Single pile design in accordance with AS 2159 (2009) & 3600 (2018)

In case of high lateral load or unfavorable soil conditions, 杭基礎は浅い基礎よりも好ましい. 杭を回避するために、土壌改良方法などの試みを行うことができます, しかしながら, these methods may involve expensive processes, wherein this case, 山はおそらくさらに安い.

SkyCiv Foundation Design module includes the design of piles conforming to American Concrete Institute (ACI 318) およびオーストラリアの基準 (なので 2159 & 3600).

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基礎設計計算機

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_d,g) is equal to the ultimate geotechnical strength (R_d,と) 地盤工学的削減係数を掛けたもの (ø_g) as specified on なので 2159 セクション 4.3.1.

\({R}_{d,g} = {ø}_{g} × {R}_{d,と}\) (1)

R_d,g = Design geotechnical strength

R_d,と = Ultimate geotechnical strength

ø_g = Geotechnical reduction factor

Ultimate Geotechnical Strength (R_d,と)

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

\( {R}_{d,と} = [{R}_{s} × ({f}_{メートル,s} × {あ}_{s} )] + ({f}_{b} × {あ}_{b} )\) (2)

R_s = Reduction factor for shaft resistance

f_{メートル,s} = Shaft-frictional resistance

あ_s = Lateral surface area

f_b = Base resistance term

あ_b = Cross-sectional area at the tip of the pile

より詳細なガイドについて, 計算に関する記事をご覧ください 皮膚摩擦抵抗とエンドベアリング能力.

Geotechnical Reduction Factor (ø_g)

The geotechnical reduction factor is a risk-based calculation for the ultimate design which takes into account different factors, サイトの状態など, パイルデザイン, and installation factors. その値の範囲は、一般的に 0.40 に 0.90. なので 2159 4.3.1 また、式に示すようにその値を推定する方法についても述べています (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) そして (5). Pile load testing is discussed briefly in Section 8 ASの 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

テーブル 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. ASの 2159. The outcome of the said procedure is Individual Risk Rating (内部利益率) および全体的な設計 平均リスク評価 (到着) which shall be used to determine the value of ø_GB 表に示すように 2.

基礎地盤強度低下係数 (øGB)
平均リスク評価 (到着)	リスクカテゴリー	øGB for low redundancy systems	øGB for high redundancy systems
ARR ≤ 1.5	とても低い	0.67	0.76
1.5 < ARR ≤ 2.0	非常に低いから低い	0.61	0.70
2.0 < ARR ≤ 2.5	低	0.56	0.64
2.5 < ARR ≤ 3.0	Low to moderate	0.52	0.60
3.0 < ARR ≤ 3.5	中程度	0.48	0.56
3.5 < ARR ≤ 4.0	Moderate to high	0.45	0.53
4.0 < ARR ≤ 4.5	高い	0.42	0.50
到着 > 4.5	Very high	0.40	0.47

テーブル 2: Values for Basic Geotechnical Reduction Factor, (なので 2159 テーブル 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 杭.

Design Structural Strength

杭は柱とほぼ同じ構造設計. 設計強度 (R_d,s) 究極の能力が必要, 軸力やせん断力など, と曲げモーメント. コンクリート杭の設計構造強度は、設計極限強度に相当します。 (R_我ら) 強度減少係数で減少 (ø_s) および具体的な配置係数 (k), セクションで述べたように 5.2.1 ASの 2159.

\( {R}_{d,s} = {ø}_{s} × k × {R}_{我ら} \) (6)

ø_s = Strength reduction factor

k = Concrete placement factor

R_我ら = Ultimate design strength

The values for the strength reduction factor are shown in Table 3. コンクリート配置係数の範囲は 0.75 に 1.0, 杭工法による. しかしながら, for piles other than concrete and grout, k は 1.0.

