- 12903 -

A Preliminary Proposal: Executive

Control of Root Piles

Alfran Sampaio Moura DSc, Professor at the Department of Hydraulic and Environmental Engineering,

Federal University of Ceará, Fortaleza/CE, Brazil e-mail:alfransampaio@gmail.com

Diana Rodrigues de Lima MSc, Department of Civil and Environmental Engineering, Federal University of

Cariri, Cariri/CE, Brazil e-mail: drldiana@hotmail.com

Fernando Feitosa Monteiro Eng, Department of Hydraulic and Environmental Engineering, Federal

University of Ceará, Fortaleza/CE, Brazil e-mail: engffmonteiro@gmail.com

ABSTRACT During the execution of the foundations of buildings, the evaluation of the failure load is commonly determined by specific methods, which vary depending on the type of pile. The executive control of root piles are usually performed by load tests. This paper proposes an empirical formulation for root piles failure load estimation, using some variables that are monitored during the execution of the piles, using a digital speedometer. Therefore, slow static load test in three root piles monitored with diameters of 350 to 410mm were conducted. Several combinations between portions of tip resistance, shaft resistance, and the monitored variables, were tested using computer programs as Excel and Maple. Afterwards, an equation for the determination of the piles load capacity was estimated, as a function of the monitored variables, according to polynomial relations, exponential, logarithmic and linear combination, referencing to the value obtained in Van Der Veen`s method (1953). It was found that there is a correlation between the load capacity and the monitored variables, and the results obtained by the proposed expression were concordant with the reference values for the tested piles. KEYWORDS: Root Pile; Load Capacity; Executive Control.

INTRODUCTION One of the great challenges facing foundation engineering is to understand the behavior of

foundations, particularly with regard to load-bearing capacity and load transfer. The technical community uses analytical tools as common practice to determine the forces that act on deep foundations [1]. Among the many features of the foundation engineering, the executive control of piles is one of the subjects that demands a special regards, once the foundation is the structural element responsible for bear forces and its transference to the soil, generating a soil-structure interaction. The design and the type of foundation depends on the soil profile where the foundation is executed and on the acting load, in addition to other variables. On the design phase, foundation’s behavior is evaluated by an estimative of load capacity through empirical, semi-empirical and theoretical methods. On the

Vol. 20 [2015], Bund. 26 12904 foundation executive phase, load capacity of root piles are guaranteed by load tests. In deep foundations studies, there are several methods regarding the performance check; from traditional to modern methods, as the method described by Silva e Camapum (2010) [2], for continuous flight auger pile. In case of bored piles, variables measurement on field, as torque and energy, for instance, during pile execution, it becomes an effective implement in this process.

The aim of this paper is to propose a semi-empirical formulation that assists the executive control of root piles. The research is composed by studies on executive control and failure loads estimation methods; data storage; root piles execution monitoring; supervising static load tests on two Fortaleza’s sites; and finally, a semi-empirical formulation proposal using the data stored from the supervision at those sites, based on load capacity values estimated by ABNT NBR 6122(2010) [3].

ROOT PILES EXECUTIVE CONTROL The executive control is a necessary procedure for site verification of piles performance and such

procedure depends on the type of pile. In the design phase, the executive control occurs by means of semi-empirical formulations used in the prediction of load capacity piles. Those formulations use values of static penetration resistance or dynamic penetration resistance obtained in cone penetration tests (CPT) and standard penetration tests (SPT) respectively, where the SPT is the most utilized in Brazil. The coefficients determined in the model are affected by factors such as tests procedures, type of load test, determination of failure load, constructive procedures and its effects on soils properties. Among the semi-empirical methods for evaluation of load capacity, there are traditional methods used for driven and bored piles, and specific methods for root piles. Those are the most used methods: Aoki e Velloso (1975), Lizzi (1982), Salioni (1985), Cabral (1986) and Bransfond (1991) [4-8]. On Table 1 an abstract of those semi-empirical methods are shown.

Table 1: Semi-empirical methods for estimation of pile load capacity

For driven piles, the executive control can be done through the refusal verification, that correspond

to the medium pile penetration due to the application of 10 blows of the pile driver`s hammer; and from the elastic peal, that represents to the elastic portion of maximum displacement of the section of a pile , caused by the pile driving impact . Another technique of executive control for this type of pile is the dynamic load test for performance verification. In the case of precast piles as hand turned piles, Franki pile and Strauss Pile, it is possible to observe the material quality and its consumption to

Vol. 20 [2015], Bund. 26 12905 assure the correct execution of all steps of the process, checking tolerance as to angular deviations and performing static load tests (Figure 1) and pile integrity tests (PIT) as tools for executive control.

