Abstract

The interaction mechanisms related to the group effect between piles and between pile groups significantly influence the soil-structure interaction process. This interaction causes the superposition of stresses and, in general, makes the pile group settlement different from the settlement of an isolated pile. The objective of the present paper is to evaluate the soil-structure interaction mechanisms of buildings with foundations of monitored continuous flight auger piles (CFA) in a stratified soil mass, with the presence of an intermediate soft soil layer. Hence, it is particularly analyzed the group effect between piles of a group and the group effect between all pile groups from a foundation of a study case instrumented by means of numerical modeling, considering the effect of the soft soil layer. The results show the significant group effect on displacements, showing the increase in settlement due to the overlapping of the tension bulbs of the piles and neighboring pile groups.

Keywords:
Group effect; Continuous flight auger pile; Finite element method; Deep foundation; Soil-pile interaction

1. Introduction

The soil-structure interaction (SSI) is responsible for the redistribution of efforts through structural rebalancing, which occurs with the construction evolution. The study of the processes of soil-structure interaction is important for predicting the behavior of the structure during the construction sequence. The interaction mechanisms related to the group effect between piles and pile groups significantly influence the soil-structure interaction process, more specifically, the pile-soil interaction process. This interaction causes overlap of the tension bulbs and, in general, makes the settlement of the group of piles different from the settlement of an isolated pile.

The group effect, defined by NBR 6122 (ABNT, 2019ABNT NBR 6122. (2019). Projeto e execução de fundações. ABNT - Associação Brasileira de Normas Técnicas, Rio de Janeiro, RJ (in Portuguese).) as the process of interaction of the various elements that constitute a foundation by transmitting the loads applied to them to the soil, causes the overlap of the tension bulbs and causes the settlement of the group be, in general, different from the settlement of the isolated element. Velloso & Lopes (2010)Velloso, D. A., & Lopes, F. R. (2010). Fundações: critérios de projeto, investigação do subsolo, fundações superficiais, fundações profundas. Oficina de Texto (in Portuguese). define the group effect as the perceived difference in load capacity and settlement measured in a group of piles, connected by a pile block, and in an isolated pile, due to the interaction that occurs through the soil.

In the last decades, several studies, with different methodologies, have been dedicated to the analysis of the group effect between piles connected by the same block (Poulos & Mattes, 1971Poulos, H.G., & Mattes, N.S. (1971). Settlement and load distribution analysis of pile groups. In Institution of Engineers (Org.), Golden jubilee of the International Society for Soil Mechanics and Foundation Engineering: commemorative volume (pp. 18-28). Institution of Engineers.; Randolph & Wroth, 1979Randolph, M.F., & Wroth, C.P. (1979). An analysis of the vertical deformation of pile groups. Geotechnique, 29(4), 423-439.; Poulos & Davis, 1980Poulos, H.G., & Davis, E.H. (1980). Pile foundation analysis and design. Wiley.; Poulos & Randolph, 1983Poulos, H.G., & Randolph, M.F. (1983). Pile group analysis: a study of two methods. Journal of Geotechnical Engineering, 109(3), 355-372.; Randolph, 1994; Guo & Randolph, 1999Guo, W.D., & Randolph, M.F. (1999). An efficient approach for settlement prediction of pile groups. Geotechnique, 49(2), 161-179.; Poulos, 2006Poulos, H.G. (2006). Pile group settlement estimation - research to practice. In R.L. Parsons, L. Zhang, W.D. Guo, K.K. Phoon & M. Yang (Eds.), Foundation analysis and design: innovative methods (pp.1-22). American Society of Civil Engineers.; Sheil & McCabe, 2012Sheil, B., & McCabe, B.A. (June 28-30, 2012). Predictions of friction pile group response using embedded piles in PLAXIS. In Turkish National Committee of Soil Mechanics Geotechnical Engineering & Near East University (Orgs.), Third International Conference on New Developments in Soil Mechanics and Geotechnical Engineering (pp. 1-5). Nicosia, North Cyprus: Near East University.; Guo, 2013Guo, W.D. (2013). Theory and practice of pile foundations. CRC Press.; Randolph & Reul, 2019Randolph, M.F., & Reul, O. (May 23-24, 2019). Practical approaches for design of pile groups and piled rafts. In INCOTEC S.A., Society of Engineers of Bolivia & Bolivian Society of Soil Mechanics and Geotechnical Engineering (Orgs.), 4th Bolivian International Conference on Deep Foundations (pp. 1-27). Santa Cruz, Bolivia: ISSMGE.; among others). However, the analysis of the generalized group effect, that is, the group effect between all pile groups in the building, is generally disregarded. This is due, in general, to the computational effort required for the analysis of the entire foundation. Therefore, numerical analyzes of the group effect on piles are usually restricted to relatively small groups of piles (Randolph, 1994Randolph, M.F. (January 5-10, 1994). Design methods for pile groups and piled rafts. In International Society for Soil Mechanics and Geotechnical Engineering (Org.), 13th International Conference on Soil Mechanics and Foundation Engineering (pp. 61-82). London, United Kingdom: ISSMGE.). However, with the development of technology, the use of the finite element method becomes more efficient and makes it possible to solve more complex problems, such as, for instance, the analysis of problems involving stratified subsoil, with a greater number of piles and pile blocks, enabling a more representative analysis of the performance of the entire building and the generalized group effect.

