Conception à pile unique selon AS 2159 (2009) & 3600 (2018)

En cas de charge latérale élevée ou de conditions de sol défavorables, les fondations sur pieux sont plus préférées aux fondations peu profondes. Des tentatives telles que les méthodes de modification du sol peuvent être faites pour éviter les tas, toutefois, ces méthodes peuvent impliquer des processus coûteux, dans lequel ce cas, des piles peut-être encore moins cher.

Le module SkyCiv Foundation Design comprend la conception de pieux conformes à l'American Concrete Institute (ACI 318) et normes australiennes (COMME 2159 & 3600).

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Calculatrice de conception de fondation

Design geotechnical strength of a pile

Vertical loads applied on piles are carried by the end-bearing of the pile and the skin or shaft-friction along its length. The design geotechnical strength (R_ré,g) is equal to the ultimate geotechnical strength (R_ré,ug) multiplied by a geotechnical reduction factor (ø_g) as specified on COMME 2159 Section 4.3.1.

\({R}_{ré,g} = {ø}_{g} × {R}_{ré,ug}\) (1)

R_ré,g = Design geotechnical strength

R_ré,ug = Ultimate geotechnical strength

ø_g = Geotechnical reduction factor

Ultimate Geotechnical Strength (R_ré,ug)

The ultimate geotechnical strength is equal to the sum of the factored skin friction of the pile (F_m,s ) multiplied by the lateral surface area and base resistance multiplied by the cross-sectional area at the tip of the pile.

\( {R}_{ré,ug} = [{R}_{s} × ({F}_{m,s} × {UNE}_{s} )] + ({F}_{b} × {UNE}_{b} )\) (2)

R_s = Reduction factor for shaft resistance

F_m,s = Shaft-frictional resistance

UNE_s = Lateral surface area

F_b = Base resistance term

UNE_b = Cross-sectional area at the tip of the pile

Pour un guide plus détaillé, consultez notre article sur le calcul la résistance au frottement cutané et la capacité portante en bout.

Facteur de réduction géotechnique (ø_g)

The geotechnical reduction factor is a risk-based calculation for the ultimate design which takes into account different factors, comme les conditions du site, pile design, and installation factors. Its value ranges commonly from 0.40 à 0.90. COMME 2159 4.3.1 also states how to estimate its value as shown in equation (3).

\( {ø}_{g} = {ø}_{gb} + [K × ({ø}_{tf} – {ø}_{gb})] ≥ {ø}_{gb} \) (3)

ø_gb = Basic geotechnical strength reduction factor

ø_tf = Intrinsic test factor

K= Testing benefit factor

Intrinsic test and testing benefit factors both rely on which type of load testing used on the piles. Their values are specified in Table 1 and on equations (4) et (5). Pile load testing is discussed briefly in Section 8 d'AS 2159.

Intrinsic Test Factor (øtf)
Static load testing	0.90
Rapid load testing	0.75
Dynamic load testing of preformed piles	0.80
Dynamic load testing of other than preformed piles	0.75
Bi-directional load testing	0.85
No testing	0.80

Table 1: Intrinsic Test Factor Values

Testing benefit factor for static load testing:

\( K = \frac{1.33 × p}{p + 3.3} ≤ 1\) (4)

Testing benefit factor for dynamic load testing:

\( K = \frac{1.13 × p}{p + 3.3} ≤ 1\) (5)

p = Percentage of the total piles that are tested and meet the acceptance criteria

The basic geotechnical strength reduction factor is evaluated using a risk assessment procedure discussed in Section 4.3. d'AS 2159. The outcome of the said procedure is Individual Risk Rating (IRR) and an overall design Average Risk Rating (ARR) which shall be used to determine the value of ø_gb comme indiqué dans le tableau 2.

