Mechanical and Numerical Behavior of Groups of Screw (Type) Piles Foundedin a Tropical Soil of the Midwestern Brazil

C.C. Mendozaa, R. Cunhab, A. Lizcanoc

aPilot University of Colombia, Bogota, Colombia, Department of Engineering, Civil EngineeringbUniversity of Brasılia, Brasılia - DF, Brazil, Department of Civil and Environmental Engineering

cSRK consulting (Former director of geotechnical research group at the University of Los Andes), Vancouver, Canada

Abstract

This paper presents and discusses the behavior of standard groups and piled rafts constructed with helical screw pilesfounded in the typical soil of the Federal District of Brazil (DF). The paper initially characterizes the soil deposit ofa new Experimental Site in the DF via laboratory (standard characterization, triaxial) and field (standard penetrationand flat dilatometer) tests. It then moves to explain a recently adjusted (hypoplasticity) constitutive model that takeson consideration the inherent soils structure to simulate the behavior of this typical geotechnical material. The modelwas calibrated via point load test analyses and incorporated into a finite element methodology (FEM) routine internalto the traditional Abaqus software. Real scale field load tests on standard pile groups and piled rafts executed withthis pile type were carried out in the new site. FEM analyses were used to calibrate the model and to expand theknowledge on the shearing mechanisms, generated stresses, displacement fields, load sharing, group e�ciency, andon the contribution of the supporting raft to the overall systems performance. Conclusions of practical and academicinterest are given for this new type of foundation employed in the region.

Keywords: Standard pile group, piled raft, hypoplasticity, finite element analysis, load test, tropical soil, foundationdesign

1. Introduction

The city of Brasilia, the Brazilian capital, is situatedin the Midwest central area of the country, a flat plateauwith a common (tropical) soil deposit. Generally speak-ing, this region contains in its initial few meters a highlyweathered, laterized and collapsible clayey type soil, lo-cally known as the Braslia porous clay. Research the-ses and past publications from the University of Braslia(UnB), as those from Araki [1], Cunha et al. [2], Car-doso [3], Mota [4] or Anjos [5] have already extensivelystudied this material and others in the DF. Since it cov-ers more than 80% of the districts surface, it is also log-ical to study the behavior of deep foundation systemsin a site with similar characteristics, specially for piledrafts where the soil-raft contact do intervene in the me-chanical performance of the system.

Alluvial Anker piles, as locally known in Braslia, area modified type of the common helical screw pile (welldescribed by Clayton [6]). It has recently been intro-duced in construction sites in this city [7] where thesoil reinforcement is done underneath bridge or viaduct

abutments. It can also be adopted for light foundationsin similar structures or others (transmission towers, si-los, etc). Although it is not a new foundation technol-ogy, its usage, design, and mechanical behavior, stilllacks a better understanding for the tropical deposits inwhich it is currently being founded.

Therefore, this paper focuses on the experimental be-havior, on the numerical simulation, and on the derivedtraditional variables for group and piled raft systems,constructed in the tropical soil of the DF with this piletype.

Real (large) scale load tests on several foundationsystems constructed in a new Experimental Site in thiscity were carried out. The site was thoroughly inves-tigated via laboratory and in situ tests in order to pro-vide backbone data to calibrate geotechnical models.The hypoplasticity was then adopted as the frameworkfor the constitutive model to be assessed herein. Thismodel, with the incorporation of the soils cementingstructure, was further developed and incorporated into anumerical FEM (Abaqus) routine. With this tool, it waspossible to carry out numerical simulations in which the

Preprint submitted to Computers and Geotechnics September 3, 2014

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load curves, the stress and strain regimes, the failureand working loads, and the load share from the sys-tems components (soil, pile, raft), among other vari-ables, could be assessed. Some of them were directlycompared to the experimental instrumented data (as theload versus displacement curves), enabling conclusionson the mechanical behavior of the loaded systems.

The paper discusses and concludes on aforemen-tioned issues that are undoubtedly of interest for prac-tical design engineers or researchers in this area. It isbased on a recently defended D.Sc. Thesis (Mendoza2013 [8]) of the University of Brasılia.

2. Experimental Site

All the experiments are related to a new Experimen-tal Site located in Solotrat Ltd’s headquarters in the DF,in the outskirts of the city of Brasılia. Fig. 1 graphicallydepicts the location of the city within the national (Mid-west), regional (DF) and local (district) context. Ap-proximate coordinates of the site are 15�48’59”(S) and47�57’58”(W), with a mean elevation of 1084 m abovesea level.

Figure 1: Approximate location of Solotrat’s site (Google Maps and

Earth and Arcview).

Within this site several standard penetration tests with(SPTT) and without (SPT) torque measurements werecarried out, together with Marchetti Dilatometer tests(DMT), and load tests on foundation systems (isolated-I, standard groups-PG and piled rafts-PR), within a par-ticular arrangement depicted in Fig. 2. Undisturbed soilblocks were also retrieved from a trench excavated inthe site (see this same figure).