Therefore, the objective of this work is to evaluate, by means of three-dimensional numerical modeling, the soil-structure interaction mechanisms of a building with a monitored continuous flight auger pile foundation in a stratified subsoil, with the presence of an intermediate soft soil layer. Specifically, the group effect between piles connected by the same block and the group effect between all pile groups in the building of an instrumented case study are analysed. The effect of the soft soil layer is also evaluated.

2. Case study

The case study consists of a residential building with 19 floors with reinforced concrete structure and sealing masonry in ceramic material, located in the city of Campos dos Goytacazes-RJ, Brazil. The location of the case study is shown in Figure 1. The building consists of 3 garage floors that occupy the entire area of the terrain and the body of the building with 14 type floors and a penthouse, in addition to the water tank, occupying the central area.

The region where the case study is located is marked by the presence of plains of fluvial-marine origin and Cenozoic sedimentary basins, characterized by sub-horizontal surfaces consisting of well-selected sandy or clayey to clayey deposits, with extremely smooth and convergent gradients towards watercourses (Lazaretti et al., 2017Lazaretti, A.F., Pinho, D., Dantas, M.E., & Pôssa, J.T. (2017). Carta geomorfológica: município de Campos dos Goytacazes. CPRM (in Portuguese).).

The elevated part of the municipality presents soils resulting from the weathering of Pre-Cambrian rocks (gneisses and granites) and Tertiary sediments of the Barreiras Formation (Costa et al., 2008Costa, A.N., Polivanov, H., & Alves, M.G. (2008). Mapeamento geológico-geotécnico preliminar, utilizando geoprocessamento, no município de Campos dos Goytacazes. Anuário do Instituto de Geociências, 31(1), 50-64 (in Portuguese).).

The investigation and characterization of the soil profile was performed through 8 standard penetration test (SPT) holes.

The foundation used were monitored continuous flight auger-type deep piles, with diameters of 500 mm, under the main body of the building, and of 400 mm, under the extension of the garage area. The monitored pillars and piles are positioned in the body of the building. All piles are 18m long, armed in the first four meters. Therefore, they are settled in a layer of silty clay with sand, which showed a high N_SPT value, with an average N₆₀ value of approximately 58 blows.

The piles considered in the numerical model are located under the main body of the building and are divided, according to the loading level, into peripheral, intermediate and central piles.

Figure 2 shows the stakeout project, the location of instrumented piles, the division of piles into peripheral, intermediate and central piles and the location of SPT holes.

The following soil layers were identified in the SPT: yellow silty clay from 3.7 to 6.4 meters deep, clayey sand from 11.3 to 13.7 m, dark gray peaty clay from 11.3 to 13.7 m and impenetrable hard light gray silty clay from 19.5 to 20.5 m, as shown in Figure 3.

