S-FOUNDATION Verification Example - Reinforced Concrete Pile Design

The reinforced concrete pile design example shown here is a slightly modified version of Example 9.7.9 from the Cement Association of Canada’s Concrete Design Handbook – Third Edition*.  This document is divided into three sections:

1. We first review and perform the hand calculations required to design the pile.
2. Next, we show how S-FOUNDATION generated the design results.
3. Both results, hand calculations and S-FOUNDATION design results, are summarized.

In this example, we use a cast-in-place reinforced concrete pile, 12m in length.

The material properties are:

• Concrete
• Steel
• Rock end bearing:
• Side friction,

 

The factored loads calculated at the top of the pile are:

• 
•  shear

 

The construction tolerance is 75mm, meaning that the compressive load can lead to a negative or positive moment due to an eccentricity of 735kNm.

For this example, the lateral behavior of the soil is modeled by assuming all lateral springs representing the soil are linear.  However, less attention is paid to modeling the pile’s vertical behavior.  Therefore, the pile support on the rock at the bottom is assumed to be vertically fixed.  Also, the friction springs stiffness is assumed to be zero.

• Linear spring constant in upper 10m:
• Linear spring constant in lower 2m:

 

We assume a spring support spacing of 1.0m c/c.  The spring constant is established as:

Where A = 1.0m (Spring Spacing) x Pile Diameter.

 

Let’s determine the pile diameter required.  We treat the pile as a circular column, and assume

• 35M bars
• 15M ties
•  

 

Using Table 7.1.2 à

Let’s now calculate our spring constants:

Bearing capacity check:

Pile Area: A = 0.785

Pile Perimeter: C = 3.14m

Bearing capacity check (compression):

By performing a structural analysis in S-FOUNDATION, or any other structural analysis software, (which is less time-consuming than doing by hand) we determine the cross-sectional forces in a pile.  The following are screenshots from the program showing shear force and moment diagrams for positive and negative eccentric moments + shear load and axial compression:

Figure 1: Shear and Bending Force diagram for Pile with Factored Loads + Negative Eccentric Moment

 

Figure 2: Shear and Bending Force diagram for Pile with Factored Loads + Positive Eccentric Moment

 

As we can see, the maximum moment demand for these two cases is 1411kNm, and the maximum shear demand is 574kN.

 

From Table 7.7.4, with γ=0.90 à

Use 8-35M bars à

Determine Max Stirrup Spacing using 15M ties

Clause 7.6.5.2 – tie spacing is the smallest of:

Use 15M ties @560mm

Clause 11.3.6.3

Clause 11.3.4

Clause 11.3.5.1

Now let’s determine if the minimum shear reinforcement requirements are met:

Clause 11.2.8.2

Try tie spacing of 450mm

Updated shear resistance, with new tie spacing:

 

 

S-FOUNDATION Design Results

To recreate this model in S-FOUNDATION, begin by defining the piles.  In the DefineàPiles dialogue, you can set the reinforcement (35M vertical bars x 8) and 15M bar ties @450mm spacing.  The diameter is 1000mm, and the length of the pile is 12m.

 

For this example, we analyze the pile on its own.  S-FOUNDATION requires all foundations to have pads.  To ignore the pad’s contribution to the pile’s behavior, set the pad depth to a very small value, and remove all pad reinforcement.  This is done in the DefineàPads/Pile Caps Dialogue.

 

We can now define a pedestal on this foundation that provides us with an insertion point for our factored loads.  Make this change under the DefineàPedestal’s dialogue.  The pedestal adds a joint at the foundation top which is used to apply our loads.  The pedestal is given a diameter equivalent to the pile diameter with a height of zero millimeters.

 

 

These settings ensure that the pedestal does not contribute structurally behavior of our pile, but does allow us to apply joint loads to the top of the pile.

Let’s now consider our soil properties, which effectively represent the springs discussed earlier in this example.  We use a ‘multi-layer’ soil using linear spring types and a termination depth of 13m.  Specifying the number of soil layers, which we have set to 13, we can define a new soil every 1m which allows us to specify unique soil spring stiffness at each layer (if desired).  Since we are explicitly defining the stiffness of the linear springs, we do not focus on the individual soil definitions in each layer.

 

To specify our lateral spring stiffness, click the ‘Lateral’ tab in the Define Soil Profiles dialogue, enter the Stiffness in the field indicated on the right side of the window.

