Annex B

Example Calculations for Pile Resistance Analysis and Verifications

Note: Some of the following examples were taken from [58]. Further examples can be found in [64].

# B1 Determining the Axial Pile Resistances from Static Pile Load Tests, and Ultimate and Serviceability Limit State Analyses

## B1.1 Objectives

Figure B1.1a shows a foundation situation with a pile of diameter D = 1,2 m and a permanent load FG,k= 1,5 MN, in addition to a variable load FQ,rep,k = 1,0 MN. Two static pile load tests were executed, the results of which are included in Figure B1.1b and Table B1.1 as Rm1 and Rm2. The ultimate settlement is defined as sg = sult = 0,1 · 120 cm = 12 cm using Eq. (5.1). Because the static pile load tests were only executed up to a settlement s = 10 cm, the ultimate settlement was extrapolated.

The analysis comprises the characteristic pile resistances in the ultimate limit state (ULS) for “flexible” and “stiff” piles after 5.2.2 and the characteristic boundary lines in the serviceability limit state (SLS) after 5.2.3, and the external capacity and serviceability for the specified pile load. An allowable

pile settlement allow. sk = 2,0 cm is specified by the structural design for the serviceability limit state (SLS).

The static pile load tests can be taken from [154].

## B1.2 Deriving the characteristic pile resistances in the ultimate and serviceability limit states

The characteristic, ultimate pile resistance Rc,k is given by the lesser of either the mean value (Rc,m)mean or the minimum value (Rc,m)min of the pile load test results using Equation (A4.1) as follows:

The correlation factors ξ1 and ξ2 depend on the number of static pile load tests performed and are selected after Annex A4. The correlation factors given there apply to “flexible” compression piles. If “stiff” compression piles are used, the correlation factors may be divided by 1,1, assuming that ξ1 does not become smaller than 1,0.

For the range of small pile settlements, after 6.4, Eq. (6.13), characteristic boundary lines were derived for the serviceability limit state analysis using the k values (based on [59]). For the present case k = 0,15 was adopted to relate to the average of the measured values.

Note: The method adopted here for the characteristic boundary lines in the service load range represents only one possible option. Other reasoned procedures are also possible.

Figure B1.2 and Table B1.1 show the results for the determination of Rc,k(SLS) and Rc,k = Rc,k (ULS).

Using the results from Table B1.1, the characteristic pile resistance Rc,k in the serviceability limit state (ULS) can be determined for “flexible” and “stiff” piles in Table B1.2.

## B1.3 Bearing capacity analysis

The limit state condition after 6.2 and 6.3:

Fc,d ≤ Rc,d

must be adhered to for ultimate limit state (ULS) analysis.

a) For single piles acting independently (“flexible” piles):
Fc,d = FG,k · γG + FQ,rep,k · γq = 1,500 · 1,35 + 1,000 · 1,50 = 3,525 MN
Rc,d = Rc,kt = 4,163/1,10 = 3,785 MN
Fc,d = 3,525 MN < Rc,d = 3,785 MN
b) For load distribution by means of a rigid capping slab (“stiff” pile):
Fc,d = 3,525 MN
Rc,d = Rc,k/γt = 4,565/1,10 = 4,150 MN
Fc,d = 3,525 MN < Rc,d = 4,150 MN

## B1.4 Serviceability analysis

When determining the pile resistances R(SLS) in the serviceability limit state, differentiation after 6.4 is required whether minor or major (adopted here) differential pile settlements are to be expected. To this end, the characteristic boundary curves in the service load range were derived from the recorded pile load test data in Table B1.1 and Figure B1.1b.

The specified allowable settlement (e.g. specified in the structural design) in the example is allow. sk = 2 cm.

Using Figure B1.3a, serviceability is demonstrated via pile forces after 6.3, Eq. (6.11) as:

Fd (SLS) = Fk = 2,500 MN < Rd (SLS) = Rk (SLS) = 2,7 MN.

Analysis by comparing settlements in accordance with Figure B3.3b after 6.3, Eq. (6.12) results to:

exist. sk,max = 1,8 cm < allow. sk = 2,0 cm

# B2 Characteristic Axial Pile Resistances from Dynamic Load Tests

## B2.1 Objective

Dynamic pile load tests were performed to determine the ultimate capacity of reinforced concrete displacement piles and then calibrated against a static load test from a different, but comparable site. Evaluation using the direct method (CASE equation) resulted in the following measured data for the compressive resistance of the ground against the pile in the ultimate limit state:

The respective characteristic ultimate limit state resistances for “flexible” and “stiff” compression piles shall be derived from the measured data of the dynamic pile load tests.

## B2.2 Characteristic pile resistances

The characteristic pile resistance in the ultimate limit state (ULS) Rc,k is given by the lesser of the mean value (Rc,m)mean or the minimum value (Rc,m)min of the pile load test results using Equation (A4.3) as follows:

The correlation factors ξ5 and ξ6 to be adopted are given in Annex A4.2 and are derived from the base values of the correlation factors ξ0.5 and ξ0 6, the increased value Δξ and the model factor ηD. The correlation factors ξ5 and ξ6 may be divided by 1.1 for “stiff” compression piles.

