Ultimate load

MP NX computes the ultimate vertical load with static formulae, for each investigation vertical and each combination, then applies the ξ factors and the γ_R factors. This page explains the choices in the Pile card and how to read the Ultimate load tab.

Net ultimate load

In compression:

Q = Q_p + Q_s − W − Q_neg

with Q_p the base resistance, Q_s the shaft resistance, W the pile weight and Q_neg the adhesion of the layers in negative skin friction. In tension the base does not work: Q = Q_s + W.

Base resistance

Q_p = A·(σ′_v·N_q + c·N_c), with σ′_v the effective vertical stress at the toe, including the surcharge q_pc. N_q and N_c depend on the Method for N_q:

Method	Nq	Nc
Berezantsev	function of φ and L/D; for D > 0.8 m interpolation on L/D	(Nq − 1)/tan φ; 9 for φ = 0
Berezantsev (L/D = 32)	0.48·exp(4.97·tan φ)	as above
Terzaghi	Terzaghi's formula (1943)	(Nq − 1)/tan φ, minimum 5.7
Janbu	function of φ and of the relative density Dr (ψ = 60° + 0.45·Dr)	(Nq − 1)/tan φ; 5.74 for φ = 0
Hansen	exp(π·tan φ)·tan²(45° + φ/2) with shape and depth factors	with the same factors; 5.14 for φ = 0
Vesic	function of φ and of the rigidity index Ir = 1.7·Dr	(Nq − 1)/tan φ
Nq utente (user value)	the value of the Nq assigned field	(Nq − 1)/tan φ; 9 for φ = 0

With Janbu and Vesic the D_r field appears, the relative density in %. The full formulae and the control values at φ = 30° are in the validation document.

The Friction angle for the shaft resistance field corrects φ before the calculation: φ, φ − 3° (bored), ¾ φ + 10° (driven) or (φ + 40°)/2. The corrected angle also enters N_q: in Bowles' example 16.10, φ = 32° becomes 34° at the toe.

Shaft resistance

Q_s = π·D·Σ (K·tan δ·σ′_v,mean + α·c)·t, summed over the layers of thickness t.

• Earth pressure coefficient K: 0.5; 1; 1 − sin φ; 1 − tan² φ; or User value.
• Soil-pile friction angle: δ = φ, ⅔ φ, ¾ φ, 20° or 25°.
• α and c (or c_u) come from the layer.

In rock layers the frictional term is zero and τ = α·R_cᵏ. The adhesion above the founding plane of the footing is removed. For tapered driven piles the taper factor F_w applies.

K is computed with the unreduced φ

With K = 1 − sin φ or 1 − tan² φ the program uses the friction angle of the layer, not the one reduced by the M factors or corrected for driving. It is the behaviour of the desktop program, declared in the validation document.

From Q to R_k and R_d

For each combination the program computes Q_p and Q_s on all the verticals, then:

1. takes minimum and mean, and with ξ₃ and ξ₄ obtains R_k,p and R_k,s;
2. divides by γ_b and γ_s and subtracts the weight: R_d = R_k,p/γ_b + R_k,s/γ_s − W;
3. compares with the action: FS_v = R_d/|E_d,v|.

The weight W is that of the first vertical. The factors are described in Loads, combinations and design code.

Ultimate lateral load (Broms)

H_max is computed with Broms' method, in Viggiani's formulation: cohesive soils (with c_u) and cohesionless soils (with Rankine's K_p), free or fixed head according to the Head restraint in General data. The mechanism depends on the ultimate moment of the section M_y and is shown in the table as Short pile, Intermediate pile or Long pile.

Where M_y comes from:

• if you enter M_y in the Materials and reinforcement card, your value prevails;
• if M_y = 0 and the FEM analysis is enabled, the ultimate moment of the reinforced section at N = 0, computed by the program, is used;
• for the tubular micropile with M_y = 0 the moment of the composite tube + grout section is used;
• if M_y = 0 and the FEM is off, the lateral check is not performed.

The design resistance is R_d,h = R_k,h/γ_T and the check FS_h = R_d,h/E_d,h.

Seismic correction

With a/g > 0 in the Seismic action card the ultimate load is reduced with one of three methods:

Method	Correction
Vesic	φ reduced by 2°
Okamoto	base and cohesive shaft term multiplied by 1 − a/g
Sano	φ reduced by atan(a/(g·√2))

Vesic and Sano restart from the unreduced angle φ: with the M2 factors the reduction of φ is not cumulated. This too is declared in the validation document.

Reading the Ultimate load tab

At the top is the outcome, Check satisfied or Check NOT satisfied, with the Governing combination, that is the one with the lowest safety factor. The four tiles report R_d, E_d, R_k and the Safety factor on a scale from 1 to 3.

Then comes one card per combination. The header says whether it is in Compression or Tension and reports E_d,v and E_d,h. The table has one row per vertical:

Column	Meaning
Nq, Nc	bearing capacity factors used
φp, cp	friction angle and cohesion at the toe, after corrections and factors
σ′v,p	vertical stress at the toe
Qp, Qs, W	base, shaft, pile weight
Q	net ultimate load; in brackets the negative skin friction subtracted
Hmax, Mechanism	Broms' ultimate lateral load and mechanism

Below the table, four groups: Investigation verticals (n, ξ₃, ξ₄, minimum, mean and maximum of Q_p and Q_s), Characteristic resistances, Design resistances with γ_b, γ_s and FS_v, and Ultimate lateral load (Broms) with FS_h. Any messages from the calculation appear at the bottom.

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