 

Under the ‘Friction’ tab, enter zero for the friction springs from depth 0m to 12m, as we are ignoring the friction spring stiffness.

 

 

Having defined the pile, pad, pedestal, and soil profile, we can specify a few more parameters used for controlling the code checks and pile spring spacing.  This is done in the ‘Design Input’ window’s ‘Settings’ tab.

 

Since we ignore the checks on the pad and pedestal, we set the cover to 0mm, and uncheck the Pad and Pedestal Code Checks, thus ensuring they are not performed after the analysis.  We will use a pile rebar cover of 75mm.  Finally, we must also specify our pile element size to dictate the spacing of our pile springs.  We use a spacing of 1000mm.

Now start drawing our foundation.  Click on the ‘Isolated Footing’ tool. In the Tool window, ensure the ‘Pile Foundation’ box is toggled, and choose your newly defined Soil Profile, Pad, and Pedestal (you can also specify these parameters in the tool window if you prefer).  When you toggle on the ‘Pile Foundation’ check mark, you have access to the ‘Pile Cap’ container, where you can specify the number of piles (set this to ‘1’).  Once done, left-click your mouse in the modeling space to place your foundation.

 

Once the foundation is placed, we can define our applied loads.   Start by defining two new load cases (DefineàLoad Cases).  We have one load case for the factored compressive load (-9800kN), and shear (700kN) with positive moment (735kNm), and another with negative moment (-735kNm). 

 

The last thing we explore is the Pile Cap ground connectivity.  In the DefineàPads/Pile Caps dialogue, use the ‘Pile Cap’ tab to configure how the top of the pile connects to the pile cap (if applicable) and how the bottom end of the pile connects to the ground.  We assume that the base of the pile is fixed in vertical translation.

 

Run the Analysis and Code Check in S-FOUNDATION.

As a reminder, we elected to run the analysis using the Rigid and Flexible approach.  You may receive warning messages stating that certain checks are only available during a Flexible Analysis, which is not an issue since we are running both a Rigid and Flexible analysis. 

In the Design Output window, drill down into the code check results.  Let’s start with the Shear and Torsion Pile Checks.  Left-click on the name of the code check in the Design Output window to see a list of the load cases in descending order based on the utilization ratio.  We can see that our pile has a utilization ratio of 0.70 with a demand of 574kN and a capacity of 815kN.  S-FOUNDATION will automatically show us the governing scenario for the code check of interest.  Notice the pile is divided into several even segments and code checked with the loads at each segment using the S-CONCRETE Design Engine.

 

 

It is worth mentioning that S-FOUNDATION’s results vary slightly from our hand calculations.  This is because the S-CONCRETE Design Engine uses a strain compatibility approach to determine the area of steel in tension, and depending on the loading scenarios, this can lead to a slightly different effective depth and effective shear depth than our hand calculations.  In the above example, S-FOUNDATION/S-CONCRETE determines dv = 760mm.

Let’s also check the Moment Results.  Expand the ‘Axial Force vs. Moment’ code check results to view the governing scenario.  The governing scenario occurs at 2m in depth along the pile.  We can see the demand is 1411kNm and the capacity is slightly higher at 1462kNm leading to a utilization ratio of 0.97. 

 

 

This result confirms that the 8-35M bars and 15M stirrups @ 450mm spacing are sufficient to resist the applied loads.

We can see the breakdown of results between the hand calculations and S-FOUNDATION below:

 

Result Summary and Comparison

	Hand Calculations	S-FOUNDATION
Effective depth, d	891.5mm	891.15mm
Effective shear depth, dv	802.4mm	760mm
Bending resistance, Mr	1500kNm *from table 7.7.4	1462kNm
Concrete Shear Resistance, Vc	514kN	487kN
Steel Shear Resistance, Vs	346kN	328kN

 

As shown in the above comparison, the results between the two platforms are close but not identical.  The primary reason for this discrepancy is that S-FOUNDATION uses a strain compatibility approach to determine the effective shear depth.  This approach leads to a slightly smaller effective shear depth when compared to the hand calculation method, which is simply a ratio of the effective depth. 

The difference in effective shear depth used leads to a slightly lower shear capacity in S-FOUNDATION and a more conservative design.  The magnitude of this discrepancy is related to the amount of steel in tension, and may not always be as pronounced for every section/loading scenario.

The bending resistance comparison is an approximation taken from the interaction diagram, table 7.7.4 in the Concrete Design Handbook, but the numbers are within an acceptable range.