The correlation factors ξ5 and ξ6 are provided in Table B2.1 and the determination of the characteristic compression pile resistances Rc,k in Table B2.2.

# B3 Determining the Characteristic Axial Pile Resistances from Empirical Data for a Bored Pile

## B3.1 Objective

Figure B3.1 (example taken from DIN 4014:1990-03) summarises the information on soil type, ground strength and pile geometry necessary for the determination of the axial pile resistance Rc,k(s) based on empirical data.

The characteristic resistance-settlement curve shall be determined using the table data after 5.4.6 (Tables 5.12 to 5.15).

## B3.2 Analysis for lower and upper table values

Note: Reference is made to the application principles and limitations in 5.4.3, in particular with regard to the upper table values. In the example presented here both the lower and the upper table values are used as examples (not as a rule).

### B3.2.1 Determining the pile shaft resistance Rs,k

The ultimate limit state skin friction values for the sand and the clay are given in Tables 5.13 and 5.15 in 5.4.6.2. By adopting the associated pile skin areas, the ultimate limit state pile shaft resistances Rs,k,i are provided in Table B3.1.

The settlement ssg, in cm, is calculated as follows, adopting the ultimate limit state pile shaft resistance Rs,k in MN:

sSg = 0,50 · Rs,k + 0,50.

Using the figures from the example the pile head settlement is:

ssg = 0,50 · 1,243 + 0,50 = 1,1 cm for the lower table values and

ssg = 0,50 · 1,726 + 0,50 = 1,4 cm for the upper table values.

### B3.2.2 Determining the pile base resistance Rbk

A mean soil strength is adopted in a region from 1 · D (0,9 m) above and 3 · D (3 · D = 2,70 m) below the pile base to determine Rb,k. For this zone a mean cone resistance qc,m = 17,5 MN/m2 is shown in the penetration test diagram in Figure B3.1.

The pile base capacity can be calculated by adopting the figures from Table 5.12 in 5.4.6.2 and taking the previously determined value of qc,m into consideration. Table B3.2 reproduces the calculated figures.

### B3.2.3 Characteristic resistance-settlement curve

The pile resistances calculated from the pile base and pile shaft resistances are listed in Tables B3.3 and B3.4 as a function of the pile head settlement and are given for the lower and upper values. The settlement of the pile head for each value of the pile resistance Rc,k is given by the characteristic resistance settlement curve in Figure B3.2.

# B4 Determining the Characteristic Axial Pile Resistances from Empirical Data for a Prefabricated Driven Pile

## B4.1 Objective

Figure B4.1 summarises the information on soil type, ground strength and pile geometry required to determine the axial pile resistance Rc,k(s) based on empirical data.

The characteristic resistance-settlement curve shall be determined using the table data after 5.4.4 (Tables 5.1 to 5.4).

## B4.2 Characteristic axial pile resistance from empirical data for lower and upper table values

Note: Reference is made to the application principles and limitations in 5.4.3, in particular with regard to the upper table values. In the example presented here both the lower and the upper table values are used as examples (not as a rule).

### B4.2.1 Determining the pile shaft resistance Rs,k

The empirical skin friction values in the zones of the load-bearing noncohesive soil and the weak cohesive soil are given by Tables 5.2 and 5.4 in Section 5.4.4. Together with the corresponding pile skin areas, taking the correlation factor for the skin area from Table 5.5 in Section 5.4.4 into consideration, the pile shaft resistance upon mobilisation of the ultimate limit state state Rs,k (ssg*) is given in Table B4.1 and the pile shaft resistance Rs,k (sg) at failure in Table B4.2.

Upon mobilisation of the failure state the settlement in cm for the skin friction ssg*, adopting Rs,k(ssg*) in MN, is determined using the following equation for the pile shaft resistance Rs,k(ssg*):

ssg* = 0,50 · Rs,k(ssg*).

Using the figures from the example the pile head settlement is:

 ssg* = 0,50 · 0,715 = 0,4 cm for the lower table values and ssg* = 0,50 · 1,002 = 0,5 cm for the upper table values.

### B4.2.2 Determining the pile base resistance Rb,k

For determination of Rb,k a mean soil strength is adopted from 4 · Deq below to 1 · Deq above the pile base..

The equivalent pile diameter of a square prefabricated driven pile is determined using:

Using the dimensions of the example the equivalent pile diameter is:

The nominal value of the square pile base area in this case is:

The penetration test diagram in Figure B4.1 displays a mean characteristic cone resistance along the respective length of:

Using the figures in Table 5.1 of these Recommendations and referring to the previously determined value of qc,m and the correlation factor for the pile base area in Table 5.5 (5.4.4), the pile base resistance can be calculated. Table B4.3 contains the determined numerical values.

### B4.2.3 Characteristic resistance-settlement curve

Tables B4.4 and B4.5 contain the pile resistances calculated for the lower and upper values from the pile base and shaft resistances as a function of the pile head settlement. The settlement of the pile head for each value of the pile resistance Rc,k is given by the characteristic resistance-settlement curve in Figure B4.2.