Figure 1: Static Load Test

For continuous flight auger pile, besides the traditional executive control methods, a different approach was proposed by Silva (2011) [10], in which he verified that the measured energy during the pile execution is directly proportional to its load capacity, therefore, enabling an accurate executive control during the execution of those piles.

The root pile, this work subject of study, is a bored pile with grouting, where an injection of compressed air is applied on the top of the pile to mold the pile shaft made of mortar; being able to be performed at various angles from zero to 90 degrees. The executive process of root piles is composed of the following phases: pile pointing, drilling, reinforcement introduction, mortar filling, revetment removal and application of compressed air. This type of pile has a differentiated execution process, thereat; it has some advantages over other executive processes, depending on local conditions and on soils properties that the pile will be performed.

According to Velloso and Lopes (2010), root piles can be performed in vertical or inclined orientations; it can also be performed in places with headroom limitations due to the small dimensions of its drilling equipment [11]. Root piles a high productivity and a high tension resistance; the possibility of crossing a wide variety of terrain including, in many cases, rock, boulders, concrete and masonry; the absence of vibration, the soil decompression and the low level of noise pollution are advantages of this foundation solution. The effective performance as a foundation element of root piles have great applicability in geotechnical jobs, such as foundations reinforcement, retaining walls for excavation protection, slope stabilization, off-shore foundations , foundations in places near buildings in poor condition or with restrictions on noise, rock foundation, among others.

Currently the executive control of root piles during its executive process is carried out in compliance with the following variables: consumption of cement bags, number of compressed air blows, comparing the excavated soil with the soil obtained from SPT through tactile-visual analysis, excavation duration, injection time and reinforcement introduction duration. The experience seems to be a determining factor in this case.

After the pile performing, the executive control is done by field tests, in order to check performance and integrity of the structural element. For performance verification, the field tests that stands out are the dynamic loading tests and the static tests or static load test, detailed above. For integrity verification, it is used the sonic integrity test, the Cross-Hole and Cross Hole Sonic Logging

Vol. 20 [2015], Bund. 26 12906 – CSL, whose purpose is to check the quality of the shaft concreting, through the emission and reception of ultrasound pulses. To determine the variation of the concrete characteristics along the pile shaft, it is performed the integrity test itself, which constitutes attachment high-sensitivity accelerometer at the top of the pile by means of viscous material, such as petroleum wax , and applying successive blows with a hand hammer. The signal obtained through accelerometer is scanned by a microcomputer and then integrated to obtain the velocity. This test may be used as equipment Pile Integrity Tester - PIT, which is the most usual integrity test in Brazil.

It is assumed that the feasibility of monitoring some parameters related to the soil resistance during the excavation could indeed be a tool of control or even be used in load capacity estimation. This monitoring constitutes a challenge due to their complexity and the external factors involved, such as perception and action of the operator; the lack of monitoring devices for the equipment used in the pile execution; and even the mud produced in the excavation phase.

METHODOLOGY The proposed methodology for the development this research was based on the preformation of the

following steps: literature review; choosing the research site; data collection; capacity of installed piles review; monitoring the implementation of piles; static load test execution; results analysis; and conclusions.

CASE STUDY Two locations were selected for this case study, site 01 and site 02; both locations are situated in

Fortaleza, CE. In both sites, root piles are being performed as the foundation of residential buildings. Site 01 is located at Armando Dallóllio Street in Guararapes neighborhood and Site 02 is located in an area between Justino Café Neto Street, Francisco Farias Filho and Marinha Holanda Street in Coco neighborhood. A view of the location of areas of study is shown in Figure 2, for the Site 01 and Figure 3 for the Site 02.

Figure 2: Location of site 01

Vol. 20 [2015], Bund. 26 12907

Figure 3: Location of site 02

MONITORING The monitoring consisted in the implementation and control measurements of some variables

preliminarily selected during the pile execution. Thus, to control pile preformation, the following variables were observed: execution time; air injection pressure; number of air blows and cement consumption.