Basic Geotechnical Strength Reduction Factor (øgb)
Average Risk Rating (ARR)	Catégorie de risque	øgb for low redundancy systems	øgb for high redundancy systems
ARR ≤ 1.5	Very low	0.67	0.76
1.5 < ARR ≤ 2.0	Very low to low	0.61	0.70
2.0 < ARR ≤ 2.5	Faible	0.56	0.64
2.5 < ARR ≤ 3.0	Low to moderate	0.52	0.60
3.0 < ARR ≤ 3.5	Modérer	0.48	0.56
3.5 < ARR ≤ 4.0	Moderate to high	0.45	0.53
4.0 < ARR ≤ 4.5	Haute	0.42	0.50
ARR > 4.5	Very high	0.40	0.47

Table 2: Values for Basic Geotechnical Reduction Factor, (COMME 2159 Table 4.3.2)

Low redundancy systems are heavily loaded single piles while high redundancy systems include large pile groups under large pile caps or pile groups with more than 4 pieux.

Design Structural Strength

Piles are structurally designed almost the same as a column. Design structural strength (R_ré,s) nécessite des capacités ultimes, telles que les forces axiales et de cisaillement, et moment de flexion. The design structural strength of a concrete pile is equivalent to the ultimate design strength (R_nous) réduit par un facteur de réduction de résistance (ø_s) et un facteur de placement concret (k), comme indiqué par la section 5.2.1 d'AS 2159.

\( {R}_{ré,s} = {ø}_{s} × k × {R}_{nous} \) (6)

ø_s = Strength reduction factor

k = Concrete placement factor

R_nous = Ultimate design strength

The values for the strength reduction factor are shown in Table 3. The concrete placement factor ranges from 0.75 à 1.0, depending on the pile construction method. toutefois, for piles other than concrete and grout, k shall be taken as 1.0.

Facteurs de réduction de la force (ø)
Axial force without bending	0.65
Bending without axial force (øpb)	0.65 ≤ 1.24 – [(13 × keuh)/12] ≤ 0.85
Bending with axial compression:
(je) Nu ≥ Nub	0.60
(ii) Nu < Nub	0.60 + {(øpb – 0.66) × [1 – (Nu/Nub)]}
Tondre	0.70

Table 3: Strength reduction factors (Table 2.2.2, COMME 3600-18)

Capacités axiales et flexibles d'un seul pieu

Similar to columns, piles may also be subjected to combined compression and bending load. Les capacités axiales et en flexion sont vérifiées à l'aide d'un diagramme d'interaction. Ce diagramme est une représentation visuelle du comportement des capacités de flexion et axiales causées par une augmentation de la charge du point de flexion pur jusqu'à ce qu'un point d'équilibre soit atteint.

 

Figure 1: Diagramme d'interaction de colonne

Squash Load (N_euh)

Le point de charge de squash est un point sur le diagramme où le pieu se rompra en compression pure. À ce point, the axial load is applied on the plastic centroid of the section to remain in compression without bending. Charge de courge (N_euh) et l'emplacement du centre de gravité plastique (ré_q) sont calculés comme indiqué dans les équations (7) & (8). Bien que l'emplacement du centre de gravité plastique puisse être considéré comme 1/2 of the total depth of the cross-section for symmetrical sections with symmetrical reinforcement layout.

\( {N}_{euh} = ø × [({UNE}_{g} – {UNE}_{s}) × ({une}_{1} × f’c) + ({UNE}_{s} × {F}_{le sien})] \) (7)

UNE_g = Gross cross-sectional area

UNE_s = Total area of steel

une₁ = 1.0 – (0.003 × f’c) [0.72 ≤α₁ ≤0.85]

f’c = Concrete strength

F_{le sien} = Yield Strength of steel

\( {ré}_{q} = frac{[(b × D) – {UNE}_{s}] × ({une}_{1} × f’c) × \sum_{je=1}^{n} ({UNE}_{bi} × {F}_{le sien} × {ré}_{en fonction de la valeur de la barre de déformation})}{{N}_{euh}} \) (8)

b = Pile cross-sectional width

D = Pile cross-sectional depth or diameter

UNE_bi = Area of reinforcing bar being considered

ré_{en fonction de la valeur de la barre de déformation} = Depth of reinforcing bar being considered

Squash load point through to decompression point

Decompression point is where the concrete strain at the extreme compressive fibre is equal to 0.003 et la déformation dans la fibre de traction extrême est nulle. Strength of the pile between the squash load and the decompression points can be calculated by linear interpolation with strength reduction factor (ø_s) de 0.6.