The monitoring of the work, since the first stages of construction, was carried out by Waked (2017)Waked, L.V. (2017). Transferência de carga de estacas hélice contínua monitorada em maciço sedimentar durante a construção de um edifício [Master’s dissertation]. Universidade Estadual do Norte Fluminense Darcy Ribeiro (in Portuguese). and Prellwitz (2016)Prellwitz, M.F. (2016). Aplicação de monitoramento de recalque para estimativa de parâmetro de interação solo-estrutura [Unpublished doctoral thesis]. Universidade Estadual do Norte Fluminense Darcy Ribeiro (in Portuguese).. Waked (2017)Waked, L.V. (2017). Transferência de carga de estacas hélice contínua monitorada em maciço sedimentar durante a construção de um edifício [Master’s dissertation]. Universidade Estadual do Norte Fluminense Darcy Ribeiro (in Portuguese). monitored the displacement relative to the pillars of 4 piles, using telltales and strain gauges, and Prellwitz (2016)Prellwitz, M.F. (2016). Aplicação de monitoramento de recalque para estimativa de parâmetro de interação solo-estrutura [Unpublished doctoral thesis]. Universidade Estadual do Norte Fluminense Darcy Ribeiro (in Portuguese). monitored the settlement of all the pillars of the building, using a monitoring system based on the principle of communicating vessels and the data acquisition was done using photogrammetry.

3. Numerical modeling

The analysis of the soil-structure interaction of the case study was carried out from three-dimensional numerical modeling using a software based on the finite element method (FEM), Plaxis 3D.

The piles used in the model are 0.5 m in diameter and 18 m long. The dimensions of the blocks are shown in Table 1.

The soil parameters were validated from parametric retroanalysis in a three-dimensional model based on correlations with the N_SPT obtained at the site and based on parameter values suggested by authors such as Décourt (1995)Décourt, L. (October 28, 1995). Prediction of load-settlement relationships for foundations on the basis of the SPT-T. In W. Van Impe & M. Madhav (Eds.), Ciclo de Conferencias Internacionales Leonardo Zeevaert (pp. 85-104). Mexico City, Mexico: Universidad Nacional Autónoma de México., Marangon (2018)Marangon, M. (2018). Geotecnia de fundações. Departamento de Transporte e Geotecnia/Universidade Federal de Juiz de Fora., Ortigão (2007)Ortigão, J.A. (2007). Introdução à mecânica dos solos dos estados críticos (3rd ed.). Terratek., Godoy (1972)Godoy, N.S. (1972). Fundações. Notas de aula: curso de graduação. Escola de Engenharia de São Carlos/Universidade de São Paulo (in Portuguese). & Bowles (1997)Bowles, J.E. (1997). Foundation analysis and design (5th ed.). The McGraw-Hill Companies.. The validation of soil layer parameters is presented in Leite (2021)Leite, L.S. (2021). Análise numérica tridimensional do efeito de grupo entre estacas e entre blocos em fundação do tipo hélice contínua monitorada em maciço com presença de solo mole [Master’s dissertation]. Universidade Estadual do Norte Fluminense Darcy Ribeiro (in Portuguese).. The parameters used in numerical modeling are presented in Table 2.

The numerical model developed is presented in Figure 4. The finite element mesh is formed by tetrahedral elements of 10 nodes and has a medium degree of refinement. The number of soil elements is 80,610, and the number of nodes is 119,303.

Sensitivity analyses showed that there was no significant change in the settlement values obtained in the models with the change in the degree of mesh refinement.

The water level was considered with the average depth identified in the soundings, 3.5 m. Therefore, the soil above this depth was configured as dry.

The adopted boundary conditions consider the deformations of the massif normally fixed horizontally (X_min, X_max, Y_min and Y_max), fully fixed at Z_min and free at Z_max and the groundwater flow closed at Z_min and open in the other directions.

The constitutive model used to represent the elements of piles and blocks was the Linear Elastic (LE), for the soft clay layer the linear elastic perfectly plastic model, called Mohr Coulomb model (MC), was used, the LE model was used for the other soil layers.

The modeling was carried out in several stages, in order to evaluate the effect of the interaction between pile groups. Initially, a model with an isolated pile was simulated, followed by a model with an isolated pile group, connected by the same pile block, the next stages included pile groups located at a radius n times the largest dimension (B) of the block considered initially. This evaluation process, increasing the simulated radius in the numerical model, was performed 9 times, 3 starting with peripheral blocks (B1, B6, B12), 3 with intermediate blocks (B15, B33, B129) and 3 with central blocks (B20, B23/30, B27). The location of these blocks is illustrated in Figure 5a. The division of blocks according to the distance to the center of block B129 is shown in Figure 5b.

Figure 6 shows the configuration sequence of the calculated models for the case in which the analysis started with block B129.