The average angular velocity and the maximum angular velocity of the drill rotator; roller cone bit penetration elapsed time or penetration of the drill bit in a pre-determined excavation lengths; Excavation lengths (penetration) at regular prescribed time intervals; an equivalent linear distance traveled by the drill rotator, the measured time interval.

Measurements were performed using a digital speedometer, positioned in the rotator of the equipment used in the pile execution. The device provides a real-time display of the current speed, distance, riding time, time of digging and current time, and easy viewing of the maximum speed, average speed, total time, total distance and rotations per minute of the rotator. The device consists of three parts: (a) Magnet; (b) Sensor and (c) cycling computer, which were laid down in parts 1, 2 and 3 of the drill machine, respectively, as is shown in Figure 4.

Figure 4: Location of the parts of the device during monitoring

Vol. 20 [2015], Bund. 26 12908

Each rotation of the rotator, the magnet attached thereto approached the sensor, attached to the machine's hose, which in turn, sent the data to the computer, and the information it processed were made available on the clock display. The computer has been previously set based on the diameter of the rotator; and the values obtained were converted proportionally, based on the diameter of the roller cone bit or used in excavation. From the variables monitored during the execution of the analyzed piles, it was possible to estimate correlations using relationships of the elementary classical physics, the variables are the rotator spin frequency, the roller cone bit spin frequency and the roller cone bit penetration speed.

TESTS RESULTS AND DISCUSSIONS

Standard Penetration Tests The location of the probes contained in the reports of the sites 1 and 2 are shown in Figure 5 and

Figure 6, respectively. In site 1, the root pile performed has the following characteristics: 350 mm diameter; length of 12.0 m; grout injection pressure of 300 kPa and working load of 800 kN. In site 2, the two root piles have the following characteristics: 410 mm diameter; length of 12.00 m and 16.00 m; grout injection pressure of 300 kPa and working load of 1200 kN;

Figure 5: Location of the monitored pile in Site 1

Vol. 20 [2015], Bund. 26 12909

Figure 6: Location of the monitored piles in Site 2

In Figure 7, one of the standard penetration tests results is shown in a chart that presents the soil

profile and the blows x depth curve.

Figure 7: SPT results on Site 1

Analyzing the probe profile of Figure 7, the NSPT ranges from 2 to 42, reaching a maximum value

at 15.0 m and impenetrable at 22.37 m. The soil profile consists of the following materials: silty sand, clayey sand, silty-sandy clay and sandy clay, which is the thickest layer. The ground water level was identified at a depth of 6.74 m.

Vol. 20 [2015], Bund. 26 12910

In site 1, there were four standard penetration tests performed, Figure 8 shows the results of those tests, presenting a blows (Nspt) x depth curve, it also presents an average blows (Nspt) x depth curve, which was the curve used for the analysis on this paper.

Figure 8: SPT average on Site 1

According to the probe profile of Figure 8, it is clear that the soil has a slight variation of the resistance index up to 4.0 m; from 4.0m down to 8.0m depth, occurs a small variation of blows, converging at 10.0m and 12.0m. After this depth, the difference between blows has a slightly increase, converging right before the impenetrable layer.

The probe profile shown in Figure 9a, the NSPT ranged from 4 to 63, reaching a maximum value at 11.0 m; and reached the impenetrable layer at 23.10 m. The soil profile consists of layers of clayey silt and silty sand, which is the thickest layer. The ground water level was identified at a depth of 4.0 m.

According to the profile of probe shown in Figure 9b, the NSPT ranged from 4 to 65, reaching a maximum value at 22.0 m; and then reached the impenetrable layer. The stratigraphy is composed of layers of silty sand, silt and clayey silt, being a little silty sand layer thicker. The water level was identified at a 3.85m depth.

Vol. 20 [2015], Bund. 26 12911

(a) (b)

Figure 9: SPT results on Site 2

Static Load Tests According to Figure 10, the pile 1 received a maximum load of 1620 kN, applied in 9 stages of

loading, reaching a 15.10 mm maximum settlement. After unloading, it was observed a residual settlement of 10.10 mm. In this case, the 10th load stage to reach twice the workload was not applied because the pile showed verge of failure.

As shown in Figure 11, the pile 2 received a maximum load of 2400 kN (twice the workload), having 10 stages of loading applied, reaching a maximum settlement of 13.19 mm. After unloading, it was a residual settlement of 3.54 mm. The chart in Figure 12, shows that the pile 3 received a maximum load of 2400 kN, with 10 loading stages applied, reaching a maximum settlement of 25, 04 mm. After unloading, it was verified a residual settlement of 18.28 mm.

