The following content summarizes the design calculation steps presented in lecture June 28, 2012.

q = 30 kPa

10.0 m

In-place soil soil (medium sand): γ= 17.0 kN/m3 φ = 34°

1. Wall design parameters are given in the figure above. 2. K a = 0.283 and K p = 3.537, calculated using Rankine earth pressure equations. 3. The pressure diagram is drawn (below) to show the active earth pressure behind the wall and the factored (FS = 1.5) passive passive earth pressure in front of the wall. This pressure diagram was was drawn using a spreadsheet with an increment size of 0.05 m.

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Pressure Diagram -150

-100

pressure (kPa) -50 0 0 8.48

50

100

pore pressure behind wall active earth pressure behind wall

2 horizontal tieback force

4

passive earth pressure behind wall

6

) m ( h t p e d

8 10

-98.21

56.54

passive earth pressure in front of wall pore pressure in front of wall sum

12 14

4. An initial tieback depth of 3 m from the top of the wall is assumed. This value may need to be revised depending on the outcome of the subsequent analyses. Moments are summed about the tieback depth on the wall. The embedment depth is changed until the sum of the moments is nearly equal to zero. The optimum embedment depth is accordingly found to be 2.45 m. 5. Summing the forces in the horizontal direction, the required horizontal tieback load required to balance horizontal forces is equal to 203.56 kN/m (note the direction of the horizontal tieback force in the figure. Assuming a 1 m horizontal spacing between tiebacks installed into the face of the wall, this force corresponds to a 204 kN force per tieback. Assuming a 20° installation angle to the horizontal, the design tieback tension is

ˠ=

204 ˫˚ cos 20°

= 217 ˫˚

Referring to the DYWIDAG Soil Anchor tables, a 26 mm diameter bar (70% ultimate strength = 397 kN) is sufficient to provide this tension. Assuming the bar is installed into a grouted hole 0.15 m in diameter, the circumference a of the grouted anchor is

I = ˖ = {0.15 ˭ = 0.471 ˭ Referring to Table 16.4 from Macnab, A. (2002), Earth Retention Systems Handbook , a possible presumptive ultimate bond stress for this anchor is 100 kPa (2 kips/ft 2). Using this presumptive ultimate bond stress, the minimum bonded anchor length is

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H =

217 ˫˚ 100 ˫˜I

= 2.2 ˭

The minimum unbonded length is found considering the geometry of the Rankine wedge as shown in the following figure:

70° 10.0 m

82° 7m 45°- φ/2 = 28°

Using the law of sines, the unbonded length is found

H sin28°

=

7˭ sin 82°

⇒ H = 3.3 ˭

Therefore, the total required length of the tieback behind the wall is 3.3 m + 2.2 m = 5.5 m. 6. A bending moment diagram is generated using a spreadsheet to numerically integrate the pressure diagram (including unfactored passive earth pressure) and resulting shear diagram. The output moment diagram is plotted below.

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moment (kNm/m) -400

-350

-300

-250

-200

-150

-100

-50

0

50

100

0

2

4

) m ( h t p e d

6 -334.63

8

10

12

14

The maximum moment for the final constructed wall is therefore 335 kNm/m. 7. Assuming a 0.6 m excavation below the tieback prior to tieback installation, the maximum bending moment is calculated using the following pressure diagram:

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Pressure Diagram -600

-400

pressure (kPa) -200

0

200

0

pore pressure behind wall

2

active earth pressure behind wall

4 ) m ( h t p e d

6 8 10 12 14

The maximum moment is calculated from the resulting moment diagram:

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passive earth pressure behind wall passive earth pressure in front of wall pore pressure in front of wall

moment (kNm/m) -100

-50

0

50

100

150

200

0

1

2

) m ( h t p e d

3

4

5

152.12

6

7

The maximum pre-tieback bending moment in the wall is therefore 152 kNm/m. Since this value is significantly less than the maximum moment calculated for the completed wall, the tieback elevation can be optimized by increasing the depth of the tieback. 8. The tieback depth is adjusted within the spreadsheets to arrive at a maximum moment that is nearly equal for steps (6) and (7) above. The optimum tieback depth is found to be 3.75 m. The resulting required horizontal tieback load is 218 kN/m. The resulting maximum moments are 240 kNm/m and 238 kN/m for the final wall and pre-tieback configurations, respectively. 9. Taking the maximum computed moment as 240 kNm/m, the ultimate moment for steel design is calculated by applying an 80% reduction factor:

= {0.8{240 ˫˚˭/˭ = 192 ˫˚˭/˭ Considering a load factor of 1.6 and a resistance factor of 0.9, the required nominal bending moment resistance of the sheet piling is computed

0.9 ≥ 1.6 1.6 {192 ˫˚˭/˭ ≥ 0.9 ≥ 341 ˫˚˭/˭

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For ASTM A572 Gr. 60 steel, F y = 415 MPa (415,000 kPa). For nominal moment resistance greater than or equal to 341 kNm/m, the corresponding elastic section modulus requirement is computed

˟≥

341 ˫˚˭/˭

415,000 ˫˚/˭$ ˟ ≥ 0.000822 ˭% /˭ = 822˭% /˭ Referring to the Skyline Steel PZ/PS section tables, the PZ 22 section, with an elastic section modulus of 973 cm 3/m, is sufficient for this design.

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