Design of Reinforced Concrete Bored-Piles to Eurocode

Introduction

The last post on piling described the need for piled foundations, the types of piled foundation, design responsibilities and the methods of testing piles Piled foundations are one of the first aspects of scheme design a structural designer must consider during the course of project development. It is at the stage the structural designer is required to make recommendations based on the limited knowledge they have on the subject.

This post describes how to design concrete piles according to the BS-EN7 (Geotechnical design of Structures). It describes how to interpret the soil conditions from the result of a site investigation and then design piles to match.

This post concern the design of a single pile to Eurocode. The design of pile groups is beyond the scope of this post as their design is rather tedious process mostly requiring the use of spreadsheets or softwares to obtain the load distribution and settlement of each pile.

Design Principles

The design of piles is hinged on two solid principles. The friction between the soil and the pile and the end-bearing resistance offered by the soil against the tip of the pile. This two principle forms the cornerstone of pile design. In some instances, only one of the two interactions can be relied on based on the result of the soil report into which the pile will be installed. Hence the resistance of a pile is defined by its skin friction resistance and/or end-bearing resistance.

Assessing Actions

Before a pile can be designed, the actions the pile is to support must be determined. Eurocode 7, Part 1 (BS EN 1997-1:2004+A1:2013) has a very specific requirement for how pile loads are communicated, as there are many partial factors that need to be applied to each action. See Table in BSEN- 1997- (Geotechnical Design general rules).

Readers familiar with the design of piles to the now superseded codes of practice will see how much more complex the pile schedule table is for BS EN 1997-1. This is because piles are subject to ultimate limit state design and each action they are subjected to has a corresponding partial factor applied to it.

Design Approach & Combinations

An added level of complexity arises from the action combinations that need to be considered in pile design. The three-letter terms are defined in BS EN 1991 (Eurocode 1) and refer to the unique load combinations structural elements are typically subjected to (Table 1). Each combination is constructed from a series of actions that have the appropriate partial factor applied to them. With respect to pile design, the STR/GEO combinations are of primary concern and will be described in detail here.

TABLE 1: LOAD COMBINATIONS AS DEFINED IN BS EN 1991

‘A1’ and ‘A2’, ‘M1’ and ‘M2’, and ‘R1’ and ‘R4’ are terms drawn from BS EN 1997-1 that refer to sets of partial factors that need to be applied to actions, material properties of the soil and those that are applicable to resistance of the piles to applied actions.

A1 partial factors:

γG,j = 1.35 for unfavourable permanent actions and 1.0 for favourable permanent actions γQ,j = 1.5 for unfavourable variable actions and 0 for favourable variable actions.

A2 partial factors:

γG,j = 1.0 for unfavourable permanent actions and 1.0 for favourable permanent actions γQ,j = 1.3 for unfavourable variable actions and 0 for favourable variable actions.

Partial factors for key material properties of the soil into which the piles are installed are labelled as ‘M1’ and ‘M2’ (Table 2).

TABLE 2: PARTIAL FACTORS FOR MATERIAL PROPERTIES OF SOIL

Partial resistance factors are applied to the pile itself and take into account its composition and installation. For Set ‘R1’ all the relevant factors have a value of 1.0 for bored piles. For Set R4 they are as stated in Table 3.

TABLE 3: PARTIAL RESISTANCE FACTORS FOR PILE INTERACTIONS WITH SOIL

Finally, when calculating the capacity of a pile, a model factor (γR;d) is used to bring the characteristic capacities in keeping with existing UK experience in terms of reliability and settlement. Where piles are being designed based solely on soil data, he model factor is equal to 1.4. Where a representative maintained pile load test is performed on site (taken to the calculated unfactored resistance of the pile), this can be reduced to 1.2.

Detailed Design of Piles

As with the bearing capacity check for spread foundations the following expression must be satisfied for a single pile or group of pile

{ F }_{ d }\le { R }_{ d }

Where:

F_d is the applied action on the pile or group of piles R_dis the design resistance of the pile or group of piles.

The following section describes how the value of R_dis derived using the factors described in the previous section concerning partial factors.

For axially loaded piles, which this note is primarily concerned with, the variables F_d and R_d can be replaced with F_c;d and R_c;dand F_t;dand R_t;d for compression and tension piles respectively.

When considering compression piles, both end bearing and skin friction can be taken into account, provided the end bearing material has sufficient integrity to be able to resist a force at the end of the pile. These resistances are typically considered separately:

Skin friction for compression resistance pile is defined as:

{ R }_{ s;d }=\frac { { R }_{ b;k } }{ { \gamma }_{ s } }

End bearing resistance is defined as :

{ R }_{ b;d }=\frac { { R }_{ b;k } }{ { \gamma }_{ b } }

Where:

R_s:k_isis the characteristic skin friction resistance of the pile
R_b:kis the characteristic end bearing resistance of the pile.