Vol. 20 [2015], Bund. 26 12912

Figure 10: Pile 1 Load-displacement curve

Figure 11: Pile 2 Load-displacement curve

Figure 12: Pile 3 Load-displacement curve

Vol. 20 [2015], Bund. 26 12913

Load Capacity Evaluation The load capacity evaluations of the three piles studied were made using the methods proposed

by: Aoki Velloso (1975), Lizzi (1982), Salione (1985), Cabral (1986), Brasfond (1991) and Aoki Velloso - Monteiro (1997) [4-9]; The results are shown in Table 2.

Table 2: Load capacity evaluation by semi-empirical methods

As shown in Table 2, with the exception of Lizzi’s method (1982) [5], estimates for pile 1 presented low variation with an average of 693.84 kN. For pile 2, the expected load capacities ranged from 2134.65 to 2697.14 kN, with an average of 2494.77 kN. It is noteworthy that in this case the values predicted by all methods were quite close, where, Cabral’s method (1986) [7], presented the lowest value. For the pile 3, the load capacity varied widely from 1205.19 to 3688.88 kN, whereas, similarly to what happened for the estimation for the pile 2, the lowest estimated value was obtained from the use of Cabral’s (1986) method [7].

Failure Load Evaluation As of the results obtained from the static load tests, using the method described in the standard

ABNT NBR (2010) [3], load capacities were determined for each pile. The failure load obtained for the pile 1 was 1550 kN. As for the pile 2, a 2400 kN failure load was determined, and for pile 3, a failure load of 2150 kN was obtained. The ABNT NBR (2010) [3] standard method indicates tensile strength values of the tested piles considering a conventional rupture. It was also applied the established Van Der Veen’s method (1953) [12] (Table 3), considering a physical failure of the pile.

Table 3: Results from Van Der Veen (1953) method

As shown in Table 3, the results obtained from Van Der Veen’s method for pile 1, pile 2 and pile 3 were 1626 kN, 2400 kN and 2430 kN respectively.

Monitoring Results The data obtained during the root piles execution were recorded and listed as follows :pile length,

execution time, air injection pressure, number of air blows applied, and cement consumption Such information is presented in Table 4.

Vol. 20 [2015], Bund. 26 12914

Table 4: Data obtained during the root piles execution

From Table 5, it is observed that the execution time of the piles 1 and 3, both 12.0 m long, differed greatly, and the cement consumption differed as well . Those differences are due to two main factors: suspension of the piles execution to solve mechanical problems in equipment, such as the disruption of conductive grout hose in pile 3 case; and differences between the soil profiles.

Table 5: Monitoring results during piles execution

On pile 1 excavation, it is observed a rotation increase due to the penetration progress, which occurs due to stress that the drill machine applies to the soil, overcoming the resistance of the same, generating a positive resultant force, resulting in angular acceleration of the drill. On pile 2 excavation, the increase in rotation through penetration reduction shows that the tip resistance controls the excavation process, once the skin friction is smaller, allowing the number of rotations increase, but without having penetration increase. On pile 3 excavation, the greater penetration time is explained by the high resistance index at the end of drilling. However, the number of rotations decreased because the skin friction was fully mobilized during the executive process, a fact that did not occur at the tip. Thus, there was a negative acceleration, resulting in the reduction of the angular velocity.

The load capacity of each of the three piles has been studied related to the monitoring variables in order to find an empirical expression that is able to assist the root piles executive control. Thus, two variables have been selected: rotation and penetration velocity, since the first variable is associated with the side friction and the second with tip resistance, as to previous analyzes. In addition to the rotation variable rotation and penetration velocity, a load capacity experimental prediction was done by analyzing the load capacity distribution along the depth, according to the following variables: tip resistance index (NSPT, tip) , average lateral resistance index (NSPT,lat), pilediameter (D), unit length (Δl) and pile lenght (L).

ROOT PILES EXECUTIVE CONTROL PROPOSAL On the executive control of root piles equation development, it was taken in consideration that the

total resistance is composed by two components : lateral resistance and tip resistance.

