Acta Polytechnica CTU Proceedings https://doi.org/10.14311/APP.2023.45.0059 Acta Polytechnica CTU Proceedings 45:59–65, 2023 © 2023 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague CONSIDERATIONS ON AN EMBEDDED PILE’S EFFECTIVE LENGTH IN AN ANALYTICAL CALCULATION ACCORDING TO THE COMMENTARY ON THE STN 73 1002 STANDARD Jakub Stacho∗, Monika Súľovská Slovak University of Technology in Bratislava, Faculty of Civil Engineering, Department of Geotechnics, Radlinského 11, 810 05 Bratislava, Slovakia ∗ corresponding author: jakub.stacho@stuba.sk Abstract. The analytical model for calculating the bearing capacity of a pile, presented in the commentary to STN 73 1002 – Pile Foundations, gives a recommendation to reduce the pile’s length in the calculation of the shaft resistance. The recommendation is based on Caquot-Kérisel’s theory. Especially in the case of embedded piles, reducing a pile’s length in the calculation can cause the shaft friction of the embedded pile to be neglected, and the calculated resistance of the pile is thus significantly lower. The results of instrumented static load tests of embedded piles were analysed. The main aim of the study was to verify the validity of reducing the pile’s length in the analytical calculation of the shaft resistance. The results of the static load tests analysed did not show any reduction in the shaft friction on the embedded part of the pile. In the form of a parametric study, the effect of reducing the pile’s length in the calculation of shaft friction was analysed for different dimensions of embedded piles. Keywords: Design of pile, effective length of pile, length of pile, resistance of pile, shaft resistance. 1. Introduction The vertical bearing capacity of the pile can be de- termined using various analytical calculation models, e.g., [1–3]. The analytical calculation model, which is stated in detail in the commentary on the STN 73 1002 standard [4], is the one most used in Slovakia and the Czech Republic. This calculation model is also customarily deployed in the analytical calculation of the pile’s bearing capacity using the geotechnical soft- ware FINE Geo5. The individual calculation models presented by the authors referenced just above differ from each other in local experience, typical engineer- ing geological conditions or piling technology. The differences between each calculation model lie in the considered mechanism of the failure of the earth envi- ronment in the vicinity of the pile, which was stated by, e.g., [5]. The analytical calculation models determin- ing the pile’s bearing capacity have been constantly developed and modified by many authors to consider different geological, geometrical, and technological as- pects, see e.g., [6? –17]. These calculation models apply different coefficients, which can consider the geometry of the pile, the adhesion and friction in the pile body-soil interaction, the lateral earth pressure acting on the pile’s shaft, and the piling technology. The analytical model given in the commentary on the STN 73 1002 standard also mentions the matter of the shortening of the pile’s length in calculating the shaft friction according to Caquot-Kérisél’s theory [4]. They pointed to creating an area of plastic stresses near the base of the pile, which begin to arise when the vertical load reaches the vertical bearing capacity of the pile. In the case of other frequently used calcu- lation models, mostly in other countries, a reduction of the pile’s length in calculating the shaft friction is not used in this form. The decrease of the shaft friction for the loads that reach the pile’s bearing capacity and a relatively large settlement is mainly attributed to the residual stress state in the pile-body soil interface. When the effective length is applied in calculating the pile’s shaft resistance, especially in the case of an embedded (end-bearing) pile, this often means that the shaft resistance of the embedded part of the pile is neglected. The aim of the study pre- sented was to analyse the results of the instrumented static load tests of embedded piles with a focus on the distribution of axial force and the justification of a shortening of the pile’s length in the calculation of its bearing capacity. 