Therefore, the value of R_t:d can be calculated as follows:

{ R }_{ t;d }=\frac { { R }_{ t;k } }{ { \gamma }_{ s;t } }

The principal method of designing piles to the Eurocode is based on the characteristic soil parameters, as derived from on-site investigations. This method requires data on key variables of the soil’s properties, to which material factors are then applied. These are designated as M1 and M2 and vary depending on what action combination set is being considered.

When using this method, piles under compression are designed based on Equation 1 (skin friction) and Equation 2 (end bearing):

{ R }_{ s;k }=\int { \frac { { q }_{ s;k }{ P }_{ s }dL }{ { \gamma }_{ R;d } } } ———(1)

Where:

q_s;kis the shaft resistance based on the characteristic soil properties
P_s is the perimeter length of the pile L is the shaft length of the pile
dL is the equation integrated along the length of the pile

γ_R;dis the model factor.

{ R }_{ b;d }=\frac { { A }_{ b }{ q }_{ b;k } }{ { \gamma }_{ R;d } } ———(2)

Where:

A_bis the cross-sectional area at the base of the pile

q_b;kis the base resistance of the pile based on the characteristic soil properties.

By combining Eqs. 1 and 2 and applying the relevant partial factors, it is possible to calculate the compressive resistance capacity of the pile (Equation 3).

{ R }_{ c;d }=\frac { { R }_{ s;d }+{ R }_{ b;d } }{ { \gamma }_{ R;d } } \quad \quad \quad———(3)

For tension piles equation 4 & 5 apply

{ R }_{ t;k }=\int { \frac { { q }_{ t;k }{ P }_{ s }dL }{ { \gamma }_{ R;d } } } ———(4)

Where:

q_t;kis the shaft tension resistance based on the characteristic soil properties
P_s is the perimeter length of the pile L is the shaft length of pile

dL is the equation integrated along the length of the pile
γ_R;dis the model factor.

{ R }_{ t;d }=\frac { { R }_{ t;k } }{ { \gamma }_{ s;t } }———(5)

When considering piles within different materials, the equations given in Table 5 cross-reference soil type against the pile capacity in terms of its skin friction and end bearing. The model factor is then applied to convert these calculated values into characteristic values through Equations 6 and 7:

TABLE 4: PILE RESISTANCE CAPACITY EQUATIONS BASED ON SOIL INVESTIGATION SURVEY DATA

{ R }_{ s;k }=\frac { { R }_{ s;cal } }{ { \gamma }_{ R;d } } ———–(6)

{ R }_{ b;k }=\frac { { R }_{ b;cal } }{ { \gamma }_{ R;d } } ———–(7)

Where:

R_s:calis the calculated skin friction resistance based on Table 5
R_b:calis the calculated end bearing resistance based on Table 5

γ_R;dis the model factor of 1.4 or 1.2 as described previously

As a point of caution when considering pile foundations within higly variable strata or if there are risk of deterioration resulting in localized collapse, then specialist advice should be sort. The effect of high water table on the soil properties must also be considered as it may have an adverse effect.

Serviceability

Piles, like other structural elements, must comply with movement criteria that are established by the design of the structure the piles are ultimately supporting. Typically, piles settle soon after their installation as they are exposed to significant permanent actions. The settlement of an isolated pile when it is subjected to all the characteristic working actions is typically between 0.5% and 1% of the diameter of the pile, or 10mm, whichever is the lesser.

Piles that are entirely reliant on the end bearing to support the actions being applied to them are much more prone to settlement than their skin-friction resistance-based counterparts. They can settle between 10% and 15% of the pile diameter and this should therefore be allowed for in substructure design with respect to vertical displacement.

Reinforced concrete piles that are cast in situ have to comply with certain criteria to determine whether they are of sufficient size and depth for the actions they are required to resist.

The reinforcement within bored piles must comply with minimum areas, which are based on the cross-section of the pile. The minimum amount of longitudinal reinforcement within a bored pile is defined within Table 3 of BS EN 1536:2010+A1:2015 (reproduced here as Table 5). The configuration of bars can be as a minimum of four longitudinal bars that are 12mm in diameter.

TABLE 5: MINIMUM LONGITUDINAL REINFORCEMENT

Worked Example

A building in the F.C.T Nigeria is to have 500mm diameter double-pile, from grade C50/55 concrete to support a compressive action consisting of 2150 permanent actions and 1750 Variable actions. The soil profile is as shown in figure 1. Check that the proposed size of the pile, assuming 26m depth required to support these actions, is adequate using BS EN 1997-1:2004+A1:2013.

N:B No pile tests have been carried out prior to design, but a soil investigation has been carried out and shear strength of each strata of soil type has been determined

N:B This example is worked to the U.K national annexe of BS-EN7 as Nigeria currently has no code of practice for geotechnical design and adopts the U.K code of practice. The U.K National annexe considers combination 2 more onerous and therefore the pile will be considered for only combination 2 here.