Vol. 20 [2015], Bund. 26 12915

Qult = Qlat + Qtip

Several combinations of Qtip,Qlat and variables described in the previous section were tested, using Excel and Maple computer programs. An estimation of the piles 1, 2 and 3 failure load was sought, with reference to the value obtained in the method of Brazilian standard ABNT NBR (2010) [3] as a function of the monitored variables, according to relations of polynomial, exponential, logarithmic and linear combinations. From the analyzes, it was possible to assume that the portion on the tip resistance, Qp must be composed by the following variables: Tip Area (Ap), penetration velocity (va) and tip resistance index (NSPT, tip); while the portion related to lateral friction (Qlat) should be composed of the following variables: Rotation (r), pile perimeter (U = πD), pile unit length (ΔL), pile length (L) and lateral resistance index (NSPT , lat).

The constants involved in the euqation formulation were determined through numerical analysis, using Excel and Maple programs. According to the expressions in test, equations systems were developed and depending on the system solution, constants were calculated. Subsequently, the solution found in the linear systems has been subjected to a calibration procedure based on the least squares method, so that for the three piles, the difference square sum of the values of the reference load capacity and estimated load capacity presented the smallest value. Thus, considering the load capacity Qult, is given by equation 1, equation 2 relates to the tip resistance portion, wherein the α coefficient is obtained from Table 6 due to the pile diameter,and equation 3 related to the shaft resistance portion as shown:

𝑄𝑄𝑝𝑝 = 𝛼𝛼𝐴𝐴𝑝𝑝𝑣𝑣𝑎𝑎𝑁𝑁𝑆𝑆𝑆𝑆𝑆𝑆,𝑆𝑆𝑇𝑇𝑝𝑝0,7

𝑄𝑄𝑙𝑙𝑎𝑎𝑙𝑙 =2,09𝑟𝑟𝑁𝑁𝑆𝑆𝑆𝑆𝑆𝑆,𝑙𝑙𝑙𝑙𝑙𝑙

1,22

𝑈𝑈𝑈𝑈

Table 6 – Values of α

The load capacity evaluation results for the piles 1, 2 and 3 using the proposed expression are shown in

Table 7 – Load capacity evaluation by the proposed method

According to Table 7, it is observed that the percentage error between the estimated values and the

reference values were, at least 0.2% and at most 12%. Figures 13, 14 and 15 presents a comparison between load capacity values estimated by the Brazilian standard (NBR 2122 / 2010) method, the Lizzi’s (1982) method, the Cabral’s (1986) method and the proposed method for the piles 1, 2 and 3.

(1)

(2)

(3)

Vol. 20 [2015], Bund. 26 12916 As shown in Figure 13, it is observed that the load capacity values for pile 1 obtained by the Lizzi’s (1982) method and the proposed method are almost coincident on a 5m depth. Estimates made by the proposed method outperformed those obtained by Lizzi’s method (1982) from 8 m length only. It is worth noting that for the 12 m length piles, the estimated Qult value who came the closest to the reference value (obtained by ABNT NBR (2010)), was the value predicted by the proposed method. The values obtained by Cabral’s (1986) method remained inferior to the others, throughout the depth [3-7].

Figure 13: Load capacity values comparison for pile 1

For the pile 2, according to Figure 14, it is possible to observe that the results estimated by Cabral’s method (1986) [7] remained at average variation range, up to the 9m mark, peaking at 11 m length. The values obtained by the proposed method and Lizzi (1982) [5] tend to approach from 13m depth. It can also be noted that a good agreement between the Qult value estimated by the proposed method and the reference value.

Vol. 20 [2015], Bund. 26 12917

Figure 14: Load capacity values comparison for pile 2

As shown in Figure 15, it can be observed a certain proximity of the results obtained by the

proposed method and Lizzi’s (1982) [5] method on a 9m. The load capacity values obtained for pile 3 by Cabral’s (1986) [7] method were below the others methods along the entire depth. The method that presented the nearest values to the reference value was the proposed method.

Vol. 20 [2015], Bund. 26 12918

Figure 15: Load capacity values comparison for pile 3

CONCLUSION The load capacity evaluation by semi-empirical methods of the piles 1 and 3 had a high variation,

with values up to 3 times in comparison to the lowest estimated value. However, for the pile 2, the variation was only 26 %. From the results of the load tests, it was observed that the pile-soil presented a safety factor of two for the piles 2 and 3; and 1.8 for pile 1. In the static load test of pile 1, it was observed a verge of physical failure at the end of the last load test stage applied, while in the static load test of pile 3, it was observed the occurrence of conventional failure. On the pile 2 static load test, there was no occurrence of failure, and it is necessary to estimate its failure load by the Van der Veen’s (1953) method.