2. Calculation of the vertical resistance of the pile according to commentary on STN 73 1002 The calculation model and the detailed description of the calculation procedure are given in the commentary to the STN 73 1002 standard [4]. This calculation model is also taken by other authors, e.g., [9, 10]. The static scheme of the calculation model is shown in Figure 1. Determining the design value of the pile’s vertical resistance and the influence of partial factors of different design approaches was presented by, e.g., [18]. The characteristic resistance of the pile (Rk) is given by the sum of the characteristic base resistance (Rb,k) and characteristic shaft resistance 59 https://doi.org/10.14311/APP.2023.45.0059 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en Jakub Stacho, Monika Súľovská Acta Polytechnica CTU Proceedings Figure 1. The static scheme of the calculation of the vertical pile resistance (according to [9]). (Rs,k) according to the following formula: Rc,k = Rb,k + Rs,k, (1) where Rb,k can be calculated as: Rb,k = K1 Ab Rk, (2) Rk = c′ d,2 · Nc,2 + q′ · Nq,2 + 0.7 · γ2 · D 2 · Nγ,2, (3) Rk =1.2 · c′ d,2 · Nc,2 + ( 1 + sin φ′ d,2 ) · q′ · Nq,2 + 0.7 · γ2 · D 2 · Nγ,2, (4) where Nc,2, Nq,2, and Ng,2 are the ultimate bearing ca- pacity factors; φ′ d,2 and c′ d,2 are drained shear strength properties; γ2 is the unit weight of the soil; and q′ is the effective geostatic stress in the depth of the pile’s base. The characteristic value of the shaft resistance can be determined using the following formula: Rs,k = π · D n∑ i=1 hi · fs,i, (5) where D is the diameter of the pile, hi is the length of the pile’s shaft in the i-layer, and fs,i is the friction on the pile’s shaft in the i-layer, determined from the Equation 6 as follows: fs,i = K2 · σor,i · tan ( φ′ d γr,1 ) + c′ d γr,2 . (6) The values of coefficients γr,1, γr,2, and K2 are presented by [4]. The parameter σor,i is the geostatic stress in the middle of the i-layer. The calculation model also states that the effective length of the pile, used in the shaft resistance calcu- lation, can be shortened according to Caquot-Kérisel by the length of Lp (Figure 1) [4]. This reduction in length can be calculated using the following formula: Lp = N2/3 q · D 4 , (7) where Nq is the ultimate bearing capacity factor given by the formula (8) as follows: Nq = exp (π · tan φ′ d) tan2 ( 45 + φ′ d 2 ) . (8) Based on equations (7) and (8), the reduction length Lp is controlled by parameters D and φ′. The de- pendence between these input parameters and the resulting Lp value is shown in Figure 2. It can be seen that especially for coarse-grained soils, which have a value of φ′ d mostly greater than 30◦, the reduction length Lp can be significant. In the case of gravel soil with an angle of shear strength of 40◦ and the pile with a diameter of 1.5 m, the reduction in length can reach up to 6 m. 60 vol. 45/2023 Embedded Pile’s Effective Length Figure 2. Diagram for determining Lp length. Figure 3. The resistance of the pile determined from a typical load-settlement curve. 3. Analysis of the results of the instrumented static load tests A load-settlement curve of the pile can have differ- ent shapes. This mainly depends on the engineering- geological conditions and the pile’s geometry. Accord- ing to the shape of the load-settlement curve (Fig- ure 3), the following resistances can be determined [9]: • ultimate resistance (Figure 3 – A); • resistance on the limit of the proportionality (Fig- ure 3 – B); • resistance on the limit of the deformation (Figure 3 – C); • indicative resistance (Figure 3 – D). In the case of end-bearing (embedded) piles, de- pending on the shape of the load-settlement curve, a settlement of the pile’s head equal to 10 % of the pile diameter should be considered as the limit of the failure according to STN EN 1997-1. This corresponds with determining the characteristic resistance of the pile according to Figure 3 - C. In this case, the load- settlement curve must be executed up to the pile’s settlement equal to 10 % of its diameter. The load- settlement curves of different end-bearing piles, which fulfilled the criteria of the required settlement of 10 % of the pile’s diameter, were selected for the analysis presented. The tested piles were instrumented, i.e., the piles were equipped with strain gauges. This al- lowed for analysis of the load distribution over the pile’s length. Subsequently, the results of one tested pile are pre- 61 Jakub Stacho, Monika Súľovská Acta Polytechnica CTU Proceedings Figure 4. Load-settlement curve of the pile determined by the static load test (left), load-settlement curves of the base and total resistance of the pile used in the calculation (right). Figure 5. Load transfer over the pile’s length determined by the static load test. sented in detail. The pile tested had a diameter of 410 mm and a length of 17.9 m. The geological condi- tions at the testing site consisted of fine-grained soils (F) up to a depth of about 13.9 below the surface and coarse-grained soils, sand (S) and gravel (G), below