B - base length of the retaining structure,H - retained height of the soil plus the toe depth of the retaining structure,

Hgw - height of groundwater above the base of the retaining structure,

This spreadsheet produces calculations for the maximum resultant active pressure (Pa) of retaining walls using the trial wedge method. Reference is made to Figures 21, 22 and 39 of Geoguide 1, 2nd Ed. (1993). Shaded cells indicate calculated values whereas unshaded cells indicate manually input values. The upper portion of the spreadsheet replaces the normal graphical constructions performed in the trial wedge method to calculate the resultant active pressure on a plane.

area of the wedge of soil bounded by the chosen trial failure surface and the retaining structure,

'

angle of action of the active pressure to the normal of the plan upon which the active pressure of the retained soil acts

Hgw

q

W

c'L

Ra

+'

Pa

+

U2

U1

L

Determination of Maximum Pa

Pah =

Pav =

The forces involved in the calculation of Pa are:

W+q - weight of the soil wedge plus the surcharge influencing the wedge, u1 - horizontal component of pore water pressure for both locations,

- vertical component of pore water pressure at the trial failure surface,

-

-

-

-

Ra - resultant resisting force acting on the chosen trial failure surface due to active pressure,

-

-

Other Calculated Values

Certain values are required to be calculated as intermediate steps in the overall process. These are:

W -

- angle normal to the chosen trial failure surface,- angle at which Ra acts,

The value of the force acting on the retaining structure due to active earth pressure, Pa is calculated from the initial input and the following formulae using its components;

tan( + ')∙(u2 h - u1

h - c'∙L

h ) - u1

v - u2

v -c'∙L

v + (W + q)

tan(+) + tan (+ ')Pah∙tan(+)

The components of the forces involved in the calculation of Pa are calculated and shown in the second table on the spreadsheet.

u2v

c'Lh horizontal component of the effective cohesion multiplied by the length of the chosen trial

failure surface,c'L

v vertical component of the effective cohesion multiplied by the length of the chosen trial failure surface,

Rah horizontal component of the resultant resisting force acting on the chosen trial failure surface

due to active pressure,Ra

v vertical component of the resultant resisting force acting on the chosen trial failure surface due to active pressure,

Pah horizontal component of the force acting on the retaining structure due to active earth

pressure,Pa

v vertical component of the force acting on the retaining structure due to active earth pressure,

The results for Pa are shown on the graph. The graphing of Pa allows the identification of the maximum value, should the critical failure surface lie between the chosen trial failure surfaces. The maximum value of Pa observed from the graph is entered as Pa

max, to the right of the second table. This is then used in the

final calculation for the factors of safety.

self-weight of the soil wedge. Equal to the area multiplied by the unit weight (buoyant unit weight of soil used for submerged area of wedge),

+ '