INSTALLATION TORQUE OF MULTI VARIABLE 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 angle of shearing resistance (f) degrees Enter the value of the unit weight of sand (g) lb/ft3 Enter the depth of anchor (H) ft Enter the outer diameter of the largest screw blade (B) ft Enter the inner diameter of the upper surface of the screw blade (B0) ft Enter the inner diameter of the lower surface of the screw blade (B1) ft the average blade diameter Bav = (B + B0)/2 = Enter the diameter of anchor shaft (D) in Enter the pitch of the largest screw blade (p) in Enter the thickness of the screw blade (t) in the average angle of the helix = y = tan-1 p/pBav = degrees Forces to be overcome by applied torque: 1. Passive lateral earth pressure exerted on the entire embedded length of the anchor shaft (P1). This force has two components (P1x and P1y) of frictional resistance, the first component produces moment acting on the shaft resisting its rotation (T1), and the second one produces frictional moment acting on the anchor blade (T2). 2. Force (P2) 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 (P2) has two components (P2x and P2y), the first component produces no torsional resistance, while the second one reflects its influence as a frictional moment acting on the anchor blade (T3). It should be noted that P2y will be proportioned to smaller forces (P'2y, P''2y, and P'''2y) acting on the individual blades of the helical unit. 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 (T4 and T5) 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 (T6) 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 (T7). constant Z1 = [(pB)2/4 + p2]1/2 =

constant Z2 = [(pB1)2/4 + p2]1/2 =

actual surface area of the top surface of the screw blade = At = (2/p) [(pB/4) Z1 + p2 ln(pB/2 + Z1) - (pB0/4) Z2 - p2 ln(pB0/2 + Z2)] = ft2

actual surface area of the bottom surface of the screw blade = Ab = (2/p) [(pB/4) Z1 + p2 ln(pB/2 + Z1) - (pB1/4) Z2 - p2 ln(pB1/2 + Z2)] = ft2

the coefficient of active earth pressure = Ka = (1 - sin f) / (1 + sin f) =

the coefficient of passive earth pressure = Kp = (1 + sin f) / (1 - sin f) =

the modified coefficient of passive earth pressure = Kp' = 0.3 Kp =

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

 Sand Type Factor (f) used in calculating modified coefficient passive earth pressure Dense 0.4 - 0.5 Medium 0.3 - 0.4 Loose 0.2 - 0.4

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 = Kf = tan d =

the force causing bearing resistance = F = (1/2) g H Kp (1 + p) p = kips

Components of installation torque:

T1 = resisting moment acting on the anchor shaft due to the force P1x.

T2 = resisting moment acting on the anchor blade due to the force P1y.

T3 = resisting moment acting on the anchor blade due to the force P2y.

T4 = 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.

T5 = 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.

T6 = resisting moment due to the bearing force F acting on the entire height of the screw pitch.

T7 = resisting moment acting on the outer perimeter of the thickness of the screw blade.

torque T1 = g H2 cos d Kp' Kf (pD) (D/4) = kip.ft

torque T2 = g H2 cos d Kp' tan (d + y) (pD) (D/4) = kip.ft

torque T3 = g H2 cos f Kp' tan (d + y) (pB) (B/4) = kip.ft

torque T4 = g H cos d Ka At tan (d + y) [(B + B0)/4] = kip.ft

torque T5 = g H cos d Kp Ab tan (d + y) [(B + B0)/4] = kip.ft

torque T6 = F [(B - B0)2/8] = kip.ft

torque T7 = g H Kp Kf (pB) (B/2) t = kip.ft

total torque T = T1 + T2 + T3 + T4 + T5 + T6 + T7 = kip.ft

Components of vertical thrust force:

V1 = vertical component (P1y) of the force P1 acting on the anchor shaft.

V2 = vertical component (P2y) of the force P2 acting on the sand column overlying the anchor blade.

V3 = force resulting from the passive bearing resistance acting on the lower surface of the screw blade.

V4 = drag force acting on the upper surface of the screw blade due to the acting active earth pressure.

vertical force V1 = g H2 sin d Kp' (pD/2) = kips

vertical force V2 = g H2 sin f Kp' (pB/2) = kips

vertical force V3 = g H Kp Ab cos y = kips

vertical force V4 = g H Ka At cos y = kips

total vertical thrust force V = V1 + V2 + V3 + V4 = kips

Effect of Multi variable pitch screw

The main reason for using a variable pitch screw anchor, although it is very difficult to manufacture, is to have a constant helix angle (y), i.e., the blades are parallel.

Experimental investigation, together with a theoretical analysis suggest that the torque required to install multi variable pitch screw anchor with tapered (conical) configuration is 10 - 15% lower than that calculated for a single pitch screw anchor with a diameter and helix angle equal to those of the largest blade of the multi pitch one.

range of required torque kip.ft - kip.ft

Summary of Design

Angle of shearing resistance (f) degrees

Unit weight of sand (g) lb/ft3

Depth of anchor (H) ft

Outer diameter of the largest screw blade (B) ft

Inner diameter of the upper surface of the screw blade (B0) ft

Inner diameter of the lower surface of the screw blade (B1) ft

Diameter of anchor shaft (D) in

Pitch of the largest screw blade (p) in

Thickness of the screw blade (t) in

Total torque (T) kip.ft

Total vertical thrust force (V) kips

Range of required torque kip.ft - kip.ft