# B5 Determining the Characteristic Axial Pile Resistances from Empirical Data for a Fundex Pile

## B5.1 Objective

Figure B5.1 summarises the information on soil type, ground strength and pile geometry required for determination of the axial pile resistance Rc,k(s) based on empirical data.

The characteristic resistance-settlement curve using the table data after 5.4.8.2 (Tables 5.24 and 5.25) shall be determined.

## B5.2 Characteristic axial pile resistance from empirical lower and upper table values

Note: Reference is made to the application principles and limitations in 5.4.3, in particular with regard to the upper table values. In the example presented here both the lower and the upper table values are used as examples (not as a rule).

### B5.2.1 Determining the pile shaft resistance Rs,k

The ultimate limit state skin friction values in the load-bearing, non-cohesive soil are contained in Table 5.25 in 5.4.8.2. Adopting the associated pile skin areas, the ultimate pile shaft resistance Rs,k is provided in Table B5.1.

The settlement in cm for the skin friction ssg with Rs,k in MN is determined using the following equation for the pile shaft resistance Rs,k:

Using the figures from the example the pile head settlement is:

 ssg = 0,50 · 0,316 + 0,5 = 0,7 cm for the lower table values and ssg = 0,50 · 0,430 + 0,5 = 0,7 cm for the upper table values.

Note: Load-bearing strata with qc ≥ 7,5 MN/m2 are not considered if they are underlain by weak strata.

### B5.2.2 Determining the pile base resistance Rb,k

To determine Rb,k a mean soil strength qc.m = 17,5 MN/m2 is adopted from 4 · Deq below to 1 · Deq above the pile base.

The nominal value of the pile base area in this case is:

Adopting the figures from Table 5.24 in 5.4.8.2 and taking the previously determined value of qc,m into consideration, the pile base capacity can be calculated. Table B5.2 contains the determined figures.

### B5.2.3 Characteristic resistance-settlement curve

The pile resistances calculated from the pile base and pile shaft resistances are given in Tables B5.3 and B5.4 as a function of the pile head settlement for the lower and upper values. The settlement of the pile head for each value of the pile resistance Rc,k is derived from the characteristic resistance-settlement curve in Figure B5.2.

# B6 Principle of the Evaluation of a Static Pile Load Test Using a Prefabricated Driven Pile shown on an Example and Comparison with Empirical Data after 5.4.4.2

## B6.1 Objective

Figure B6.1 summarises the tested or measured value Rc,m from a static load test for the resistance-settlement curve of a prefabricated reinforced concrete driven pile. It also contains the information on soil type, ground strength and pile geometry required to determine the axial pile resistance Rc,k(s) based on empirical data after 5.4.4.2.

For the comparison with the results of the static load test, the characteristic resistance-settlement curve shall be determined using the empirical data after 5.4.4.2 (Tables 5.1 to 5.4). In addition, the design resistance in the ultimate limit state (ULS), based on both static load tests and on empirical data, is determined.

Note: Comparison of the axial pile performance derived from a static pile load test with the empirical data after 5.4 requires that the pile skin friction is adopted over the entire length of the pile. The calculation of the resistance-settlement curve after 5.4.4.2 deviates from the previous procedure for determining characteristic axial pile resistance (see example B4) inasmuch as non-load-bearing or weak strata with qc ≤ 7,5 MN/m2 or cu,k ≤ 60 kN/m2 (approximate extrapolation of table values) are taken into consideration.

## B6.2 Characteristic axial pile resistance from empirical lower and upper table values

Note: Reference is made to the application principles and limitations in 5.4.3, in particular with regard to the upper table values (not as a rule). In this example the upper table values are adopted to evaluate the static pile load tests.

### B6.2.1 Determining the pile shaft resistance Rs,k

The empirical skin friction values in the zone of the load-bearing non-cohesive and the weak cohesive soil are given by Tables 5.2 and 5.4 in Section 5.4.4.2 and, together with the corresponding pile skin areas, taking the correlation factor for the skin area from Table 5.5 into consideration, the pile shaft resistance upon mobilisation of the ultimate limit state Rs,k (ssg*) is given in Table B6.1 and the pile shaft resistance Rs,k(sg) at failure in Table B6.2.

Upon mobilisation of the failure state the settlement in cm for the skin friction ssg*, adopting Rs,k(ssg*) in MN, is determined using the following equation for the pile shaft resistance Rs,k(ssg*):

Using the figures from the example analysis the pile head settlement is:

### B6.2.2 Determining the pile base resistance Rb,k

For determination of Rb,k a mean soil strength is adopted in a region from 4 · Deq below to 1 · Deq above the pile base..

The equivalent pile diameter of a square prefabricated driven pile is determined using the following equation:

Using the dimensions of the example the equivalent pile diameter is:

The nominal value of the square pile base area in this case is:

The penetration test diagram in Figure B6.1 displays a mean characteristic cone resistance along the respective length of:

Using the figures given in Table 5.1 of 5.4.4.2 and taking the previously determined value of qc,m and the correlation factor for the pile type as given in Table 5.5 into consideration, the pile base resistance can be calculated. Table B6.3 contains the determined figures.

