Pile Capacity in Geotechnical Engineering

What you’ll learn

What are Piles and When to use them?

Piles are structural members made of steel, concrete, or timber that serve as deep foundations where the depth or length is significantly larger than the width. Unlike shallow foundations, deep foundations require special equipment and skilled labor, making them more expensive than conventional spread footings.

When are Pile Foundation recommended?

There are different types of foundation. Pile foundation should be considered when shallow foundations prove inadequate.

Weak Ground Conditions
Cannot withstand the heavy load from the structure
Resisting Uplift
Compaction Piles

Types of Pile Foundation

Steel Pile
Concrete Pile

What is Pile Capacity?

Pile capacity refers to the maximum load a pile can safely support without experiencing excessive settlement or structural failure. It encompasses two critical components:

Ultimate Pile Capacity (Qu)

The maximum load the pile can sustain before failure occurs, combining both shaft resistance and end-bearing capacity.

The ultimate load carrying capacity (Qu) of a pile is given by the fundamental equation:

$Q_{u}=Q_{eb}+Q_{sf}$

where:
$Q_u = Ultimate \: Pile \: Capacity (kN)$
$Q_b$ = Point \: Bearing \: Capacity \: of \: Pile \: Tip (kN)Q_f = Frictional \: Resistance \: from \: soil-pile

$  <h3 class="wp-block-heading has-medium-font-size" id="allowable-load-capacity">Allowable Load Capacity (Qa)</h3>   The safe working load obtained by dividing the ultimate capacity by an appropriate factor of safety, typically ranging from 2.0 to 3.0.   The <strong>allowable load capacity </strong>provided a safety margin against failure:   <div class="wp-block-columns has-border-color has-palette-color-4-color has-palette-color-6-background-color has-text-color has-background has-link-color" style="border-color:#4adede;border-width:2px;border-radius:20px;margin-top:0;margin-bottom:0;padding-top:17px;padding-right:20px;padding-bottom:17px;padding-left:20px"> <div class="wp-block-column"> <span class="ql-right-eqno"> </span><span class="ql-left-eqno"> </span><img src="https://civilengghub.com/wp-content/ql-cache/quicklatex.com-770c7dd270d3a5dab3c046a23cf6655d_l3.png" height="37" width="74" class="ql-img-displayed-equation quicklatex-auto-format" alt="\[Q_{a}=\frac{Q_{u}}{FS}\]" title="Rendered by QuickLaTeX.com"/> </div> </div>     where:$

Q_{all} = Allowable \: pile \: capacity (kN)FS = Factor \: of \: Safety

$    <h2 class="wp-block-heading has-large-font-size" id="component">Component of Pile Capacity</h2>   <h2 class="wp-block-heading has-medium-font-size" id="1">1. Shaft Resistance (Skin Friction)</h2>   Shaft resistance develops along the embedded length of the pile through friction and adhesion between the pile surface and surrounding soil.   <h2 class="wp-block-heading has-medium-font-size" id="end">2. End Bearing Capacity</h2>   End bearing resistance occurs at the pile tip, where the load is transferred directly to the bearing stratum. This component becomes dominant when:   <ul class="wp-block-list"> <li>Piles are driven to hard rock or dense soil layers </li>   <li>The pile diameter is relatively large </li>   <li>Using short, stubby piles</li> </ul>     <h3 class="wp-block-heading has-large-font-size" id="point-bearing-capacity-for-cohesive-soils"><mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-palette-color-2-color">Piles on Sand</mark></h3>   <strong>End-Bearing Capacity </strong>   <div class="wp-block-columns has-border-color has-palette-color-4-color has-palette-color-6-background-color has-text-color has-background has-link-color" style="border-color:#4adede;border-width:2px;border-radius:20px;margin-top:0;margin-bottom:0;padding-top:17px;padding-right:20px;padding-bottom:17px;padding-left:20px"> <div class="wp-block-column"> <span class="ql-right-eqno"> </span><span class="ql-left-eqno"> </span><img src="https://civilengghub.com/wp-content/ql-cache/quicklatex.com-950be3836ea18691e5cbc4864638e005_l3.png" height="21" width="113" class="ql-img-displayed-equation quicklatex-auto-format" alt="\[Q_{Eb}= \sigma' A_pN_q\]" title="Rendered by QuickLaTeX.com"/> </div> </div>     where:  $

\sigma ‘ = effective \: vertical \:stressA_p=area \: of \: pile \: tipN_q=bearing \: capacity \: factor

$  <strong>Skin Friction Resistance</strong>   <div class="wp-block-columns has-border-color has-palette-color-4-color has-palette-color-6-background-color has-text-color has-background has-link-color" style="border-color:#4adede;border-width:2px;border-radius:20px;margin-top:0;margin-bottom:0;padding-top:17px;padding-right:20px;padding-bottom:17px;padding-left:20px"> <div class="wp-block-column"> <span class="ql-right-eqno"> </span><span class="ql-left-eqno"> </span><img src="https://civilengghub.com/wp-content/ql-cache/quicklatex.com-3e39aa46a8e87248a243460454fc6631_l3.png" height="19" width="131" class="ql-img-displayed-equation quicklatex-auto-format" alt="\[Q_{sk}=\mu p A_{p.diag}k\]" title="Rendered by QuickLaTeX.com"/> </div> </div>   where:$