強度低下係数 (ø)
Axial force without bending	0.65
Bending without axial force (øpb)	0.65 ≤ 1.24 – [(13 × k=最も近いサポートの面までのせん断が考慮されているセクションの距離)/12] ≤ 0.85
Bending with axial compression:
(私) Nあなた ≥ Nub	0.60
(ii) Nあなた < Nub	0.60 + {(øpb – 0.66) × [1 – (Nあなた/Nub)]}
剪断	0.70

テーブル 3: 強度低下要因 (テーブル 2.2.2, なので 3600-18)

単一杭の軸方向および曲げ能力

Similar to columns, パイルは、圧縮と曲げの複合荷重を受けることもあります。. 軸方向および曲げ能力は、相互作用図を使用してチェックされます. This diagram is a visual representation of the behavior of the bending and axial capacities caused by an increase in load from pure bending point until a balanced point is reached.

 

図 1: 列の相互作用図

Squash Load (N_{=最も近いサポートの面までのせん断が考慮されているセクションの距離})

The squash load point is a point on the diagram where the pile will fail in pure compression. この時点で, the axial load is applied on the plastic centroid of the section to remain in compression without bending. Squash load (N_{=最も近いサポートの面までのせん断が考慮されているセクションの距離}) and the location of the plastic centroid (d_q) are computed as shown in equations (7) & (8). Although location of the plastic centroid can be taken as 1/2 of the total depth of the cross-section for symmetrical sections with symmetrical reinforcement layout.

\( {ϕN}_{=最も近いサポートの面までのせん断が考慮されているセクションの距離} =ø× [({あ}_{g} – {あ}_{s}) × ({a}_{1} ×f’c) + ({あ}_{s} × {f}_{彼の})] \) (7)

あ_g = Gross cross-sectional area

あ_s = Total area of steel

a₁ = 1.0 – (0.003 ×f’c) [0.72 ≤α₁ ≤0.85]

f’c = Concrete strength

f_彼の = Yield Strength of steel

\( {d}_{q} = frac{[(b × D) – {あ}_{s}] × ({a}_{1} ×f’c) × \sum_{i=1}^{ん} ({あ}_{バイ} × {f}_{彼の} × {d}_{する})}{{N}_{=最も近いサポートの面までのせん断が考慮されているセクションの距離}} \) (8)

b = Pile cross-sectional width

D = Pile cross-sectional depth or diameter

あ_バイ = Area of reinforcing bar being considered

d_する = 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 極限引張繊維のひずみはゼロです. Strength of the pile between the squash load and the decompression points can be calculated by linear interpolation with strength reduction factor (ø_s) の 0.6.

Decompression point through to pure bending

純粋な曲げ点は、軸方向の耐荷重がゼロになる場所です。. The transition from decompression point to pure bending uses a strength reduction factor of 0.6 に 0.8 and an input parameter (k_あなた) is introduced. The value of k_あなた starts at 1 at decompression point and decreases until pure bending is reached. Between the transition of the two points, バランスの取れた状態が達成されます. この時点で, コンクリートのひずみは限界にあります (e_c= 0.003) 外側の鋼のひずみが降伏に達する (e_s= 0.0025), The value of k_あなた at this point is approximately 0.54 with a strength reduction factor of 0.6.

Once a value of k_あなた 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):

\( {F}_{cc} = {a}_{2} × f’c × {あ}_{c} \) (9)

a₂ = 0.85 – (0.0015 ×f’c) [a_{2 ≥}0.67]

あ_c = Compression block area (図を参照 2)

= b × γ × k_あなた ×d (rectangular cross-section)

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

γ = 0.97 – (0.0025 ×f’c) [c _≥0.67]

図 2: Concrete Compression Block Area

力 (F_そして) と瞬間 (M_私) contributed by each individual bar:

Each reinforcing bar of the section exerts a force that could either be compressive or tensile, depending on the value bar strain (e_そして) shown in equation (10).

\( {e}_{そして} = frac{{e}_{c}}{({k}_{あなた} ×d)} × [({k}_{あなた} ×d) – {d}_{する}] \) (10)

d_する = Depth to the bar being considered

e_c= Concrete strain = 0.003

If ε_そして < 0 (bar is in tension)

If ε_そして > 0 (bar is in compression)

Bar in compression:

\( {F}_{そして} = {σ}_{そして} × {あ}_{バイ} \) (11)

σ_そして = Stress in bar = 最小 [(e_そして × E_s ), f_彼の]

E_s = Modulus elasticity of steel

あ_バイ = Bar area

Bar in tension:

