The allowable lateral load on piles is determined from the following two criteria:

The smaller of the two above values is the one actually adopted as the design lateral load.

Methods of calculating lateral resistance of vertical piles can be broadly divided into two categories.

- Pile Parameters

Pile TypePile Dia. Thickness

(b, mm) (t, mm) (My, kg-cm) (D, m)

PC

400 65.0 4.0E+05 106,435 0.0 9.2E+05 8.0

(b, in) (t, in) (Ep, psi) (My, lb-in) (D, in)

15.7 2.6 5.6E+06 2,557 0.0 8.0E+05 315.0

1) The general soil type within the critical depth (approximately 4 to 5 pile diameters = 2.0 m) below the ground surface is

considered to be very loose sand (cohesionless soil) from the soil report.

2) Determine the coefficient of horizontal subgrade reaction (Kh) within the critical depth for cohesionless soils.

Values of the coefficient of modulus variation Kh are obtained from the following Table.

(The values of given in following table were determined by Terzaghi.)

Soil Density

Loose 7 4

Medium 30 20

Dense 65 40 Choose from the Table = 7 lb/in3 (above ground water)∴

3) Determine the dimensionless length factor

= 0.0137 /in : for cohesionless soils

= 0.0137 x (Embedded pile length) = 0.0137 x 315 in

= 4.31 in > 4.0 long pile caculation procedure!∴

4) Determine the other required soil parameters over the embedded length of the pile.

a) The Rankine passive earth pressure coefficient for cohesionless soil (Kp)

= 2.77

b) The average effective unit weight of the soil

(psi)= 1.7 t/m3 = 0.06 lb/in3

◆ Lateral Pile Capacity Caculation using Broms's Method (Free head type)

①  Allowable lateral load is obtained by dividing the ultimate (failure) load by an adequate factor of safety.

② Allowable lateral load is corresponding to an acceptable lateral deflection.

Elastic Modulus

Moment ofInertia ec

Pile yieldMoment

PileLength

(Ep,kgf/cm2) ( Ip, cm4) (ec, mm)

( Ip, in4) (ec, in)

※ ec : Eccentricity of applied load for free-headed piles (i.e., vertical distance between ground surface and lateral load)

1. Methods of Calculating Ultimate Lateral Resistance

Kh (lb/in3)

Above Groundwater

Below Groundwater

η=5√Kh /EIηD

K p= tan2 (45+φ /2)

γ

5) Determine the ultimate lateral load for a single pile (Qu)

Long free headed pile in cohesionless soil – using (and for free headed case)

enter Figure 1 and select the corresponding value of and solve for

= 0 / 15.75 = 0.0

= 797741.4 / [ 0.06 × 15.75^4 × 2.77 ] = 78.04

= 30

30 x 2.77 x 15.75^3 x 0.06 = 19.47 kips = 8.83 ton

3.0 = 2.94 ton

Calculate corresponding to a given design deflection at the ground surface (y) or the deflection corresponding

to a given design load.

Free headed pile in cohesionless soil – using (and for free headed case) enter Figure 2 and

select the corresponding value of and solve for of y.

= 0.0 , = 4.31 , y = 1.0 cm = 0.39 in

= 0.55

0.39 x (5574602.1 x 2556.83)^0.6 x (7)^0.4 / (0.55 x 314.96)

= 6.12 kips = 2.78 ton

Since Qa = 2.78 ton < Qm = 2.94 ton , use Q_allow = 2.78 ton (for Pile Foundation Design)

∴ =

6) Calculate the maximum allowable working load for a single pile (Qm)

2. Methods of Calculating Acceptable Deflection at Working Lateral Load

1) Calculate the working load for a single pile (Qa)

∴ =

3. Determination of Allowable Lateral Capacity

Compare Qa to Qm

If Qa < Qm use Qa and y

M y /γb4 K p ec/b

Qu /K pb3γ Qu

ec/b

M y /γb4 K p

Qu /K pb3γ

Qu

Qm=Qu/¿ ¿

Qa

ηD ec/Dy (EI )3/5K

h2/5/QaD Qa

ec/D ηD

y (EI )3/5Kh2/5

/QaD

Qa

Attachment

Figure 1. Ultimate Lateral Load Capacity of Long Pile in Cohesionless Soils

Figure 2. Lateral Deflection at Ground Surface of Piles in Cohesionless Soils

Soil Type

Loose Sand