Lateral Loading Analysis

PART 3

Design Strategies

11 Lateral Loading Analysis

11.1

Winkler Modulus for Piles

Springs are often used to model the soil–pile interaction. These springs are known as Winkler springs after Winkler who was the first to use springs to model pile behavior.

Modeling of Skin Friction Using Winkler Springs The skin friction of a pile can be represented using a series of springs.

Springs to model vertical forces (Skin friction)

Figure 11.1

Springs to model horizontal forces

Winkler spring model

248

Pile Design and Construction Rules of Thumb

Spring Constant (k) • The spring constant (k) is defined as k = f/w w = displacement).

(f = force or pressure;

Soil Spring Constant (Coefficient of Subgrade Reaction) • Coefficient of Subgrade Reaction = Pressure/displacement; (Units  lbs/cu ft)

Methods to Find Coefficient of Subgrade Reaction All techniques used to find the subgrade modulus can be divided into three categories. • Experimental methods • Numerical methods • Simple theoretical models

Vertical Spring Constant (Vertical Modulus of Subgrade Reaction—k) k=Gs ¼ 1:3 ðEp =Es Þ1=40 ½1 þ 7 ðL=DÞ0:6  Gs ¼ soil shear modulus; L ¼ pile length D ¼ pile diameter

ðMylonakis, 2001Þ

Ep and E s ¼ pile and soil Young’s modulus;

(Note: The above equation should be used only for vertical springs.)

Reference Mylonakis, G., ‘‘Winkler Modulus for Axially Loaded Piles,’’ Geotechnique, 455–460, 2001.

11.2

Lateral Loading Analysis—Simple Procedure

• Lateral loads are exerted on piles due to wind, soil, and water. In such cases, lateral pile capacity needs to be designed to accommodate the loading.

Chapter 11

249

Lateral Loading Analysis Wind Soil pressure

Transmission tower

Earth retaining structure

Figure 11.2

Lateral loads

• The deformation of piles due to lateral loading is normally limited to the upper part of the pile. Lateral pile deflection, 8 to 10 diameters below the ground level, is negligible in most cases. • Piles that can carry heavy vertical loads may be very weak under lateral loads.

11.2.1 Design Methodology of Laterally Loaded Piles • It is assumed that the pile is being held by springs as shown in Figure 11.3. The spring constant or the coefficient of subgrade reaction varies with the depth. In most cases, the coefficient of subgrade reaction increases with depth. • Simplified analysis of lateral loads on piles can be conducted by assuming the coefficient of subgrade reaction to be a constant with depth. For most cases, the error induced by this assumption is not significant. M H k

• When a pile is subjected to a horizontal load, it will try to deflect. • The surrounding soil will generate a resistance against deflection. • The resistance provided by the soil is represented with a series of springs. The spring constant is taken as the coefficient of subgrade reaction (k). • In reality (k) changes with depth. • Simplified analysis is conducted assuming (k) to be a constant. • For most cases, this assumption does not produce a significant error.

Figure 11.3

Lateral loading model

250

Pile Design and Construction Rules of Thumb

• The equation for lateral load analysis is as follows: u ¼ ð2Þ1=2 ðH=kÞ  ðlc =4Þ1 þ ðM=kÞðlc =4Þ2

ðMatlock and Reese, 1960Þ

u = lateral deflection H = applied lateral load on the pile (normally due to wind or earth pressure) k = coefficient of subgrade reaction (assumed to be a constant with depth) M = moment induced due to lateral forces (when the lateral load is acting at a height above the ground level, then moment induced also should be taken into consideration). lc = critical pile length (Below this length, the pile is acting as an infinitely long pile.) lc is obtained using the following equation: lc = 4 [(EI)p/k]1/4 (EI)p = Young’s modulus and moment of inertia of the pile. In the case of wind loading, the moment of inertia should be taken against the axis, which has the minimum moment of inertia, since wind load could act from any direction. In the case of soil pressure and water pressure, the direction of the lateral load does not change. In these situations, the moment of inertia should be taken against the axis of bending. A similar equation is obtained for the rotational angle (q) at the top of the pile. q ¼ ðH=kÞ  ðlc =4Þ2 þ ð2Þ1=2 ðM=kÞðlc =4Þ3 The derivation of the above equations is provided by Matlock and Reese (1960).

Reference Matlock, H., and Reese, L.C., ‘‘Generalized Solution for Laterally Loaded Piles,’’ ASCE J. of Soil Mechanics and Foundation Eng. 86, SM 5 (63–91), 1960.