Decompression point through to pure bending

Le point de flexion pur est l'endroit où la capacité de charge axiale est nulle. The transition from decompression point to pure bending uses a strength reduction factor of 0.6 à 0.8 and an input parameter (k_u) is introduced. The value of k_u starts at 1 at decompression point and decreases until pure bending is reached. Between the transition of the two points, une condition équilibrée est atteinte. À ce point, la déformation du béton est à sa limite (e_c= 0,003) et la déformation extérieure de l'acier atteint le rendement (e_s= 0,0025), The value of k_u at this point is approximately 0.54 avec un facteur de réduction de résistance de 0.6.

Once a value of k_u is selected, tensile and compressive forces of the section can be calculated. The axial load on the section is equivalent to the sum of tensile and compressive forces, while the bending moment is calculated by resolving these forces about the neutral axis. Calculation for the compressive and tensile forces are enumerated below

Force due to concrete (F_cc):

\( {F}_{cc} = {une}_{2} × f’c × {UNE}_{c} \) (9)

une₂ = 0.85 – (0.0015 × f’c) [une_{2 ≥}0.67]

UNE_c = Compression block area (refer to Figure 2)

= b × γ × k_u × d (rectangular cross-section)

=(1/2) × (θ – sinθ) × (D/2)² (circular cross-section)

γ = 0.97 – (0.0025 × f’c) [c _≥0.67]

Figure 2: Concrete Compression Block Area

Obliger (F_et) et moment (M_je) contributed by each individual bar:

Each reinforcing bar of the section exerts a force that could either be compressive or tensile, en fonction de la valeur de la barre de déformation (e_et) en fonction de la valeur de la barre de déformation (10).

\( {e}_{et} = frac{{e}_{c}}{({k}_{u} × d)} × [({k}_{u} × d) – {ré}_{en fonction de la valeur de la barre de déformation}] \) (10)

ré_{en fonction de la valeur de la barre de déformation} = Depth to the bar being considered

e_c= Concrete strain = 0.003

If ε_et < 0 (en fonction de la valeur de la barre de déformation)

If ε_et > 0 (en fonction de la valeur de la barre de déformation)

en fonction de la valeur de la barre de déformation:

\( {F}_{et} = {σ}_{et} × {UNE}_{bi} \) (11)

σ_et = Stress in bar = Le minimum [(e_et × E_s ), F_{le sien}]

E_s = Modulus elasticity of steel

UNE_bi = Bar area

Bar in tension:

\( {F}_{et} = [{σ}_{et} – ({une}_{2} × f’c)] × {UNE}_{bi} ≥ 0\) (12)

σ_et = Stress in bar = Le minimum [(e_et × E_s ), –F_{le sien}]

E_s = Modulus elasticity of steel

UNE_bi = Bar area

Moment by each bar:

\( {M}_{je} = {F}_{et} × {ré}_{en fonction de la valeur de la barre de déformation} \) (13)

Axial capacity of the pile:

\( {øN}_{u} = ø × [ {F}_{cc} + {Σ}_{je=1}^{n} {F}_{et}]\) (14)

Flexural capacity of the pile:

\( {douloureux}_{u} = ø × [ ({N}_{u} × {ré}_{q}) – ({F}_{cc} × {et}_{c}) – {Σ}_{je=1}^{n} {M}_{je}] \) (15)

Design bending moment:

Section 7.2 specifies that piles are required to have a out-of-position tolerance of 75mm for the horizontal positioning of the piles. This requirement may induce a bending moment equal to axial load multiplied by the eccentricity of 75mm. aditionellement, a minimum design moment shall also be considered which is equivalent to the axial force multiplied by 5% of the overall minimum width of the pile. Par conséquent, the design bending moment should be the greater value between equations 16a and 16b.