As previously noted, the main di↵erence between theloaded systems was the contact (PR), or not (PG), ofthe top raft with the superficial soil during tests. In theparticular conditions of the former case, it was strictly

followed the general definition of Janda et al. [9] for PRsystems.

As one can finally note in Fig. 2, systems of 1 to 6piles (PG and PR) were tested with distinct internal ar-rays for some cases, which demanded a multitude ofreaction piles (also depicted) all around the systems.

Figure 2: Location details of systems and in situ tests.

3. Soil Characteristics

3.1. In situ testsSPT, SPTT and DMT tests were carried out in the site

to geotechnically characterize it and to provide an initialbasis of model parameters for subsequent analyses. Dis-turbed samples from the SPT thick-walled standard tubewere also retrieved, and helped in the visual & tactileassessment of the distinct soil layers. All tests were car-ried out in accordance to the Brazilian NBR6484 (2001)standard [10].

Fig. 3 presents both SPT and SPTT results, in termsof blow counts and peak torque. It also describes thegeneral division for the layers at the site, in accordanceto the following depths:

• 0 to 5 m: reddish, very soft to soft, laterized siltysand (Braslia porous clay), with water level around4.5 m;

• 5 to 8 m: brownish, medium to sti↵, laterizedsandy silt (Braslia porous clay);

• 8 to 9 m: white, sti↵ to hard sandy silt (transitionlayer);

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• 9 to 14 m: brownish, very sti↵ to hard silty clay(saprolite of slate);

• Above 14 m: yellowish hard sandy silt (saproliteof slate).

Flat Marchetti dilatometer tests were carried out, inaccordance to the U.S.A. ASTM D6635-01 standard[11]. Unfortunately just one sounding with this test waspossible, as the blade got stuck at around 8 m depth, anddamaged the rods.

Figure 3: Stratigraphy and SPT-SPTT results

Fig. 4 presents the intermediate variables from theunique DMT carried out (respectively the indexes forhorizontal stress and material). From this data one con-cludes that the material behaves as normally consoli-dated silty sand up to around 5 m and as an overconsol-idated sandy silt from 5 to 8 m.

3.2. In situ testsLaboratory tests were performed not only to comple-

ment the assessment of parameters of this new site, butalso to evaluate the performance (& calibrate) a newrheological model for the soil. All tests were done withan undisburbed block sample retrieved at around 3 mdeep in the site, inside a trench (see Fig. 2) excavatedfor this purpose.

Characterization tests were composed of sieving andsedimentation analyses, plus Atteberg limits. Based onthat, the sample was classified as CH by the UnifiedClassification system, with a plastic Index of 12% and anatural unit weight around 15 kN/m3.

Ten triaxial tests in total were also performed, someof them with distinct (shearing) velocities, others withrelaxation of stresses, some with distinct stress path tra-jectories and one test with an unstructured sample. Alltests were done in saturated conditions.

Figure 4: DMT main results.

Four samples were initially submitted to ananisotropic consolidation in the triaxial chamber, withstress ratios (⌘ = deviatoric/mean stress - q/p0) respec-tively equal to 0.5-0.0, 0.3, and 0.5. Fig. 5 presents suchresults.

The first consolidation was performed with a stressratio of ⌘=0.3 (Fig. 6) to a constant vertical strain ve-locity, and the point where relaxation begins, and fin-ishes, has a mean e↵ective stress of 335 kPa. After that,consolidation continued till a p0 of 535 kPa, being un-loaded to 5 kPa afterwards. The sample was then loadedagain to a p0 of 580 kPa. In addition, a test with thissame stress path was made in a sample without struc-ture (Fig. 6). Two other samples were then anisotropi-cally consolidated from the initial unload stage, with ⌘equals to 0.0-0.5 and 0.5, as noticed in this same Fig. 5.

Figure 5: Consolidation paths in triaxial compression at distinct stress

ratios.

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Figure 6: Curve of consolidation for triaxial compression with ⌘=0.3.

The second consolidation was performed with astress ratio of ⌘=0.5 to a mean e↵ective stress (p0) of140 kPa, under a constant vertical strain velocity, beingfollowed by an unloading to the isotropic state (⌘=0.0).Subsequently, in the same sample, consolidation wasperformed in isotropic conditions (⌘=0.0) to a p0 of 590kPa. Fig. 7 shows the consolidation curve for the sam-ple at ⌘ equals to 0.5-0.0, while Figure 8 a similar oneto an ⌘ respectively equal to 0.5.

Figure 7: Curve of consolidation for triaxial compression with ⌘ =0.5-0.0.

From Fig. 7 it is observed the change of preconsolida-tion stress with the change of the stress trajectory. Notenevertheless that both two trajectories do return to thesame consolidation line.