\( {F}_{そして} = [{σ}_{そして} – ({a}_{2} ×f’c)] × {あ}_{バイ} ≥ 0\) (12)

σ_そして = Stress in bar = 最小 [(e_そして × E_s ), –f_彼の]

E_s = Modulus elasticity of steel

あ_バイ = Bar area

Moment by each bar:

\( {M}_{私} = {F}_{そして} × {d}_{する} \) (13)

Axial capacity of the pile:

\( {øN}_{あなた} =ø× [ {F}_{cc} + {Σ}_{i=1}^{ん} {F}_{そして}]\) (14)

Flexural capacity of the pile:

\( {痛い}_{あなた} =ø× [ ({N}_{あなた} × {d}_{q}) – ({F}_{cc} × {そして}_{c}) – {Σ}_{i=1}^{ん} {M}_{私}] \) (15)

Design bending moment:

セクション 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. さらに, a minimum design moment shall also be considered which is equivalent to the axial force multiplied by 5% パイルの全体の最小幅の. したがって, the design bending moment should be the greater value between equations 16a and 16b.

\( {M}_{d} = {{M}^{*}}_{適用} + ({N}^{*} × 0.075 メートル) \) (16a)

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

M_d = Design bending moment

M*_適用 = Applied moment

N* = Axial load

D = Pile width

単一杭のせん断耐力

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

\( {øV}_{あなた} =ø× ({V }_{SkyCiv Foundationには、オーストラリア規格に準拠した孤立した基礎の設計が含まれています¹} + {V }_{我ら}) ≤ {øV}_{あなた,最高} \) (17)

コンクリートのせん断強度 (V _{SkyCiv Foundationには、オーストラリア規格に準拠した孤立した基礎の設計が含まれています¹})

せん断耐力へのコンクリートの寄与は、式に示すように計算されます (18) セクションで定義されています 8.2.4.1 ASの 3600. This section also requires the value of √f’c shall not exceed 9.0 MPa. The values for the parameter k_v そして θ_v are determined by using a simplified method suggested by Section 8.2.4.3 ASの 3600.

\( {V }_{SkyCiv Foundationには、オーストラリア規格に準拠した孤立した基礎の設計が含まれています¹} = {k}_{v} × b × {d}_{v} [object Window]{f’c} \) (18)

d_v = Effective shear depth = 最大 [(0.72 ×D ), (0.90 ×d )]

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

The area of the shear reinforcement (あ_sv) is the total bar area of all the provided steel bars tied in the same direction of the applied load. セクション 8.2.1.7 ASの 3600 最小横せん断補強材の式を提供, これは:

\( \フラク{{あ}_{sv.min}}{s} = frac{0.08 [object Window]{f’c} × b}{{f}_{そしてf}} \)

f_そしてf = Yield strength of shear reinforcing bars

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

ために (あ_sv/s) < (あ_sv.min/s):

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

ために (あ_sv/s) ≥ (あ_sv.min/s):

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

棒鋼のせん断強度 (V _我ら)

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 ASの 3600.

\( {V }_{我ら} = frac{{あ}_{sv} × {f}_{そしてf} × {d}_{v}}{s} × cot{θ}_{v} \) (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 ASの 3600 (方程式 20).

\( {V }_{u.max} = 0.55 × [ (f’c × b × {d}_{v}) [object Window]{cot{θ}_{v} + cot{a}_{v}}{1 + cot^{2}{θ}_{v} }] \) (20)

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

Ultimate shear strength (V _あなた)

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

\( {V }_{あなた} = ({V }_{SkyCiv Foundationには、オーストラリア規格に準拠した孤立した基礎の設計が含まれています¹} + {V }_{我ら} ) ≤ {V }_{u.max} \) (21)

Design shear strength (øV_あなた)

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

\( {øV}_{あなた} =ø× ({V }_{SkyCiv Foundationには、オーストラリア規格に準拠した孤立した基礎の設計が含まれています¹} + {V }_{我ら} ) \) (22)

参考文献

• Pack, Lonnie (2018). Australian Guidebook For Structural Engineers. CRC Press.
• Piling Design and Installation (2009). なので 2159. オーストラリア規格
• コンクリート構造物 (2018). なので 3600. オーストラリア規格