\( {M}_{ré} = {{M}^{*}}_{appliqué} + ({N}^{*} × 0.075 m) \) (16une)

\( {M}_{ré} = {N}^{*} × (0.05 × D) \) (16b)

M_ré = Design bending moment

M*_appliqué = Applied moment

N* = Axial load

D = Pile width

Capacité de cisaillement d'un seul pieu

Calculation for the strength in shear shall be in accordance with Section 8.2 d'AS 3600. Shear strength is equivalent to a combined shear capacities of the concrete and the steel reinforcement (équation 17).

\( {øV}_{u} = ø × ({V}_{uc} + {V}_{nous}) ≤ {øV}_{u,max} \) (17)

Résistance au cisaillement du béton (V_uc)

La contribution du béton à la capacité de cisaillement est calculée comme indiqué sur l'équation (18) qui est défini sur la section 8.2.4.1 d'AS 3600. This section also requires the value of √f’c shall not exceed 9.0 MPa. The values for the parameter k_v et θ_v are determined by using a simplified method suggested by Section 8.2.4.3 d'AS 3600.

\( {V}_{uc} = {k}_{v} × b × {ré}_{v} × sqrt{f’c} \) (18)

ré_v = Effective shear depth = Maximum [(0.72 × D ), (0.90 × d )]

Determination of the minimum area of shear reinforcement (UNE_sv.min) & k_v:

The area of the shear reinforcement (UNE_sv) is the total bar area of all the provided steel bars tied in the same direction of the applied load. Section 8.2.1.7 d'AS 3600 provided the equation for the minimum transverse shear reinforcements, which shall be:

\( \frac{{UNE}_{sv.min}}{s} = frac{0.08 × sqrt{f’c} × b}{{F}_{sy.f}} \)

F_sy.f = Yield strength of shear reinforcing bars

s= Center-to-center spacing of shear reinforcing bars

Pour (UNE_sv/s) < (UNE_sv.min/s):

\( {k}_{v} = frac{200}{[1000 + (1.3 × {ré}_{v} )]} ≤ 0.10\)

Pour (UNE_sv/s) ≥ (UNE_sv.min/s):

\( {k}_{v} = 0.15 \)

Résistance au cisaillement des barres d'acier (V_nous)

The contribution of the transverse shear reinforcements to the shear capacity calculated is shown in equation (19), which is defined in Section 8.2.5 d'AS 3600.

\( {V}_{nous} = frac{{UNE}_{sv} × {F}_{sy.f} × {ré}_{v}}{s} × cot{θ}_{v} \) (19)

θ_v= angle of inclination of the compression strut = 36º

Maximum shear strength (V_u.max)

Shear capacity is limited and in no case shall exceed the maximum value specified on Section 8.2.6 d'AS 3600 (équation 20).

\( {V}_{u.max} = 0.55 × [ (f’c × b × {ré}_{v}) × frac{cot{θ}_{v} + cot{une}_{v}}{1 + cot^{2}{θ}_{v} }] \) (20)

une_v= angle between the inclined shear reinforcement and the longitudinal tensile reinforcement≈ 90º

Ultimate shear strength (V_u)

The total shear strength contributed by the concrete and shear reinforcements shall be less than or equal to the limiting value of V_u.max

\( {V}_{u} = ({V}_{uc} + {V}_{nous} ) ≤ {V}_{u.max} \) (21)

Design shear strength (øV_u)

Capacity reduction factor that shall be applied for the ultimate shear strength is ø = 0.7. Par conséquent, the design shear strength of the pile is given by:

\( {øV}_{u} = ø × ({V}_{uc} + {V}_{nous} ) \) (22)

Références

• Pack, Lonnie (2018). Australian Guidebook For Structural Engineers. CRC Press.
• Piling Design and Installation (2009). COMME 2159. Norme australienne
• Ouvrages en béton (2018). COMME 3600. Norme australienne