### B6.2.3 Characteristic resistance-settlement curve for empirical data compared to tested or measured values

The pile resistance calculated for the upper values from empirical data of the pile base and pile shaft resistance is given in Table B6.4 as a function of the pile head settlement. The settlement of the pile head for each value of the pile resistance Rc,k is derived from the characteristic resistance-settlement curve in Figure B6.2 as an upper empirical value Rc,k(s) and is listed for comparison with the tested or measured data from the load tests Rc,m(s).

## B6.3 Characteristic axial pile resistance from static load tests

The characteristic pile resistance Rc,k for the ultimate limit state (ULS) shall be derived from Rc,m using Equation (A4.1) and adopting the correlation factors ξ1 and ξ2 from Table A4.1.

Where only one pile load test is used, the correlation values are ξ1 = ξ2. If the structural system is sufficiently stiff, “stiff” compression piles can be adopted by dividing the correlation factors by 1,1, whereby ξ1 may never become smaller than 1. The determined correlation factors are:

 – ξ1 = ξ2 = 1,35 for flexible systems; – ξ1 = ξ2 = 1,23 for stiff systems.

The characteristic pile resistances Rc,k are given by the measured pile resistance in the ultimate limit state (ULS) Rc,m = 3,408 MN after Table B6.4 using:

 – Rc,k = 2,524 MN for flexible systems; – Rc,k = 2,771 MN for stiff systems.

## B6.4 Design values of pile resistances in the ultimate limit state

a) From empirical data

The design resistances in the ultimate limit state (ULS) based on empirical data Rc,d are determined by dividing the characteristic pile resistances Rc,k by the partial factor γt = 1,4 after the table in Annex A3.2.

The design values of the upper and lower table values are derived and summarised in Table B6.5. The lower table values are of comparative character only.

b) From the pile load test

To derive the design values of the pile resistances Rc,d in the ultimate limit state from the pile load test, the characteristic pile resistances Rc,k after B6.3

are divided by the partial factor γt= 1,1 from Table A3.2. The design values are given by:

 – Rc,d = 2,524 MN/1,1 = 2,295 MN for flexible systems; – Rc,d = 2,771 MN/1,1 = 2,519 MN for stiff systems.

The design values in the ultimate limit state (ULS) from empirical data and those from the static pile load test are compared in Figure B6.3.

# B7 Preliminary Design and Analysis of the Ultimate Limit State of Franki Piles Based on Empirical Data and Comparisontoa Pile Load Test Result

## B7.1 Objective

Figure B7.1 summarises the information on soil type, ground strength and pile geometry required to determine the axial pile resistance Rc,k(s) based on empirical data after 5.4.5.3.

The pile base volume necessary to accept a characteristic action Fk based on empirical data is required for the preliminary design of a Franki pile. In this example, initially the lower empirical values after 5.4.5.3 are adopted, whereby the pile base is designed for a characteristic permanent action FG,k = 1,20 MN and a characteristic variable action FQ,k = 0,40 MN.

Analysis of the ultimate limit state (ULS, GEO-2) must be performed for the necessary pile base volume determined in the preliminary design for the characteristic action, adopting the upper and lower empirical values, based on the actual driving energy expended during pile installation as shown in Figure B7.2.

To check the pile resistance based on empirical data after 5.4.5.3 the pile resistance in the ultimate limit state is compared to the static load test in Figure B7.2. To this end, the characteristic pile resistance must be determined using the upper table values and taking into consideration the non-load-bearing strata, and compared to the result of the static load test.

## B7.2 Determining the base volume from empirical data

### B7.2.1 Determining the pile shaft resistance Rs,k

The empirical skin friction values in the zone of the load-bearing boulder clay from a depth of 0,80 m above driving depth and, adopting the associated pile skin areas, the ultimate pile shaft resistance Rs,k after Table B7.1, are given in Table 5.11 in 5.4.5.3.

Note: The non-load-bearing strata and the strata overlying them were not taken into consideration for the preliminary design. The empirical ultimate skin friction for cohesive soils after Table 5.11 can be used for the boulder clay.

### B7.2.2 Determining the pile base volume of a Franki pile

The Franki pile is designed for a characteristic action Fk = FG,k + FQ,k. For Loading Case 1 this means that a characteristic axial pile resistance of:

must be verified. The necessary pile base resistance is given in Table B7.2.

A mean soil strength is adopted in the zone from 3 · Ds below to 2 · Ds above driving depth to determine Rb,k. A mean undrained shear strength cu,k = 0,140 MN/m2 is given for this zone by the penetration test diagram in Figure B7.1.

Adopting the undrained shear strength cu,k and the necessary characteristic pile base resistance Rb,k from Table B7.2 gives the pile base volume for the lower empirical values in Figure 5.10. The necessary base volume of the Franki pile for the lower empirical values is given in Table B7.2.