them. The fine-grained soils consisted of organic soil (O) and sandy silt (MS) of soft consistency. A layer of medium-dense silty sand (SM) was located at a depth of 13.9 to 16.5 m below the surface. Gravel with fines fraction (GF) was located below the sandy soil. The tested pile was reinforced using a GEWI bar. The strain gauges were installed in couples at the depths of 0.5, 13.9, 16.5, and 17.8 m. The load-settlement curve of the pile tested is shown in Figure 4 – left. During the test, an unloading and reloading were applied two times. After reaching the maximum loading, i.e., 2000 kN, the final unloading was also applied. The load-settlement curve of the total pile’s resistance and the load-settlement curve of the pile’s base resistance are shown in Figure 4 – right. When the maximum load of 2000 kN was applied, the resistance of the base reached about 772 kN. The resistance of the shaft was about 1228 kN. The load distribution over the pile’s length is shown in Figure 5. The load distribution is shown for each loading step, i.e., 333, 666, 1000, 1333, 1666, and 2000 kN. In the case of the given static load test, and similarly to the other static load tests analysed, the criterion of settlement of the pile head equal to 10 % of its diameter was met. It is evident that there was no decrease or any reduction in the shaft friction in the embedded part of the pile. The results of three static 62 vol. 45/2023 Embedded Pile’s Effective Length Pile No. 1 Vertical load [kN] 1000 1333 1666 2000 Shaft friction – Layer No. 1 – low bearing [kPa] 26 35 43 52 Shaft friction – Layers Nos. 2 and 3 – high/end bearing [kPa] 25 30 43 46 Stress below a pile’s base [kPa] 3226 4376 5488 6657 Pile No. 2 Vertical load [kN] 1000 1333 1666 2000 Shaft friction – Layer No. 1 – low bearing [kPa] 17 20 22 22 Shaft friction – Layers Nos. 2 and 3 – high/end bearing [kPa] 147 220 300 440 Stress below a pile’s base [kPa] 1569 1876 2048 2256 Pile No. 3 Vertical load [kN] 1000 1333 1666 2000 Shaft friction – Layer No. 1 – low bearing [kPa] 23 27 35 41 Shaft friction – Layers Nos. 2 and 3 – high/end bearing [kPa] 90 149 157 175 Stress below a pile’s base [kPa] 1809 2003 3255 4449 Note: Layer No. 1 (O, MG, CG); Layers Nos. 2 and 3 (SM and G-F) – see Figure 5 Table 1. Physical properties of Holocene organic soils. load tests of the end-bearing piles in similar geologi- cal conditions are presented in Table 1. The results present the shaft friction in layer No. 1 (fine-grained soil) – low bearing stratum, the shaft friction in layer Nos. 2–3 (coarse-grained soils) – high/end bearing stratum, and stress below the pile’s base. In all the cases presented, there is no evident decrease in the shaft friction of the embedded part of the pile. On the contrary, the results clearly show that the piles take over a significant part of the shaft resistance by the friction in the embedded part of the pile – even when the pile’s settlement reaches about 10 % of the pile’s diameter. Tomlinson and Woodward state that a reduction in the shaft friction can only be expected when the load-settlement curve reaches the ultimate resistance of the pile (Figure 3 – A); however, in the case of the end-bearing pile this can occur for a sig- nificantly greater load when the settlement of the pile exceeded about 20 % of the pile’s diameter. In the case of the static load test presented it can therefore be assumed that with the increase in the load, the ultimate resistance of the pile can be reached. In that case, a reduction in the shaft friction can be expected. 4. Parametric study on the effect of reducing the pile’s length in the calculation A simple parametric study was created to demonstrate how significant the effect of the pile’s length reduction can be in the shaft resistance calculation. The geo- logical profile consisted of two layers, i.e., low-bearing stratum (fine-grained soil) and high-bearing stratum (coarse-grained soil). The fine-grained soil was defined by the following properties: γ = 20 kN m−3, φ′ = 15◦, and c′ = 10 kPa. The coarse-grained soil was defined by the following properties: γ = 20 kN m−3, φ′ = 35◦, and c′ = 0 kPa. The total design resistance Rc,d and the design shaft resistance Rs,d was calculated for the end-bearing (embedded) pile of a diameter of 0.6, 0.9, 1.2, and 1.5 m; and a length of 10, 15, and 20 m. The embedded part of the pile was equal to 2 m for a 10 m long pile, 3 m for a 15 m long pile, and 4 m for a 20 m long pile. The results are presented in Table 2. The to- tal resistance of the pile Rc,d and the shaft resistance Rs,d,1 were calculated for the case when the reduction length was not considered. In the second case, the shaft resistance Rs,d,2 determined for the pile’s length reduced by Lp, was computed. A difference ∆Rs,d between both shaft resistances was determined. It can be seen that considering the reduced length of the pile in the calculation can cause a significant reduction in the shaft resistance. 