INSTALLATION TORQUE OF SINGLE PITCH SCREW ANCHORS IN SAND

The following calculations are structured according to the procedures developed by Ghaly and Hanna (1991)

Enter the value of the unit weight of sand (g) kN/m^{3}

Enter the depth of anchor (H) m

Enter the outer diameter of screw anchor blade (B) m

Enter the inner diameter of the upper surface of the screw blade (B_{0}) m

Enter the inner diameter of the lower surface of the screw blade (B_{1}) m

the average blade diameter B_{av} = (B + B_{0})/2 = m

Enter the diameter of anchor shaft (D) m

Enter the pitch of the screw blade (p) m

Enter the thickness of the screw blade (t) m

the average angle of the helix = y = tan^{-1} p/pB_{av }= degrees

Forces to be overcome by applied torque:

1. Passive lateral earth pressure exerted on the entire embedded length of the anchor shaft (P_{1}). This force has two components (P_{1x} and P_{1y}) of frictional resistance, the first component produces moment acting on the shaft resisting its rotation (T_{1}), and the second one produces frictional moment acting on the anchor blade (T_{2}).

2. Force (P_{2}) acting on the cylindrical column of the sand overlying the screw blade. This force appears due to the local compaction that the screw anchor installation causes to the sand layer. The force (P_{2}) has two components (P_{2x }and P_{2y}), the first component produces no torsional resistance, while the second one reflects its influence as a frictional moment acting on the anchor blade (T_{3}).

3. Active and passive earth pressures exerted on the upper and the lower surface, respectively, of the screw blade due to the downward advancement of the anchor. These two forces produce frictional resistances (T_{4} and T_{5}) on the upper and the lower blade surfaces, respectively, resulting in a moment acting against the applied installation torque.

4. Force (F) due to the passive lateral earth pressure exerted on the upper surface area of the screw pitch due to its inclination in the third dimension. This force produces bearing resistance against rotation and its influence translates as torsional resistance (T_{6}) against the applied torque.

5. Force exerted on the outer perimeter of the screw blade due to the frictional resistance between its thickness and the surrounding sand. The existence of this force produces frictional resisting moment (T_{7}).

constant Z_{1} = [(pB)^{2}/4 + p^{2}]^{1/2} =

constant Z_{2} = [(pB_{1})^{2}/4 + p^{2}]^{1/2} =

actual surface area of the top surface of the screw blade = A_{t} = (2/p) [(pB/4) Z_{1} + p^{2} ln(pB/2 + Z_{1}) - (pB_{0}/4) Z_{2} - p^{2} ln(pB_{0}/2 + Z_{2})] = m^{2}

actual surface area of the bottom surface of the screw blade = A_{b} = (2/p) [(pB/4) Z_{1} + p^{2} ln(pB/2 + Z_{1}) - (pB_{1}/4) Z_{2} - p^{2} ln(pB_{1}/2 + Z_{2})] = m^{2}

the coefficient of active earth pressure = K_{a }= (1 - sin f) / (1 + sin f) =

the coefficient of passive earth pressure = K_{p }= (1 + sin f) / (1 - sin f) =

the modified coefficient of passive earth pressure = K_{p}' = 0.3 K_{p} =

the angle of friction between the anchor material and the soil = d = 3f/4 = degrees

Enter, from Table above, factor (f) used in calculating modified coefficient passive earth pressure =

the coefficient of friction between the anchor material and the surrounding soil = K_{f }= tan d =

the force causing bearing resistance = F = (1/2) g H K_{p} (1 + p) p = kN

Components of installation torque:

T_{1} = resisting moment acting on the anchor shaft due to the force P_{1x}.

T_{2} = resisting moment acting on the anchor blade due to the force P_{1y}.

T_{3} = resisting moment acting on the anchor blade due to the force P_{2y}.

T_{4} = resisting moment acting on the upper surface of the anchor blade due to the acting active earth pressure which develops as a result of the downward movement of the anchor blade away from the overlying sand mass.

T_{5} = resisting moment acting on the lower surface of the anchor blade due to the acting passive earth pressure which develops as a result of the applied pushing-down force.

T_{6} = resisting moment due to the bearing force F acting on the entire height of the screw pitch.

T_{7} = resisting moment acting on the outer perimeter of the thickness of the screw blade.

torque T_{1} = g H^{2} cos d K_{p}' K_{f} (pD) (D/4) = kN.m

torque T_{2} = g H^{2} cos d K_{p}' tan (d + y) (pD) (D/4) = kN.m

torque T_{3 }= g H^{2} cos f K_{p}' tan (d + y) (pB) (B/4) = kN.m

torque T_{4} = g H cos d K_{a} A_{t} tan (d + y) [(B + B_{0})/4] = kN.m

torque T_{5} = g H cos d K_{p} A_{b} tan (d + y) [(B + B_{0})/4] = kN.m

torque T_{6} = F [(B - B_{0})^{2}/8] = kN.m

torque T_{7} = g H K_{p} K_{f} (pB) (B/2) t = kN.m

total torque T = T_{1} + T_{2} + T_{3} + T_{4} + T_{5} + T_{6} + T_{7} = kN.m

Components of vertical thrust force:

V_{1} = vertical component (P_{1y}) of the force P_{1} acting on the anchor shaft.

V_{2} = vertical component (P_{2y}) of the force P_{2 }acting on the sand column overlying the anchor blade.

V_{3} = force resulting from the passive bearing resistance acting on the lower surface of the screw blade.

V_{4} = drag force acting on the upper surface of the screw blade due to the acting active earth pressure.

vertical force V_{1} = g H^{2} sin d K_{p}' (pD/2) = kN

vertical force V_{2} = g H^{2} sin f K_{p}' (pB/2) = kN

vertical force V_{3} = g H K_{p} A_{b} cos y = kN

vertical force V_{4} = g H K_{a} A_{t} cos y = kN

total vertical thrust force V = V_{1} + V_{2} + V_{3} + V_{4} = kN

Summary of Design

Angle of shearing resistance (f) degrees

Unit weight of sand (g) kN/m^{3}

Depth of anchor (H) m

Outer diameter of the largest screw blade (B) m

Inner diameter of the upper surface of the screw blade (B_{0}) m

Diameter of anchor shaft (D) m

Pitch of the largest screw blade (p) m

Thickness of the screw blade (t) m

Total torque (T) kN.m

Total vertical thrust force (V) kN

Copyright 2007-2023 A. Ghaly. All rights reserved. Contact A. Ghaly at ghalya@union.edu

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Disclaimer: The author disclaims any and all responsibility for the application of stated principles, and shall not be liable for any loss or damage arising therefrom.