## B7.3 Analysis of the ultimate limit state (ULS, GEO-2) by means of the driving energy expended during pile installation

### B7.3.1 Characteristic pile resistance Rc,k after applying the lower empirical values

The ultimate pile shaft resistance after Table B7.1 is:

The driving energy for the final 2 m is given by the driving energy diagram in Figure B7.2 as:

The norm driving energy after 5.4.5.3, Table 5.9, for a Franki pile with Ds = 56,0 cm is:

and the norm driving energy ratio:

The pile base resistance Rb,k is given using the standard driving work ratio and the existing pile base volume after Table B7.2 from Figure 5.10:

The axial compression pile resistance in the ultimate limit state from empirical data is given by:

### B7.3.2 Characteristic pile resistance Rc,k after applying the upper empirical values

Note: Reference is made to the application principles and limitations in 5.4.3, in particular with regard to the upper empirical values (not as a rule).

The ultimate limit state pile shaft resistance using the upper values from Table 5.11 is given in Table B7.3.

Using the norm driving energy ratio:

and the existing pile base volume after Table B7.2, the pile base resistance Rb,k is given by Figure 5.11.

The axial compression pile resistance in the ultimate limit state from empirical data is:

### B7.3.3 Ultimate limit state analysis

The design value of the compressive pile resistance is given by:

and the design value of the action by:

Where γt = 1,40, γG = 1,35 and γQ = 1,50 for the DS-P design situation.

must be adhered to for analysis of the ultimate limit state. The utilisation factors are given in Table B7.4.

## B7.4 Comparison of the axial pile resistance based on empirical data with static load tests

### B7.4.1 Characteristic axial pile resistance from empirical data

The characteristic axial pile resistance based on empirical data from a static load test is examined.

Note: Comparison of the axial pile performance derived from a static pile load test with the empirical data after 5.4.5.3 requires that the pile skin friction is adopted over the entire length of the pile. The calculation of the pile resistance deviates from the previous procedure for determining characteristic axial pile resistance inasmuch as non-load-bearing or weak strata with qc ≤ 7,5 MN/m2 or cu,k ≤ 0,06 MN/m2 are taken into consideration. Reference is made also to the application principles and limitations in 5.4.3, in particular with regard to the upper table values (not as a rule). In this example the upper table values are adopted to evaluate the static pile load tests.

The empirical skin friction values in the zone of the load-bearing boulder clay from a depth of 0,80 m above driving depth are given in Tables 5.10 and 5.11 of these Recommendations and, adopting the associated pile skin areas, the ultimate pile shaft resistance Rs,k after Table B7.5.

Using the standard driving work ratio W = 0,71 after B7.3.2 and the pile base volume V = 1,05 m3 from Figure 5.11 the pile base resistance Rb,k is:

The axial pile resistance based on empirical data is:

### B7.4.2 Comparing to the static load test

Extrapolating the resistance-settlement curve from Figure B7.2 using the hyperbola method gives the axial pile resistance for an ultimate settlement sult = sg = 0,1 · Ds:

The deviation in the calculated pile resistance from the measured value is ΔR1 =-0,1%.

In this case the upper empirical data thus correspond well to the results of the static load test taken for reference.

# B8 Negative Skin Friction for a Displacement Pile as a Result of Fill

## B8.1 Objective

Table B8.1 Characteristic soil properties

 Stratum Soil properties Fill (sand) Soft stratum

The ultimate and serviceability limit states shall be analysed for a prefabricated, square, reinforced concrete pile with an edge length as = 0,35 m and a permanent action FG,k = 450 kN imposed by structural loads. The results of a static pile load test are available as shown in Figure B8.2 and Table B8.2. It is known from a settlement analysis that the soft stratum will settle by 5 cm below the assumed infinite fill. The settlements caused by the fill in the loadbearing ground can be ignored. In the serviceability limit state (SLS) a maximum pile head settlement allow. sk = 0,5 cm is permitted, which in this case is compared to a lower bound of the characteristic RSC in the serviceability limit state. The pile is also assumed to be rigid.

## B8.2 Determining the characteristic resistance-settlement curve

The characteristic pile resistance in the ultimate limit state (ULS) Rc,k is given by the measured value for Rc,m from the load test using Eq. (A4.1) as follows:

where the correlation factor is ξ1 = 1,35 after Annex A.4. The correlation factors given there refer to “flexible” compression piles and are applied for single pile behaviour, as is assumed here.

For the range of small pile settlements, after 6.4, Eq. (6.13) characteristic boundary lines with values of k = 0,15 (based on [59]), were derived to form the basis for the serviceability limit state analysis, here applied in approximation to the measured values in the serviceability limit state.

Note: The method adopted here for the characteristic boundary lines in the service load range is only one possible option. Other reasoned procedures are also possible.

Figure B8.2 and Table B8.2 show the results determined for Rc,k (SLS) and Rc,k = Rc,k (ULS).

In the ultimate limit state (ULS), sult = sg = 0,10 · Db shall be adopted for the pile head settlement, if no other criteria are selected. An equivalent pile diameter Deq = 39,5 cm = 0,395 m is given for the square pile.