It was observed a need of preservation for the machine-operator set during the performed monitoring, in order to minimize additional intervening factors that supposedly influence the executive process. The monitored variables were particularly useful for analysis, so it was possible to discuss trends of tip resistance and shaft resistance during the piles excavation.

It was found that there is a correlation between the load capacity and the monitored variables and the results obtained by the proposed expression were in agreement with the reference values for the piles 1, 2 and 3., in terms of order of magnitude. . However, for pile 3 the result was moderately

Vol. 20 [2015], Bund. 26 12919 higher than reference value. Compared to semi-empirical methods discussed in this paper, the estimates made by the proposed expression resulted in values that are more consistent with Lizzi’s (1982) method.

ACKNOWLEDGEMENTS The authors would like to thank, FUNCAP, CAPES, GEOBRASIL Company, the Federal

University of Ceará (UFC) and Federal University of Cariri (UFCA).

REFERENCES [1]. Jean Rodrigo Garcia, Paulo José Rocha de Albuquerque (2014) “Use of Numerical Modeling

to Assess Instrumented Root Piles Subjected to Axial Compression” [J] Electronic Journal of Geotechnical Engineering, 2014(19):1739-1752. Available at ejge.com

[2]. SILVA, CALOS MEDEIROS; CAMAPUM DE CARVALHO, J. Metodologia para o controle de qualidade dos estaqueamentos tipo hélice contínua - A rotina SCCAP. Revista Fundações e Obras Geotécnicas, v. 1, p. 50-57, 2010;

[3]. ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS. NBR 6122: Projeto e execução de fundações. Rio de Janeiro / RJ, 2010;

[4]. AOKI, N.; VELLOSO, D. A. An approximate method to estimate the bearing capacity of

piles. In: PAN AMERICAN CONFERENCE OF SOIL MECHANICS AND FOUNDATIONENGINEERING, 5., 1975, Buenos Aires, Argentina. Proceedings... Buenos Aires: ISSMGE, 1975. v. 1, p. 215-218;

[5]. LIZZI, F. The “paliradice” (root piles) - A state-of-the-art report. In: INTERNATIONAL SYMPOSIUM ON RECENT DEVELOPMENTS IN GROUND IMPROVEMENT TECHNIQUES, 1982, Bangkok, Thailand. Proceedings... Bangkok: ASIAN INSTITUTE OFTECHNOLOGY, 1982, v. 1, p. 417-432.

[6]. SALIONI, C. Capacidade de carga de estacas injetadas. In: SEMINÁRIO DE ENGENHARIA DE FUNDAÇÕES ESPECIAIS E GEOTECNIA - SEFE 1., 1985, São Paulo, Brasil. Anais... São Paulo: ABEF/ABMS, 1985, separata, v. 1, p. 13-27;

[7]. CABRAL, D. A. O uso da estaca raiz como fundação de obras normais. In:

CONGRESSOBRASILEIRO DE MECÂNICA DOS SOLOS E ENGENHARIA DE FUNDAÇÕES, 1986, Porto Alegre, Brasil. Anais... Porto Alegre: ABMS, 1986. v. 6, p. 71-82;

[8]. BRASFOND. Catálogo Técnico sobre Estacas Raiz, 1991.

[9]. MONTEIRO, P.F. Capacidade de carga de estacas- método Aoki-Velloso, Relatório interno

de estacas Franki Ltda, 1997.

[10]. SILVA, CARLOS MEDEIROS. Energia e Confiabilidade aplicada aos estaqueamentos tipo hélice contínua. Tese de Doutorado – Universidade de Brasília. Brasília / DF, 2011

Vol. 20 [2015], Bund. 26 12920

[11]. VELLOSO, D. A ; LOPES, F. R. Fundações: Critérios de projeto, investigação do subsolo, fundações superficiais, fundações profundas. São Paulo: Oficina de Textos, 2010

[12]. VAN DER VEEN, C. The bearing capacity of a pile. In: International Conference Of Soil Mechanics and Foundation Engineering, 3., 1953, Zurich, Switzerland. Proceedings... Zurich: ICOSOMEF, 1953. v. 2. p. 84-90

© 2015 ejge