Brinch Hansen -Lateral Capacity

Project: Part of structure Drawing ref.

M4/M5 Gantry Foundation Check F5-S36-LS (4A30) Calc by DVN

Date

7-Jun-14

Job Ref: Calc sheet no Check by

1/3 Date

Design methodology based on Brinch Hansen's Method ('Pile Design and Construction Practice' Tomlinson, third edition) Soil Parameters: g' f' c'

= = =

19.00 25.00 0.00

kN/m3 degrees kN/m2

1 2 3 4

H M

Pile Dimensions: Pile length (L) Pile diameter (B)

= =

10.50 0.75

m m

Loading Data: Hori. Force (H) Moment (M)

= =

55.00 270.00

kN kNm

Layer thickness x

Ground Profile: Slope angle (b) Reduction factor Water table bgl non effective depth Layer thickness

= = = = =

0.00 1.00 0.00 0.50 0.50

degrees m m m

1 tan b +1 tan(45-f/2)

Pressure Distribution

Summary of findings: Outputs: Point of rotation bgl Ult.moment resistance Ult.Lateral Load Applied moment FoS for Moment

= = = = =

FoS for Lateral Load

=

8.00 2190.48 169.69 710.00

m kNm kN kNm

8.11 3.09

Lateral deflection for the applied = Loading

mm

5 FOS = Mresisting/ Mapplied

G.L. non effective depth

Depth below G.L.

Calculation Method Take moments about A of soil resistance This will find the location of point x Calculate applied moment about x = M +Hx Calculate resisting moment about x = f(F1 + F2)

Req. kq kc Req. kc pz (kN/m )

Pz(kN) M(kNm)

Kc factor is calculated using Brinch Hansen method. It is a measure of effective cohesion as a function of friction angle and L/B ratio

Required Kc is Kc multiplied by the slope reduction factor. The slope reduction factor takes account of reduced passive resistance due to slope

pz is the point stress witin the layer. This is calculated as: σ.kqreq + C.kcreq

Pz is the point stress witin the layer. This is calculated as: pz . B . Layer thickness

This calculate moment of slice about ground level. This is calculated as: depth (including non effective). Pz

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pz (kN/m )

2

Pz(kN) M(kNm) M z Pz(kN) V(kN) M(kNm) M(kNm)

Shear force in pile is the applied force - slice forces above x + slice forces below.

This moment in pile is approximate and assumes the Brinch Hansen force distribution with depth is triangular. See graph to check. Moment at a point is : Applied M + Applied F. leverl arm . (Pzreq at that point * depth/2 * depth/3)

This calculates the reistance moment about x fr each slice and then sums these. The sum is the total resisting moment capacity and is used in calculating the factor of safety.

M above z M below z This is the force Pz acting on each slice. Having determined the location of the point x and entered this into the spread sheet, this automatically chooses whether to place Kq or Kq.req

Excludes reduction factor - ie force Excludes reduction factor - ie force with reduc. fac. away from slope into slope

This is depth below ground level minus that amount not considered to offer resistance. Typically 500mm is assumed to be non-effective

Point stress

This sums the moments . Where the sum of the moments = 0 is the point wher x is.

Force per layer

7-Jun-14

This sums the moments from each slice starting at the base to get total moment for a particular point

Point stress

Date Job Ref: Calc sheet no Check by

This sums the moments from each slice starting at the top to get total moment for a particular point

Calc by

These three are calculated as previous except slope reduction factor not included. Ie this is for resistance below the point x that is directed into embankment/cutting

kq

Required Kq is Kq multiplied by the slope reduction factor. The slope reduction factor takes account of reduced passive resistance due to slope

Below non eff. 2 s' (kN/m ) Depth

Kq factor is calculated using Brinch Hansen method. It is a measure of frictional resistance as a function of friction angle and L/B ratio

Effective stress. This is overburden minus any pore water pressures. Again this excludes the non-effective length

This is depth below ground level minus that amount not considered to offer resistance. Typically 500mm is assumed to be non-effective

Project: Part of structure Drawing ref. 0 2/3 Date

Determination the point of rotation The point of rotation x is determined by balancing the moment above x and below it, by taking moment about the point of application of the horizontal load. Detailed Calculations

Force per layer

Taking moment about the point of rotation x Maximum V & M from applied loadings

without reduc. fac. Includes change in direction of force

Shear in pile Moment in pile Moment in pile

Project: Part of structure Drawing ref.