\mu = coefficient \: of \: friction \: between \: pile \: on \: sandP=perimeter \: of \: the \: pile \: section A_{p.diag}= area of pressure diagramk=coefficient \: of \: lateral \: pressure \: between \: pile \: and \: sand

\alpha

$method is widely used for cohesive soils in undrained conditions:   <mark style="background-color:rgba(0, 0, 0, 0);color:#cf2e2e" class="has-inline-color"><strong>CLAP</strong></mark>   <div class="wp-block-columns has-border-color has-palette-color-4-color has-palette-color-6-background-color has-text-color has-background has-link-color" style="border-color:#4adede;border-width:2px;border-radius:20px;margin-top:0;margin-bottom:0;padding-top:17px;padding-right:20px;padding-bottom:17px;padding-left:20px"> <div class="wp-block-column"> <span class="ql-right-eqno"> </span><span class="ql-left-eqno"> </span><img src="https://civilengghub.com/wp-content/ql-cache/quicklatex.com-9efca4ab23ad4fbbe02ab6af2c1a2078_l3.png" height="25" width="131" class="ql-img-displayed-equation quicklatex-auto-format" alt="\[Q_{sk} = \sum (cL\alpha p) \]" title="Rendered by QuickLaTeX.com"/> </div> </div>   where:$

c=cohesionL=length \: of \: pile\alpha = adhesion \: factor \:p=perimeter of the pile section

$    <h3 class="wp-block-heading has-medium-font-size" id="beta-method">Beta Method</h3>   <mark style="background-color:rgba(0, 0, 0, 0);color:#cf2e2e" class="has-inline-color"><strong>BLOP</strong></mark>   <div class="wp-block-columns has-border-color has-palette-color-4-color has-palette-color-6-background-color has-text-color has-background has-link-color" style="border-color:#4adede;border-width:2px;border-radius:20px;margin-top:0;margin-bottom:0;padding-top:17px;padding-right:20px;padding-bottom:17px;padding-left:20px"> <div class="wp-block-column"> <span class="ql-right-eqno"> </span><span class="ql-left-eqno"> </span><img src="https://civilengghub.com/wp-content/ql-cache/quicklatex.com-48b457ed0070e73e65e37086fe35f0fa_l3.png" height="25" width="146" class="ql-img-displayed-equation quicklatex-auto-format" alt="\[Q_{sk} = \sum (\beta L \sigma '_m p) \]" title="Rendered by QuickLaTeX.com"/> </div> </div>   where:$

\beta= skin \: factorL= length \: of \: pile p = perimeter \: of \: the \: pile \: section $   $

\beta=(1-sin\theta)tan \theta\beta=(1-sin\theta)tan\theta\sqrt{OCR}

$  <h2 class="wp-block-heading has-medium-font-size" id="lambda">Lambda Method</h2>   <div class="wp-block-columns has-border-color has-palette-color-4-color has-palette-color-6-background-color has-text-color has-background has-link-color" style="border-color:#4adede;border-width:2px;border-radius:20px;margin-top:0;margin-bottom:0;padding-top:17px;padding-right:20px;padding-bottom:17px;padding-left:20px"> <div class="wp-block-column"> <span class="ql-right-eqno"> </span><span class="ql-left-eqno"> </span><img src="https://civilengghub.com/wp-content/ql-cache/quicklatex.com-20689e1a35904b5b621a07a723d38bf8_l3.png" height="25" width="190" class="ql-img-displayed-equation quicklatex-auto-format" alt="\[Q_sk = \sum \lambda L (\sigma_m' +2c)p \]" title="Rendered by QuickLaTeX.com"/> </div> </div>   where:$

\lambda = effective \: frictional \: factorL = length \: of \: pile \sigma’_m = average \: vertical effective pressure at mid height p = perimeter of the pile sectionc = cohesion