5. Discussion on the results presented In general, it can be stated that the resistance of the pile and its deformation behaviour is a complex mechanism that is difficult to describe and define with a simple analytical calculation model. When the pile is continuously loaded, shaft friction is first mobilized. Subsequently, with a further increase in load, it is possible to reach the limit stress at the pile base. In the case of soils, where a significant difference occurs between the peak and critical/residual shear strength, when the pile is gradually loaded, there is a subsequent decrease in the shaft friction, as shown in Figure 6. In this case, using peak shear strength parameters in the calculation can be incorrect. This effect was not observed for the testing piles analysed. This fact is related to the decrease in the shear strength (from the peak to the residual) and is not related to neglecting the shaft friction near the base of the pile. The shaft friction along the pile is usually not con- stant, e.g., [12]. Assuming homogeneous subsoil, the maximum value of the shaft friction is reached in the 63 Jakub Stacho, Monika Súľovská Acta Polytechnica CTU Proceedings L [m] D [m] 0.6 D [m] 0.9 D [m] 1.2 D [m] 1.5 Lp [m] 1.552 Lp [m] 2.329 Lp [m] 3.105 Lp [m] 3.881 R c ,d [k N ] R s ,d ,1 [k N ] R s ,d ,2 [k N ] ∆ R s ,d [% ] R c ,d [k N ] R s ,d ,1 [k N ] R s ,d ,2 [k N ] ∆ R s ,d [% ] R c ,d [k N ] R s ,d ,1 [k N ] R s ,d ,2 [k N ] ∆ R s ,d [% ] R c ,d [k N ] R s ,d ,1 [k N ] R s ,d ,2 [k N ] ∆ R s ,d [% ] 10 2370 542 354 35 4969 813 432 47 8549 1085 518 52 13140 1356 574 58 15 3849 1127 845 25 7859 1690 1056 38 13300 2254 1058 53 20190 2817 1228 56 20 5537 1920 1545 20 11060 2880 2035 29 18460 3840 2338 39 27770 4800 2453 49 Table 2. Impact of reducing the pile’s length in the calculation of shaft frictions for different dimensions of the embedded piles. Figure 6. Load-settlement relationships – mobiliza- tion of the shaft friction and resistance at the base of the pile (according to [1]). vicinity above the pile’s base. It subsequently de- creases significantly towards the pile’s base (Figure 7). According to the commentary to the STN 73 1002 standard, this decrease in the shaft friction is theo- retically taken into account in the calculation model precisely by introducing the effective length of the pile. However, only a decreasing in the shaft friction occurs, and therefore it is questionable if complete neglect of the shaft friction in this part of the pile is appropriate. Figure 7 also shows the calculation course of the shaft friction when applying the critical depth defined by, e.g., the NAVFAC DM7.02 standard. Under certain conditions, applying the critical depth appears to be more appropriate than neglecting the shaft friction near the pile base; however, the number of analysed static load tests did not allow a deeper analysis that could lead to a more detailed conclusion. In the design of the pile, both the ultimate limit state (ULS) and the serviceability limit state (SLS) must be verified. The SLS condition is often stricter and thus decisive for the design of the pile. However, in the practical design of a pile foundation, a paradox- ical situation often occurs when the SLS condition is fulfilled, the settlement of the piles is a relatively small value (e.g. about 20 ∼ 30 mm), but the calculated re- sistance of the pile does not meet the given condition. Figure 7. Transfer of the shaft friction over pile’s length (according to [16]). Especially in the case of end-bearing (embedded) piles, a significant resistance of the pile shaft is represented by the shaft friction of the embedded part of the pile, which is a complete neglect in the calculation when the effective length of the pile is considered. The crite- rion of the maximum settlement of the pile is usually lower than when the pile’s settlement equals 10 % of its diameter. Then, if the SLS condition is fulfilled, it is unlikely that the pile settlement should increase to such an extent that a significant decrease in shaft friction near the pile base can be experienced. It should be noted that the analytical calculation model stated in the commentary to the STN 73 1002 stan- dard mentions introducing the effective length of the pile into the calculation as a recommendation, not as a required condition. In the end, it is up to the designer how it will be considered in the pile design. 