M4/M5 Gantry Foundation Check F5-S36-LS (4A30) 0 Calc by

Date

7-Jun-14

Job Ref: Calc sheet no Check by

0 2/3 Date

Determination the point of rotation The point of rotation x is determined by balancing the moment above x and below it, by taking moment about the point of application of the horizontal load. Point stress

Force per layer

Point stress

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50 10.00 10.50

-5.00 -0.50 4.00 8.50 13.00 17.50 22.00 26.50 31.00 35.50 40.00 44.50 49.00 53.50 58.00 62.50 67.00 71.50 76.00 80.50 85.00 89.50

Taking moment about the point of rotation x

Force per layer

Maximum V & M from applied loadings

Includes reduction factor - ie force Excludes reduction factor - ie force with reduc. fac. away from slope into slope Below non eff. s' (kN/m2) Depth

Detailed Calculations

kq

Req. kq

kc

Req. kc

pz (kN/m2)

Pz(kN)

M(kNm)

pz (kN/m2)

Pz(kN)

M(kNm)

3.29 3.35 3.47 3.59 3.70 3.81 3.92 4.02 4.12 4.21 4.31 4.39 4.48 4.57 4.65 4.73 4.80 4.88 4.95 5.02 5.09 5.15

3.29 3.35 3.47 3.59 3.70 3.81 3.92 4.02 4.12 4.21 4.31 4.39 4.48 4.57 4.65 4.73 4.80 4.88 4.95 5.02 5.09 5.15

5.63 6.25 7.43 8.51 9.52 10.45 11.33 12.15 12.91 13.63 14.31 14.95 15.56 16.13 16.67 17.19 17.67 18.14 18.58 19.00 19.41 19.79

5.63 6.25 7.43 8.51 9.52 10.45 11.33 12.15 12.91 13.63 14.31 14.95 15.56 16.13 16.67 17.19 17.67 18.14 18.58 19.00 19.41 19.79

-16.43 -1.67 13.89 30.51 48.14 66.71 86.19 106.52 127.67 149.58 172.23 195.58 219.59 244.24 269.49 295.33 321.71 348.63 376.05 403.95 432.32 461.13

-6.16 -0.63 5.21 11.44 18.05 25.02 32.32 39.95 47.87 56.09 64.59 73.34 82.35 91.59 101.06 110.75 120.64 130.73 141.02 151.48 0.00 0.00

-3.08 -0.63 7.81 22.88 45.13 75.05 113.12 159.78 215.44 280.46 355.22 440.05 535.25 641.13 757.95 885.98 1025.46 1176.61 1339.66 1514.81 0.00 0.00

-16.43 -1.67 13.89 30.51 48.14 66.71 86.19 106.52 127.67 149.58 172.23 195.58 219.59 244.24 269.49 295.33 321.71 348.63 376.05 403.95 432.32 461.13

-6.163 -0.63 5.21 11.44 18.05 25.02 32.32 39.95 47.87 56.09 64.59 73.34 82.35 91.59 101.06 110.75 120.64 130.73 141.02 151.48 0.00 0.00

-3.0815 -0.63 7.81 22.88 45.13 75.05 113.12 159.78 215.44 280.46 355.22 440.05 535.25 641.13 757.95 885.98 1025.46 1176.61 1339.66 1514.81 0.00 0.00

without reduc. fac.

M above z M below z

-3.08 -3.71 4.10 26.98 72.11 147.16 260.29 420.07 635.51 915.97 1271.19 1711.24 2246.50 2887.62 3645.58 4531.55 5557.01 6733.62 8073.28 9588.10 0.00 0.00

Includes change in direction of force

9591.18 9591.81 9584.00 9561.11 9515.99 9440.94 9327.81 9168.03 8952.59 8672.13 8316.90 7876.86 7341.60 6700.47 5942.52 5056.55 4031.09 2854.48 1514.81 0.00 0.00 0.00

Shear in pile

Moment in pile

Moment in pile

M

z

Pz(kN)

V(kN)

M(kNm)

M(kNm)

-9594.26 -9595.52 -9579.90 -9534.13 -9443.87 -9293.77 -9067.52 -8747.96 -8317.08 -7756.16 -7045.71 -6165.61 -5095.11 -3812.85 -2296.95 -524.99 1525.92 3879.14 6558.47 9588.10 0.00 0.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50 10.00 10.50

-6.16 -0.63 5.21 11.44 18.05 25.02 32.32 39.95 47.87 56.09 64.59 73.34 82.35 91.59 101.06 110.75 120.64 130.73 141.02 151.48 0.00 0.00

61.16 61.79 56.58 45.14 27.09 2.07 -30.25 -70.19 -118.07 -174.16 -238.75 -312.09 -394.43 -486.02 -587.08 -697.83 -577.19 -446.46 -305.44 -153.96 -153.96 -153.96

297.50 325.04 351.20 373.56 389.45 395.91 389.78 367.67 326.00 261.03 168.84 45.35 -113.62 -312.42 -555.49 0.00 0.00 0.00 0.00 0.00 0.00 0.00

-52.39 -4.40 33.85 68.65 99.28 125.09 145.45 159.78 167.56 168.28 161.47 146.68 123.52 91.59 50.53 0.00 60.32 130.73 211.53 302.96 0.00 0.00