Broms method

◆ Lateral Pile Capacity Caculation using Broms's Method (Free head type) The allowable lateral load on piles is determined from the following two criteria:

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. 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 Type

PC

Pile Dia.

Thickness

Elastic Modulus

(b, mm)

(t, mm)

(Ep,kgf/cm )

( Ip, cm )

400

65.0

4.0E+05

106,435 4

(ec, mm)

Pile yield Moment (My, kg-cm)

Pile Length (D, m)

Moment of Inertia 2

4

ec 0.0

9.2E+05

8.0

(My, lb-in)

(D, in)

8.0E+05

315.0

(b, in)

(t, in)

(Ep, psi)

( Ip, in )

(ec, in)

15.7

2.6

5.6E+06

2,557

0.0

※ 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 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.) 3

Kh (lb/in ) Soil Density Above Below Groundwater Groundwater 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

  5 Kh / EI

D

= 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)

K p  tan 2 ( 45   / 2 )

=

2.77

b) The average effective unit weight of the soil



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

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

M y / b 4 K p (and ec / bfor free headed case) 3 enter Figure 1 and select the corresponding value of Qu / K p b  and solve for Qu Long free headed pile in cohesionless soil – using

ec / b = 0 / 15.75 = 0.0

M y / b4 K p

=

Qu / K p b3

=

∴ Q

797741.4 / [ 0.06 × 15.75^4 × 2.77 ] = 30

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

u

78.04

ton

= 8.83

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

Q

m

 Q u / 3.0

=

ton

2.94



D

2. Methods of Calculating Acceptable Deflection at Working Lateral Load 1) Calculate the working load for a single pile (Qa) Calculate Qa corresponding to a given design deflection at the ground surface (y) or the deflection corresponding to a given design load.

D(and

Free headed pile in cohesionless soil – using select the corresponding value of

ec / D =

0.0

y( EI )3 / 5 K h

∴ Qa

2/5

,

y( EI )

D

3/ 5

=

Kh

4.31

2/5

ec / D for free headed case) enter Figure 2 and

/ Qa D

and solve for

, y = 1.0 cm =

Qaof y.

0.39 in

/ Qa D = 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

3. Determination of Allowable Lateral Capacity Compare Qa to Qm If Qa < Qm use Qa and y Since Qa = 2.78 ton < Qm = 2.94 ton , use Q_allow = 2.78 ton (for Pile Foundation Design) y Q Q a m

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

he ground surface is

ation procedure!

on corresponding