All numerical models were configured with and without the soft soil layer, for the analysis of the influence of this layer on the group effect. The soft clay layer was replaced by the layer of greater resistance, hard gray clay, in the models without soft soil.

Only four constructive steps were considered, in order to reduce computational effort and calculation time. The steps adopted are equivalent to approximately 25%, 50%, 75% and 100% of the load calculated for the columns. It is noteworthy that 100% of the loading of each column corresponds to the last constructive stage simulated by Prellwitz (2016)Prellwitz, M.F. (2016). Aplicação de monitoramento de recalque para estimativa de parâmetro de interação solo-estrutura [Unpublished doctoral thesis]. Universidade Estadual do Norte Fluminense Darcy Ribeiro (in Portuguese)., that is, the end of the execution of the sealing masonry.

4. Results and analysis

The results of the numerical simulation, showing the vertical displacements of the soil, with settlement isocurves, of the models with the isolated pile B129c, with the isolated pile group B129 and with the pile groups located at a distance of 2B, 3B, 4B, 5B, 6B, 7B, 8B and 9B of the initially analyzed block is shown in Figure 6. The AA cut, shown in Figure 7, passes through the center of the isolated pile E129c. The location of the AA cut in the plan is identified in Figure 2. These results were obtained from models of subsoil with soft soil layer. Figure 8 shows the results of the same test sequence, however, without the soft soil layer.

The comparison between the models with and without soft soil shows the difference in the behavior of the subsoil caused by the soft gray clay layer. In the models with soft soil, there is a change in the vertical displacement pattern of the soil in the depth of the soft gray clay layer, where there is an increase in the volume of displaced soil, presenting a sudden reduction of the displaced soil in the depth of the hard clay layer, located just below the soft clay layer. Furthermore, the level of settlement in numerical models with soft soil was higher than in models without soft soil.

The results show the significant group effect on the displacements, evidencing the increase in the settlement due to the overlapping of the tension bulbs of sided-placed piles and pile groups. It was observed that this effect occurs for blocks located up to an average radius of five times the largest dimension of the block, becoming relatively unimportant for greater distances. This effect can be observed in Figure 9, which presents the curves of the relationship between the radius of influence (B) and the ratio of the block settlement in the model with a certain radius of influence and the block settlement in the model with the complete foundation, with all the foundation elements (ρ_iB /ρ_OC). There was no significant effect of the presence of soft soil layers in the analysis of the group effect between pile groups.

Several authors analyze the necessary spacing to eliminate the group effect between piles. Pressley & Poulos (1986)Pressley, J.S., & Poulos, H.G. (1986). Finite element analysis of mechanisms of pile group behaviour. International Journal for Numerical and Analytical Methods in Geomechanics, 10, 212-221. point out that for a group of piles loaded vertically, the spacing of 8 times the diameter (D) of the pile results in a failure mechanism characteristic of a single-pile, that is, without group effect. CGS (1992)Canadian Geotechnical Society - CGS. (1992). Canadian foundation engineering manual (3rd ed.). Canadian Geotecnical Society., in a foundation engineering manual, also analyzes the effect of pile spacing and states that, generally, group interaction doesn’t need to be considered when pile spacing is greater than 8D. Khari et al. (2013)Khari, M., Kassim, K.A., & Adnan, A. (2013). An experimental study on pile spacing effects under lateral loading in sand. The Scientific World Journal, 2013, 734292. observed that, for a ratio of S/D greater than 6, the interaction between piles and the group effects are eliminated, considering groups of laterally loaded piles installed in sand. Patrocínio (2018)Patrocínio, G.M. (2018). Análise paramétrica de grupos de estacas helicoidais à tração [Undergraduate thesis]. Universidade Federal do Rio Grande do Norte (in Portuguese). observed that piles work separately in a group with a ratio S/D equal to 5. Souri et al. (2020)Souri, A., Abu-Farsakh, M.Y., & Voyiadjis, G.Z. (2020). Evaluating the effect of pile spacing and configuration on the lateral resistance of pile groups. Marine Georesources and Geotechnology, 39(2), 150-162. observed, for piles installed in clay soil, that the group effect on lateral load capacity could be neglected for spacings greater than 5D. However, none of these studies analyze the group effect between pile groups.

