MDC > Theoretical Notes > Foundation Pile Computation

Sign convention

1. Vertical force Fy is positive when directed downwards;

2. Horizontal force Fx is positive when directed towards the right;

3. Couple M is positive when acting to produce movements such as those produced by horizontal force Fx.

Winkler model analysis of pile in operating status

Winkler's model enables variations in mechanical properties of terrain and layers to be taken into consideration simply.

Where material is homogeneous (K constant) Hetènyi's classification is adopted that defines three different pile behaviour for Winkler depending on relative terrain rigidity (l) soil/pile that is: short or rigid pile, relatively flexible pile, infinitely flexible pile.

Limit vertical load

Limit vertical load is calculated with static formulas that express it in function of pile geometry, of terrain properties and of the interface pile soil.

For the purposes of calculation limit load Qlim is conventionally apportioned in two parts: tip resistance Qp and lateral resistance Qs.

Tip resistance

Tip resistance qp where the terrain displays friction (j) e cohesion (c), is give by:

qp = c · Nc + γ · D V Nq

where:

γ = Terrain unit volume weight

D = Pile length;

Nc & Nq= Bearing capacity factors including form factor (circular).

Factor Nq is calculated according to Berezantzev.

Stem resistance

Lateral bearing capacity is calculated using method A proposed by Tomlinson (1971) according to the following:

fs = Α · c + q ·K ·tg δ

c = Average cohesion value (or shear resistance in undrained conditions).

q = Effective vertical pressure of the terrain.

k = Coefficient of horizontal thrust. This depends on the technique of the pile and on the previous compaction state and is calculated as:

For driven piles	K = 1 + tg2φ
For drilled piles	K = 1 - tg2φ

δ = Pile/soil friction coefficient as function of pile surface.

For driven piles	δ = 3/4 ·tg φ
For drilled piles	δ = tg φ

α is a coefficient as below:

Driven pile coefficient

c < 0.25	α = 1.00
0.25 < c < 0.5	α = 0.85
0.5 < c < 0.75	α = 0.65
0.75 < c <2.4	α = 0.50
c >2.4	α = 1.2 / c

Drilled pile coefficient

c < 0.25	α = 0.9
0.25 < c < 0.5	α = 0.8
0.5 < c < 0.75	α = 0.6
0.75 < c < 2	α = 0.4
c > 2	α = 0.8 / c

Further according to Okamoto guidelines where seismic state occurs lateral resistance ie reduced depending on the seismic coefficient kh as follows:

Creduct_coeff = 1 - kh

Finally:

1. For driven piles both resistance properties (c,φ) and the coefficient of the terrain horizontal modulus are reduced by 10%.

2.Where drag action is encountered, tip load is null and lateral load is reduced by 70%.

3.In the vertical safety margin the weight of the pile has been taken into account.

Settlements

Vertical settlements are calculated using the Davis-Poulos method, according to which the pile is considered as rigid (undeformable) embedded in an elastic medium, semi space, or layer of finite thickness.
The hypothesis considers that the interaction between pile and soil is constant for each (n) cylindrical segments in which the pile side surface is subdivided.
The settlement of the i th surface due to the load transmitted by the pile to the soil along the j th surface may be expressed as:

Wi,j = (τj / E ) · B · Ii,j

where:

τj = Increment in tension at the mid point of the segment;

E = Elastic modulus of the terrain;
B = Diameter of the pile;

Ii,j= Influence coefficient.

Total settlement is obtained by the sum of Wi,j for all j areas.