Geotech Engineer’s guide to Structural design of helical piles

As geotechnical engineers, we spend most of our time analyzing soil behavior such as bearing capacity, shear strength, and settlement. We look at a helical pile and ask: Will the intact soil matrix hold the helices?

But for slender deep foundations, the soil is only half the battle. Often, the steel shaft itself is the weakest link. To fully design a helical pile, we must step into the structural engineering realm and treat the pile not just as a load-transfer mechanism, but as a slender column. Here is a breakdown of the critical structural checks every geotech should understand, that I learned during the process.

1. Yielding vs. Buckling

If you push down on a short, thick block of steel, it will eventually crush (Yielding). But helical piles are long, slender pipes. If you push down on them, they bow sideways and snap. This is called Buckling (specifically, Euler Buckling), and predicting it is the core of structural pile design.

2. The Slenderness Ratio (KL/r)

To determine if a pile will buckle, structural codes use the Slenderness Ratio:

$Slendernessratio = kL/r$

• L (Unbraced Length): The physical length of the pile not rigidly supported by the soil.
• K (Effective Length Factor): How the pile ends are restrained (e.g., K=1.0 for a pinned head, K=0.65 for a pile perfectly fixed in a rigid concrete cap).
• r (Radius of Gyration): A geometric property of the pipe section. A 6-inch pipe has a smaller r than an 8-inch pipe, making it more slender.

3. Finding the Unbraced Length (L) via the Davisson Method

A common (and dangerous) assumption is that a pile is fully braced the moment it enters the ground. In soft soils, the pile will actually bend below the surface before the soil provides enough passive resistance to lock it in place.

To find the true unbraced length, we must find the Depth to Apparent Fixity (L_f). Davisson and Robinson (1965) presented an equivalent cantilever model to estimate L_f by pitting the pile’s bending stiffness (E_pI_p) against the soil’s subgrade reaction.

They provided two distinct stiffness factors depending on how the soil behaves with depth:

Case A: Soils with a constant subgrade modulus (e.g., Stiff Cohesive Soils)

For soils where the stiffness does not change with depth, we compute the stiffness factor R:

$R=∜((E_p I_p)/k_1 )$

(Where k₁ is the modulus of subgrade reaction of cohesive soils).

For a fixed-base equivalent, the depth to fixity is:

$L_f=1.4R$

Case B: Soils with a subgrade modulus increasing linearly with depth (e.g., Granular Soils or Normally Consolidated Soft Clays)

For these soils, we compute the subgrade reaction factor T:

$T = \sqrt[5]{\frac{E_p I_p}{\eta_h}}$

(Where n_h is the modulus of subgrade reaction varying with depth).

For a fixed-base equivalent, the depth to fixity pushes deeper:

$L_f=1.8T$

If the pile head is flush with the ground, your unbraced length for buckling calculations is exactly $L = L_f$. Below this depth, the pile is considered fully confined.

4. Evaluating Axial Capacity and Stress Ratio (RAT_a)

Once the slenderness (KL/r) is known, structural codes (like AISC) apply a buckling curve to find the allowable design axial capacity ( $\phi P_n$). Long, skinny pipes have a massively reduced capacity compared to their pure yield strength.

To see how hard the steel is working under your applied vertical design load (P), we calculate the Axial Stress Ratio:

$RAT_a = \frac{P}{\phi P_n}$

If $RAT_a = 0.928$, your vertical load is consuming $92.8\%$ of the pipe’s maximum buckling capacity, leaving very little room for any lateral stresses.

5. Bending Moment Capacity and Stress Ratios (RAT_b)

When a pile is driven slightly out of plumb or subjected to lateral forces, it experiences bending moments in both the x and y axes (M_x and M_y). The pipe’s ability to resist this bending is its design moment capacity ($\phi M_nx$) and $\phi M_ny$).

We evaluate the bending stress ratios identically to the axial ratio:

$RAT_{bx} = \frac{M_x}{\phi M_{nx}}$

$RAT_{by} = \frac{M_y}{\phi M_{ny}}$

6. The Combined Stress Check (AISC Interaction Equation)

A steel pipe only has 100% capacity to give. We must combine the axial stress and the bending stresses to ensure the pile survives both forces simultaneously.

According to the AISC code, if the axial load is dominant; specifically, if the axial stress ratio is greater than or equal to 20% ($RAT_a \ge 0.2$)—Equation H1-1a applies. This equation takes the full brunt of the axial stress while slightly reducing the penalty of the bending stresses:

$RAT = RAT_a + \frac{8 RAT_{bx}}{9} + \frac{8 RAT_{by}}{9} \le 1.0$

The final combined stress ratio (RAT) must remain below 1.0. If it exceeds 1.0, the structural steel is projected to fail, regardless of how strong the surrounding soil is.