The characteristic pile resistance in the ultimate limit state ULS in Table B8.2 is thus:

The characteristic pile resistance Rc,k(SLS) in the serviceability limit state for allow. s = 0,5 cm from Figure B8.2 and Table B8.2 is:

A settlement of exist. sk ≈ 0,3 cm results from the characteristic RSC for the existing characteristic action FG,k = 450 kN imposed on the pile by structural loads in the serviceability limit state (SLS).

Note: It is assumed in approximation that the pile resistances in the pile load test only result from the load-bearing soil and the strata above make no contribution.

## B8.3 Determining the characteristic actions Fn,k from negative skin friction

In Figure B8.3 the pile settlements under the effect FG,k for the ultimate and serviceability limit states are compared to the settlements of the soft stratum.

In the ultimate limit state (ULS) the neutral point is located 3,7 m below the ground surface and within the soft stratum. The characteristic actions from negative skin friction shown in Table B8.3 are determined using Eq. (4.1) for the soft stratum and Eq. (4.2) for the fill.

After determining the existing settlement s ≈ 0,3 cm for the serviceability limit state (SLS), the neutral point is located at a depth of 9,5 m below grade. This deviates from Figure B8.3 where the neutral point is determined for s ≈ 0,5 cm; the difference is however ignored. The characteristic actions from negative skin friction are determined in Table B8.4 for the serviceability limit state.

## B8.4 Bearing capacity analysis

For analysis of the ultimate limit state the limit state condition must be adhered to:

The negative skin friction is adopted here as a permanent action analogous to 4.4.3 (1) in the DS-P design situation.

## B8.5 Serviceability analysis

In the serviceability limit state the limit state condition:

Note: The adopted pile settlements s(SLS) and sult = sg resulting from structural loads are increased slightly by the characteristic pile effect from negative skin friction, in particular in terms of s(SLS). Iteration can normally be dispensed with, because the procedure shown here adopting s(SLS) ≈ 0,3 cm (without negative skin friction) is conservative and normally leads to an unfavourable characteristic pile effect Fc,k as a result of the large depth of the neutral point in the serviceability limit state.

## B8.6 Analysis of internal capacity(structural failure)

For analysis of internal capacity (structural failure) the largest effect at the depth of the neutral point in the serviceability limit state is given by:

The internal pile design (structural failure of the pile material) in the ultimate limit state shall be done using this effect Fk = FG,k + Fn,k,SLS.

# B9 Determining the Effect on a Laterally Loaded Pile (Perpendicular to the Pile Axis) and Analysis of Structural Failure

## B9.1 Objective

The internal capacity of the pile shown in Figure B9.1 is analysed. The soil resistance and the effect on the pile must first be determined. The pile is then designed, adhering to the corresponding internal pile capacity analyses.

The following characteristic actions are taken into consideration:

 Permanent vertical action: FG,k = 3,333 MN Variable vertical action: FQ,rep = 2,000 MN Permanent horizontal action: HG,k = 0,600 MN Variable horizontal action: HQ,rep = 0,400 MN.

The system comprising the characteristic actions, the ground profile and the depth-dependent subgrade modulus distribution is shown in Figure B9.1.

According to 6.3.2 the maximum mobilisable characteristic normal stress σh,k between the pile and the soil is limited by the characteristic passive earth pressure eph,k calculated for the plane state.

(B9.1)

The design value of the characteristic lateral normal stress resultant, referred to as the lateral soil resistance Bh,d, may not exceed the design value of the three dimensional passive earth pressure Erph,d for the embedment length of the pile as far as the pivot point (displacement zero point).

(B9.2)

Adherence to the conditions arising from Eq. (B9.1) and Eq. (B9.2) is to be checked prior to pile design.

## B9.2 Determining the characteristic action effects and stresses

Figure B9.2 b) shows the pile’s characteristic mobilised subgrade stress from the structural analysis of an elastically supported beam, adopting the subgrade reaction moduli from Figure B9.2 a). The distribution of the characteristic passive earth pressure is shown in Figure B9.2 c). It is clear from the superimposed subgrade stress and passive earth pressure in Figure B9.2 d) that the characteristic mobilised subgrade stresses σh,k in the upper region of the pile exceed the characteristic passive earth pressure eph,k. The approach for the subgrade reaction modulus distribution is modified such that Eq. (B9.1) is adhered to.

Figure B9.3 a) shows the iteratively determined subgrade reaction moduli, reduced in the upper pile region, which are subsequently adopted for further design. The corresponding characteristic mobilised subgrade stress is shown in Figure B9.3 b) and the characteristic passive earth pressure in Figure B9.3 c). The superimposed subgrade stress and passive earth pressure in Figure B9.3 d) show that the values of the characteristic mobilised normal stresses σh,k are now below the characteristic passive earth pressure eph,k. The condition in Eq. B9.1 is thus met.

While determining the action effects and stresses it must also be demonstrated that the resulting lateral soil resistance is smaller than the design value of the passive earth pressure as far as the pile pivot (zero displacement point).

The lateral soil resistance is given by integrating the mobilised subgrade stress from the pile head to the pivot (displacement zero point), located at an elevation of -13.47 m, using beam analysis. The characteristic soil resistance forces given by integrating the stress areas as shown in Figure B9.3 b) are:

The design value of the soil resistance is therefore:

(B9.3)

The three-dimensional passive earth pressure as a result of the self-weight of the soil is calculated to DIN 4085:2007-10 as follows:

(B9.4)

Where:

D: Pile diameter

z: Depth in question.