However, it is noticed that the radius of influence of the group effect between pile groups is of the same order as the radius of influence observed for the group effect between piles of the same pile group. Therefore, it is understood that it is possible to compare the group effect between pile groups to the group effect between piles of the same block. It is understood, therefore, that the pile group behave similarly to the isolated piles, influencing the sided-placed pile groups by overlapping the tension bulbs, causing an increase in the settlement of the adjacent blocks.

It should be noted that the settlement observed in each block in the model simulating the complete foundation was up to approximately 5 times greater than the settlement obtained in the models with isolated piles and up to approximately 3 times greater than the settlement obtained in the models with isolated piles.

The group factor (G), according to the equation presented by Almeida et al. (2019)Almeida, A.K.L., Oliveira, P.E.S., Gusmão, A.D., & Maia, G.B. (June 4-6, 2019). Análise do efeito de grupo em fundações profundas através do comparativo da prova de carga estática com a medição de recalques de edifícios em Recife/PE e Salvador/BA. In Associação Brasileira de Empresas de Engenharia de Fundações e Geotecnia (Org.), 9º Seminário de Engenharia de Fundações Especiais e Geotecnia/3ª Feira da Indústria de Fundações e Geotecnia (pp. 1-10). São Paulo, Brazil: ABEF (in Portuguese). and Santos et al. (2019)Santos, D.S., Gusmão, A.D., Bezerra, R.S., Burgos, R., Ferreira, S., & Maia, G.B. (June 4-6, 2019). Análise da curva carga-recalque de um edifício residencial em estacas hélice contínua da cidade do Recife. In Associação Brasileira de Empresas de Engenharia de Fundações e Geotecnia (Org.), 9º Seminário de Engenharia de Fundações Especiais e Geotecnia/3ª Feira da Indústria de Fundações e Geotecnia (pp. 1-9). São Paulo, Brazil: ABEF (in Portuguese)., defined by the relationship between the settlement of the group of piles and the settlement of the isolated pile, was up to approximately 3. That is, the effect of overlapping the stress bulbs of neighboring piles generated a settlement up to approximately 3 times greater in the pile groups compared to the settlement of isolated piles, showing the influence of the group effect on the settlements.

Figure 10 shows the relationship between settlement (ρ) and the percentage ratio between the load in a given construction phase (Q) and the estimated load at the end of monitoring (Q_EM) obtained in numerical models with isolated piles, isolated blocks and with the complete foundation. The intervals, with 95% confidence, of the load-settlement curves refer to the values obtained in 9 blocks of the models, namely: 3 peripheral (B1, B6, B12), 3 intermediate (B15, B33, B129) and 3 central (B20, B23/30, B27).

5. Conclusion

The group effect between piles and pile groups was analyzed in this research from three-dimensional numerical modeling, using software based on the Finite Element Method. It has been shown that the group effect between pile groups is significant on building behavior. It was observed in numerical models that the group effect between pile groups is similar to the group effect between piles of the same group. This, due to the influence on neighboring pile groups, by overlapping the tension bulbs, resulting in an increase in the settlement of adjacent piles and pile groups. However, this proved to be negligible for pile groups located at a distance greater than 5 times the largest block dimension.

The generalized group effect, in the model with the complete foundation, increased the settlement by up to 3 times, in relation to the settlement of the isolated pile group, and up to 5 times, in relation to the settlement of the isolated pile.

The presence of the soft soil layer generated the vertical displacement of a larger volume of soil and caused higher levels of settlement, however, it did not present a significant influence on the group effect between pile groups.

List of symbols

c cohesion value

B largest dimension of the pile block

D pile diameter

E modulus of elasticity

Q load in a given construction phase

Q_EM load at the end of monitoring

R_lat maximum lateral resistance

R_t maximum tip resistance

S center-to-center space between piles

w permeability value

γ specific weight

ν Poisson coeficient

Ƿ settlement

Ƿ${}_{tb}$ settlement of the block in a numerical model with a certain radius of influence

Ƿ_FC settlement of the block in a numerical model with the complete foundation

Acknowledgements

This research was funded by CAPES - Coordination for the Improvement of Higher Education Personnel. The authors would like to thank the researchers who provided the data referring to the work analyzed, M.Sc Lucas Waked and Ph.D. Marta Prellwitz and the researchers who collaborated with the development of this research, M.Sc. Géssica Marquezini and M.Sc Nathani Zampirolli.

Data availability

The datasets generated analyzed in the course of the current study are available from the corresponding author upon request.

References

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