$    <hr class="wp-block-separator has-alpha-channel-opacity is-style-wide"/>   <h2 class="wp-block-heading has-large-font-size" id="pile-1"><mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-palette-color-2-color">Pile Act as a Block</mark></h2>   When multiple piles are installed close together, they don't simply act as independent load-bearing elements. Instead, the soil zone around and beneath the pile group becomes stressed as a single unit.   <div class="wp-block-columns has-border-color has-palette-color-4-color has-palette-color-6-background-color has-text-color has-background has-link-color" style="border-color:#4adede;border-width:2px;border-radius:20px;margin-top:0;margin-bottom:0;padding-top:17px;padding-right:20px;padding-bottom:17px;padding-left:20px"> <div class="wp-block-column"> <span class="ql-right-eqno"> </span><span class="ql-left-eqno"> </span><img src="https://civilengghub.com/wp-content/ql-cache/quicklatex.com-e0ac2ed0b959f04d4209c7ae771e9ba8_l3.png" height="18" width="123" class="ql-img-displayed-equation quicklatex-auto-format" alt="\[Q_u=Q_{eb}+Q_{sf}\]" title="Rendered by QuickLaTeX.com"/> </div> </div>     <figure class="wp-block-image aligncenter size-full is-resized"><img src="https://civilengghub.com/wp-content/uploads/2025/10/1000015397.jpg" alt="" class="wp-image-5796" style="width:219px;height:auto"/></figure>   <h3 class="wp-block-heading has-medium-font-size" id="point">End Bearing Capacity</h3>   <div class="wp-block-columns has-border-color has-palette-color-4-color has-palette-color-6-background-color has-text-color has-background has-link-color" style="border-color:#4adede;border-width:2px;border-radius:20px;margin-top:0;margin-bottom:0;padding-top:17px;padding-right:20px;padding-bottom:17px;padding-left:20px"> <div class="wp-block-column"> <span class="ql-right-eqno"> </span><span class="ql-left-eqno"> </span><img src="https://civilengghub.com/wp-content/ql-cache/quicklatex.com-ee8330229a8113c9b75e857a6fd8aefb_l3.png" height="19" width="161" class="ql-img-displayed-equation quicklatex-auto-format" alt="\[Q_{eb}=CN_c(L_g \times B_g)\]" title="Rendered by QuickLaTeX.com"/> </div> </div>     <h3 class="wp-block-heading has-medium-font-size" id="skin">Skin Friction</h3>   <div class="wp-block-columns has-border-color has-palette-color-4-color has-palette-color-6-background-color has-text-color has-background has-link-color" style="border-color:#4adede;border-width:2px;border-radius:20px;margin-top:0;margin-bottom:0;padding-top:17px;padding-right:20px;padding-bottom:17px;padding-left:20px"> <div class="wp-block-column"> <span class="ql-right-eqno"> </span><span class="ql-left-eqno"> </span><img src="https://civilengghub.com/wp-content/ql-cache/quicklatex.com-34bf5cb8cea591d0bfc4fad2b015cf73_l3.png" height="20" width="175" class="ql-img-displayed-equation quicklatex-auto-format" alt="\[Q_{sf}=2 \alpha CL(L_g+B_g)\]" title="Rendered by QuickLaTeX.com"/> </div> </div>     <h2 class="wp-block-heading has-large-font-size" id="group">Group Efficiency</h2>   <strong>Converse-Labarre Equation</strong>   <div class="wp-block-columns has-border-color has-palette-color-4-color has-palette-color-6-background-color has-text-color has-background has-link-color" style="border-color:#4adede;border-width:2px;border-radius:20px;margin-top:0;margin-bottom:0;padding-top:17px;padding-right:20px;padding-bottom:17px;padding-left:20px"> <div class="wp-block-column"> <span class="ql-right-eqno"> </span><span class="ql-left-eqno"> </span><img src="https://civilengghub.com/wp-content/ql-cache/quicklatex.com-d5fd706e8f6ba4fc87e4712c98f03652_l3.png" height="38" width="259" class="ql-img-displayed-equation quicklatex-auto-format" alt="\[E_g=1-\frac{\theta[(m-1)n+(n-1)m]}{90mn}\]" title="Rendered by QuickLaTeX.com"/> </div> </div>     <strong>Bowles Equation</strong>   <div class="wp-block-columns has-border-color has-palette-color-4-color has-palette-color-6-background-color has-text-color has-background has-link-color" style="border-color:#4adede;border-width:2px;border-radius:20px;margin-top:0;margin-bottom:0;padding-top:17px;padding-right:20px;padding-bottom:17px;padding-left:20px"> <div class="wp-block-column"> <span class="ql-right-eqno"> </span><span class="ql-left-eqno"> </span><img src="https://civilengghub.com/wp-content/ql-cache/quicklatex.com-957cb3b8876d1adea102ba3abed8fc88_l3.png" height="38" width="206" class="ql-img-displayed-equation quicklatex-auto-format" alt="\[E_g=\frac{2(m+n-2)S+4D}{\pi Dmn}\]" title="Rendered by QuickLaTeX.com"/> </div> </div>     where:  $

E_g=efficiencym= no. \: of \: columnsn = no. \: of \: rowsD = diameter of the pileS=spacing of piles$

References:

Das, B.M. (2007). Principles of Foundation Engineering (7th Edition). Global Engineering

Rajapakse, R. (2016). Pile Design and Construction Rule of Thumb (2nd Edition). Elsevier Inc.

Tomlinson, M.J. (2004). Pile Design and Construction Practice (4th Edition). E & FN Spon.

CH 15: BRACED CUTS