For the elevation here of-13,47 m:

The three-dimensional passive earth pressure Erph,k to the elevation of -13.47 m is given by the passive earth pressure distribution in the planar case as follows:

Applying the partial factor γR,e the design value of the three-dimensional passive earth pressure is:

For analysis of the lateral soil resistance:

The three-dimensional passive earth pressure is not exceeded.

## B9.3 Design values of the action effects

The design values of the action effects are given by adopting the partial factors for the limit state in the structure and the ground (STR and GEO-2) after the EC 7-1 Handbook [44], also see Annex A2. The actions are allocated to the permanent design situation DS-P.

The design value of the normal force is:

(B9.6)

If the changeable load acts favourably, the design value is:

(B9.7)

The design value of the shear force is:

(B9.8)

The design value of the bending moment is:

(B9.8)

Figure B9.4 and Figure B9.5 show the distribution of action effect design values with reduced subgrade reaction modulus adopted for structural analyses.

## B9.4 Minimum strength class of concrete and concrete cover

The minimum concrete strength class to DIN 1045-1:2008-08 for exposure class XC2 with regard to foundation components is C16/20. DIN EN 1536:1999-06 envisages a concrete strength class between C20/25 and C30/37 for bored piles.

The nominal concrete cover cnom to DIN 1045-1:2008-08 is given by:

(B9.9)

Where cmin is the minimum concrete cover to DIN EN 1536:1999-06 as a function of D:

Δc Allowance value to DIN 1045:2008-08 as a function of the exposure class:

Giving the nominal concrete cover:

To guarantee the bond to DIN 1045-1:2008-08 the condition:

## B9.5 Design values of materials

The partial factors of the materials for the ultimate limit state are adopted from DIN 1045-1:2008-08:

The design value of the concrete compressive strength is given in accordance with DIN 1045-1:2008-08 by taking the long-term impact on the compressive strength into consideration using the factor α (α = 0,85 for normal weight concrete):

(B9.10)

Where fck = 25,0 N/mm2.

The design value of the yield strength of the reinforcement steel BSt 500 S (A) is given by:

(B9.11)

Where

Thus

## B9.6 Ultimate limit state design

### B9.6.1 Design for bending and normal force

The circular section is designed using the ω method with dimensionless coefficients.

Assuming a diameter of 12 mm for the transverse and 32 mm for the longitudinal reinforcement the centres d1 of the longitudinal reinforcement are at:

For the purposes of analysis the bending reinforcement centres are adopted at d1 = 0,1.h = 15 cm, i.e. d1/h = 0,1.

The relative bending moment is given by:

(B9.12)

The relative normal force is given by:

(B9.13)

The corresponding, necessary degree of mechanical reinforcement is given by reading the diagram for d1/h = 0,1 as:

The corresponding strains are:

The necessary longitudinal reinforcement is given by:

(B9.14)

The minimum longitudinal reinforcement to DIN EN 1536:1999-06, Table 4 is given as a function of the nominal pile diameter by:

(B9.16)

The minimum reinforcement in this case is not a governing factor.

DIN EN 1536:1999-06 requires that a minimum spacing of 100 mm and a maximum spacing of 400 mm is adhered to for the longitudinal bars.

(B9.17)

The necessary minimum spacing is therefore adhered to.

### B9.6.2 Design for shear force to DIN 1045-1

The Civil Engineering Standards Committee (NABau) interpretation states that the smaller value of the cross-sectional width between the reinforcement centroid (tension flange) and the pressure resultant (corresponds to the smallest width normal to the inner lever arm z) is used as the effective width for shear force design of circular cross-sections.

Bending design gives:

Using the longitudinal reinforcement centres adopted in bending design the height of the compression zone is:

(B9.18)

Because the zero strain line lies within the cross-section, a stress block may be adopted in simplification for the distribution of the concrete compressive stress to DIN 1045:2008-08. The height of the stress block is given by:

(B9.19)

The pressure resultant lies in the centroid of a circle segment with an opening angle αc of:

(B9.20)

The centroid distance from the circle centre is:

(B9.21)

In line with the interpretation of the Civil Engineering Standards Committee the true tensile reinforcement, i.e. the reinforcement within the tension zone, is adopted for shear force design. To determine the reinforcement centroid the reinforcement is assumed to be uniformly distributed along its centroid axis. The radius of the reinforcement centroid axis is:

(B9.22)

The centroid of the ring section with an opening angle αs of:

(B9.23)

lies at a distance from the centre of the circle:

(B9.24)

This approximation deviates from the true location of the centroid of the steel tensile forces, because stress distribution in the reinforcement is not taken into consideration. However, the approach is conservative due to the larger true lever arm.