6. Conclusions The analytical model for calculating the resistance of a single pile, given in the commentary to the STN 73 1002 standard, introduces the recommendation of applying the pile’s effective length into the pile’s shaft resistance calculation, according to the Caquot- Kérisel theory. Theoretically, the formation of an onion-shaped area of plastic stresses near the pile base is assumed when the load approaches the ulti- mate resistance of the pile. As a result of this effect, 64 vol. 45/2023 Embedded Pile’s Effective Length the shaft friction near the pile base should be ignored. Especially in the case of end-bearing (embedded) piles, this may mean that the resistance of the embedded part of the pile is not included in the total resistance of the pile, although its contribution to the pile’s to- tal resistance can be significant. The results of the instrumented static load tests were analysed, in which the settlement of the pile head equal to 10 % of their diameter was achieved, and it was assumed that the resistance on the limit deformation (Figure 3 – C) was reached. The results of the static load tests showed that even when the pile head settled at 10 % of its diameter, there was no reduction in the shaft friction in the embedded part of the pile; on the contrary, significant shaft friction was also recorded in the em- bedded part of the pile. Based on the theoretical review, it can be assumed that a decrease in shaft fric- tion could only be noted when the ultimate resistance of the pile is reached, which is particularly difficult for end-bearing (embedded) piles of the given geom- etry installed in similar geological conditions. The application of the effective (reduced) or actual length of the pile in the calculation of the resistance is at the discretion of the designer/statics. In the case of end-bearing (embedded) piles, where the serviceability limit state condition is fulfilled, the pile deformation does not exceed 10 % of its diameter – it seems more appropriate to consider the total length of the pile in the calculation of the resistance. References [1] M. Tomlinson, J. Woodward. Pile design and construction practice. Taylor & Francis e-Library, 5th edn. p. 551, 2007. [2] D. A. Brown, S. Dapp, W. R. Thompson, et al. Geotechnical engineering circular no. 8 – Design and construction of continuous flight auger (CFA) piles p. 294, 2007. [3] K. Fleming, A. Weltman, M. Randolph, K. Elson. Piling engineering. Taylor & Francis e-Library, 3rd edn. p. 398, 2008. [4] R. Pochman, J. Šimek. Pile foundations [in Czech – Pilotové základy]. Commentary to ČSN 73 1002, 1.vyd. Praha, Vydavatelství norem. 1989. p. 75. ISBN 80-85111-04-7. [5] C. Viggiani, A. Mandolini, G. Russo, et al. Piles and pile foundations. Taylor & Francis, London, UK. p. 278, 2012. [6] S. Škrabl. Bearing capacity and settlement of vertically-loaded piles. In Deep Foundations 2002: An International Perspective on Theory, Design, Construction, and Performance, pp. 53–63. 2002. https://doi.org/10.1061/40601(256)5 [7] J. Zhang, L. Hanlong, G. Yang. A simplified method for calculating ultimate bearing capacity of cast-in-place concrete pipe pile with large diameter in sandy soil. In Advances in Pile Foundations, Geosynthetics, Geoinvestigations, and Foundation Failure Analysis and Repairs, pp. 75–81. 2011. https://doi.org/10.1061/47631(410)9 [8] J. Mecsi. Geotechnical engineering examples and solutions using the cavity expanding theory Hungarian Geotechnical Society, 2013, p. 232. [9] J. Masopust. Bored piles [in Czech – Vrtané piloty]. Prague, Čenek a Ježek s.r.o., 1994, p. 263. [10] J. Hulla, P. Turček. Foundation engineering [in Slovak – Zakladanie stavieb]. Jaga Group s.r.o., Bratislava, 1998, p. 310. [11] M. Randolph, R. Dolwin, R. Beck. Design of driven piles in sand. 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In Juniorstav 2022: Proceedings of the 14th International Conference of Doctoral Students, Brno: VUT, 2012. 65 https://doi.org/10.1061/40601(256)5 https://doi.org/10.1061/47631(410)9 https://doi.org/10.1680/geot.1994.44.3.427 https://doi.org/10.1515/sgem-2015-0048 https://doi.org/10.1515/cee-2016-0018 https://doi.org/10.1680/geot.1979.29.4.361 https://doi.org/10.3390/app13052931 Acta Polytechnica CTU Proceedings 45:1–7, 2023 1 Introduction 2 Calculation of the vertical resistance of the pile according to commentary on STN 73 1002 3 Analysis of the results of the instrumented static load tests 4 Parametric study on the effect of reducing the pile's length in the calculation 5 Discussion on the results presented 6 Conclusions References