Actions

{ \gamma }_{ g }=1.00\quad ;\quad { \gamma }_{ q }=1.3\\ \\ Permanent\quad actions\quad =1.0\times 2150=2150kN\\ \\ Variable\quad actions\quad =1.3\times 1750=2275kN\\ \\ Ultimate\quad Load\quad =2150+2275=\quad 4425kN\\ \\

Material Properties

M1\quad Values\\ Clay:\quad { C }_{ u;k }=185\times 1.0=185{ kN/m }^{ 2 }\\ Sandy-Gravel:\quad { N }_{ q }=27\times 1.0=27{ kN/m }^{ 2 }\\ \quad \qquad \qquad \qquad \qquad { \phi }=40\times 1.0=40^{ \circ }\\ \\

The value of Nq is taken from ( IstructE manual for geotechnical design to Eurocode 7 /http://structurescentre.xyz/screenshot-130/

Skin Friction Resistance

Clay\quad =\quad (\pi dL)\alpha { C }_{ u;k }\\ \quad \quad { R }_{ s;k2 }\quad =\quad \pi \times 0.5\times 16\times 0.5\times 185\\ \qquad \quad \quad =\quad 2324.77kN\\ Sandey-Gravel\quad =\quad (\pi dL){ k }_{ s }{ \sigma }_{ v }’tan\left( { \phi }_{ c;k } \right) \\ \qquad { \sigma }_{ v }’\quad =\quad effective\quad stress\quad at\quad middle\quad of\quad stratum(2m)\\ \quad { \sigma }_{ v }\quad =\quad { (\gamma }_{ clay }-{ \gamma }_{ water }){ z }_{ 1 }+({ \gamma }_{ sand-gravel }-{ \gamma }_{ water })\frac { { z }_{ 2 } }{ 2 } \\ \qquad =\quad (20-9.81)16+(20-9.81)\frac { 6 }{ 2 } =193.61kN/{ m }^{ 2 }\\ { R }_{ s;k1 }\quad =\quad (\pi \times 0.5\times 6)\times 0.7\times 193.61tan40\\ \quad \quad \quad \quad =1071.7kN\\ Skin\quad friction\quad resistance\quad { R }_{ s;d }\quad =\frac { { R }_{ s;k1 }+{ R }_{ s;k2 } }{ { \gamma }_{ s } } =\frac { 2324.77+1071.7 }{ 1.6 } \\ =\quad 2122.8kN\\ \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad

N:B the weight of the fill as been ignored and the effective stress taken at the middle of the sandy gravel stratum.

End Bearing

{ R }_{ b;k }=\frac { \pi }{ 4 } ({ N }_{ q }{ \sigma ‘ }_{ v })\\ { N }_{ q }=27;\quad { z }_{ 1 }=3m;\quad { z }_{ 2 }={ 1m }\quad { z }_{ 3 }=16m;\quad { z }_{ 4 }=6m\\ { \sigma ‘ }_{ v }=\quad effective\quad stress\quad @\quad tip\quad of\quad pile\\ { \sigma }’_{ v\quad }=({ \gamma }_{ fill }{ z }_{ 1 })+({ \gamma }_{ fill }-{ \gamma }_{ water }){ z_{ 2 } }+\\ \qquad ({ \gamma }_{ clay }-{ \gamma }_{ water }){ z }_{ 3 }+({ \gamma }_{ sandygravel }-{ \gamma }_{ water }){ z }_{ 4 }\\ \qquad =\{ (18\times 3)+(18-9.81)1+(20-9.81)16+(20-9.81)6\} \\ \quad \quad \quad =\quad 286.3kN/m^{ 2 }\quad \\ { R }_{ b;k }=\frac { \pi \times 0.5 }{ 4 } (27\times 286.3)\quad =\quad 3036.5kN\\ { R }_{ b;d\quad =\quad }\frac { { R }_{ b;k } }{ { \gamma }_{ b } } \quad =\quad \frac { 3036.5 }{ 2 } =1518.25kN

Pile Capacity

{ R }_{ c;d }=\frac { { R }_{ s;d }+{ R }_{ b;d } }{ { \gamma }_{ R;d } } \quad =\frac { 2122.8+1518.25 }{ 1.4 } \\ \quad \quad \quad \quad \quad \quad =\quad 2600.75kN/pile\\ for\quad double\quad pile\quad =\quad 2600.75\times 2\\ \qquad \qquad \qquad \qquad \quad \quad =\quad 5201kN\\ unity\quad check\quad =\quad \frac { 4425 }{ 5201 } =0.85\\ \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad

Verify Capacity of Concrete to Pile

There’s a requirement for the compressive capacity of the pile to be limited to 25% of the characteristics compressive strength of the concrete at 28 days

25% of the compressive strength off the piles are:

\\ (50\times \frac { \pi \times { 500 }^{ 2 } }{ 4 } \times 0.25\times 2)\times { 10 }^{ -3 }=\quad 4908.74kN\\ 4425kN<4908.74kN\quad (ok)\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad

The structural design of the piles is the same as for an axially-loaded stocky column. For most piles minimum area of reinforcement according to Table 5 governs.