The smaller value of the cross-sectional width is therefore at the height of the pressure resultant and is:

(B9.25)

The structural height is given by:

(B9.26)

The inner lever arm is:

(B9.27)

The design value of the shear capacity without shear reinforcement in the equivalent rectangle to DIN 1045:2008-08 is:

(B9.28)

Where

η1 = 1,0 for normal weight concrete

(negative compressive force) Giving:

Shear reinforcement is therefore required.

The limitation in the compression member inclination is:

(B9.29)

Where:

(B9.30)

giving:

The design value of the maximum shear capacity is:

(B9.31)

The necessary shear reinforcement is given by:

(B9.32)

However, this approach does not take the increased effect of the shear reinforcement due to radial thrust forces caused by the continuous support of the compression strut on the circular link (boiler pressure) into consideration. Therefore, [5] derives the shear resistances from the basic equations in DIN 1045-1, taking the thrust forces of the circular link and the non-uniform distribution of the shear force on the longitudinal reinforcement into consideration for axis-symmetrical, longitudinally reinforced beams with shear reinforcement. If shear reinforcement is in helix format, the helix inclination α must also be taken into consideration. Deriving the tension strut strength for circular links leads to the design value given in DIN 1045-1:2008-08:

(B9.33)

supplemented by a factor αk known as a the effectiveness factor, dependent only on dimensionless geometry parameters and a term for the helix inclination α. Due to the small range of values of 0,715 ≤ αk ≤ π / 4 = 0,785 for practical applications, [5] proposes a simplified estimate of αk = 0,75 .

The shear force component VRd,c to DIN 1045-1:2008-08 is adopted to determine the compression strut inclination, whereby the effective width can be estimated as bw = Aeff/z ≈ 0,9 · D = 0,9 1,5 = 1,35 m. Using Eq. (B9.30):

Using Eq. (B9.29) the limitation in the compression strut inclination is:

The capacity of the compression strut is limited in accordance with DIN 10451:2008-08, whereby the effective width may be adopted as bw = 2 · RS ≈ D = 1,5 m using the approach after [5]. Given an angle of inclination of the helix of a = 85° (cf. adopted reinforcement) the capacity of the compression strut is limited to:

(B9.34)

The necessary shear reinforcement is given by Eq. (B9.33):

### B9.6.3 Design for shear force after [5]

In order to take into consideration the favourable impact of central normal compression forces, [5] divides the bearing resistance into individual components in a truss model with an additive concrete contribution, whereby the shear force transfer as a result of crack formation is ignored, such that by adopting VRd,c = 0

(B9.35)

In addition to the effect of the truss model, the resistance in the compression and failure process zone is adopted:

(B9.36)

The semi-empirical approach was adopted by [5] for shear force resistance:

(B9.37)

where the term λ · NEd considers the favourable influence of central normal compression forces via a strutted frame. The inclination of the strutted frame λ = zC /a corresponds to the change in the distance zN between the centroid axis and the centroid of the compression zone over the length a. In simplification, the length a may be estimated as the distance between the point of acting of the shear force and the location of the maximum moment where a = 892-160 = 732 cm. Hence:A normal compression force is adopted by applying the appropriate partial factor for favourable actions.

In contrast to the NABau interpretation, [5] adopts the reinforcement of the half cross-section in the tension zone in simplification for the degree of longitudinal reinforcement.

(B9.38)

Using beff = 0,9·D = 1,35m and the values previously determined in Equation (B9.37):

The required reinforcement in accordance with Equation (B9.36) is therefore:

In contrast to the NABau interpretation, the approach in accordance with [5] gives an approx. 16% lower shear force reinforcement. This is caused by the increase in shear capacity due to the strutted frame approach for the normal forces. If no, or only minor, compressive forces act on the structural element, the design approach in accordance with [5] returns more shear reinforcement than the NABau interpretation, because in this case the additional effect imposed by the circular reinforcement’s boiler pressure not covered by the DIN 1045-1:2008-08 design concept becomes governing. The approach after [5] is therefore recommended for design.

### B9.6.4 Minimum reinforcement for shear force to DIN 1045-1

The minimum reinforcement to DIN 1045-1 is given by the base value for determining the minimum reinforcement ρ = 0,068% as:

(B9.39)

The minimum diameter of the transverse reinforcement in accordance with DIN EN 1536:1999-06 is:

(B9.40)

The minimum clear bar spacing in accordance with DIN EN 1536:1999-06 may not be smaller than for longitudinal bars at:

The minimum longitudinal spacing in accordance with DIN 1045-1:2008-08 for

(B9.41)

is:

(B9.42)

The following shear reinforcement is used:

Helix 2-core dia.

## B10.1 Objective and systems

Figure B10.1 shows a bridge abutment founded on 8 tubular steel piles. The lateral pressure on the piles as a result of the backfill must be determined, based on [35].

Boundary conditions:

- Surcharge from sand layer in tidal mud, consolidated
- Surcharge from backfill in tidal mud, unconsolidated (initial state) (→ U = 0)

## B10.2 Determining the characteristic actions and effects

The characteristic actions from lateral pressure are determined in line with 4.5, whereby the characteristic flow pressure pf,k is determined using Eq. (4.5) and adopting the geometry of the pile group as shown in Figure 4.7.

The characteristic effect of the flow pressure Pf, kw