In Fig. 8 a stress ratio of 0.5 was adopted, togetherwith variable velocities of vertical strain. The test wasperformed with a deformation rate of 0.01 mm/min,being suddenly changed to 0.001 mm/min afterwards.This variation was done at two distinct e↵ective stresslevels to check the response to velocity rate e↵ects. Theresults are also consistent with the work presented byTatsuoka et al. [12], but on a smaller scale.

Six extra triaxial tests were also made, under drainedand undrained shearing conditions. Such results wereused to obtain both the critical state parameters and

Figure 8: Curve of consolidation for triaxial compression with ⌘=0.5.

the deformability moduli of the superficial soil. Fig. 9presents the stress paths in the q x p0 environment.

The three samples sheared under undrained condi-tions (with p0 of 110, 200 and 300 kPa) had a constantvertical deformation rate of 0.05 mm/min. Results inthis figure show that the paths reach the critical stateline and continue through it, leading to a gain of shear-ing resistance with strain. This is not a typical behaviorfor clays, as illustrated by Roscoe et al. [13].

Figure 9: Stress path in drained and undrained conditions for normally

consolidated soil.

Moreover, it was also observed that the higher werethe confining pressures the higher were the obtainedpeak deviator stresses at unitary strain (Fig. 10b). Atypical behavior in soil mechanics, according to Whit-low [14].

The other three samples sheared under drained con-ditions (equally with p0 of 110, 200 and 300 kPa) weretested with distinct values of deformation rate, as shownin Fig. 10a. Again, to check on the soil’s response to ve-locity rate e↵ects. Results in Fig. 9 also show that thepaths reached the critical state line. It’s noticeable thatshear velocity has no influence on test results, indicatingthat this soil has virtually no viscous e↵ect.

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(a) (b)

Figure 10: Stress and strain curves from for (a) CID triaxial tests and(b) CIU ones.

An important aspect is the presence of cementation,similar to those reported by Lagioia and Nova [15] forcemented soils. Basically one notices that, to a mean ef-fective stress of 110 kPa, the cementing influence in thesoil sti↵ness corresponds to 7% of the axial strain. To200 kPa of stress, the influence reduces to 2 to 4% of theaxial strain, and to 300 kPa the corresponding influenceof the cementation decreases to values as lower as 1.5%of the axial strain (Fig. 10a). This is an important aspectsince these values are similar to instrumented deforma-tions of typical geotechnical structures.

3.3. Soil parameters

Using the interpreted data from in situ tests via wellknown (empirical) equations proposed by Skempton[16], Meyerhof [17], Clayton [18], Marchetti [19] andLacasse & Lunne [20], together with previously shownlab. (triaxial) data, it was possible to derive estimates forstrength and deformation parameters at each soil strata.

This geotechnical interpretation set was comple-mented by published results from the traditional UnBExperimental Site, which has a similar soil profile (seeAraki [1], Mota [4] and Anjos [5]).

Table 1 presents the original derived parameters,valid in the context of a Mohr Coulomb rheologicalmodel, as initially interpreted for the Solotrat site. Lab-oratory results have also confirmed that shearing veloc-ity is not a key aspect of the problem, hence, constitutivemodels without the viscous e↵ect can be undoubtedlyused without detriment to the analyses.

In Fig. 6 the e↵ect of the structure of the soil is relatedto the di↵erences between the consolidation line of theunstructured sample and the corresponding one of thestructured sample. Similar e↵ect is observed in Fig. 9,where cohesion is noted (in the space q x p0) basicallygiven by the structure of the soil.

Table 1: Elasto-plastic (Mohr Coulomb) parameters interpreted forSolotrat’s Experimental Site

Parameter Symbols Unit Value

First layerFriction angle � 29Elasticity modulus E MPa 9Cohesion c kPa 14Poisson’s ratio µ - 0.35

Second layerFriction angle � 35Elasticity modulus E MPa 38Cohesion c kPa 20Poisson’s ratio µ - 0.29

Third layerFriction angle � 39Elasticity modulus E MPa 60Cohesion c kPa 50Poisson’s ratio µ - 0.27

Fourth layerFriction angle � 35Elasticity modulus E MPa 43Cohesion c kPa 28Poisson’s ratio µ - 0.29

4. Pile Load Tests

Several foundation systems were constructed in theExperimental Site, side by side in a layout surroundedby reaction piles that has facilitated the load tests.

The tests started on December 2010 (isolated pile)and finished on June 2011 (6 piles PR). For each system(or no. of piles), the tests with the soil in contact withthe raft (PR) were always carried out first, followed bythose without contact (PG), done in the same previouslytested system.

One should note however that by the fact that PG sys-tems were carried out at the same previously tested ones(PR), and that an excavation process took place fromone series of tests to the others, that some inherent in-put error may be included in the results, given loading-unloading e↵ects. Nevertheless, it is believed that theerrors may be of small magnitude to hinder the tenden-cies of the correct results.

Fig. 11 depicts the general characteristics of thetested systems.

The triangular shaped system with 3 piles was solelytested with the contact soil x raft (hence a PR). The sin-gle pile also had this contact with the top block (whichneeded to be constructed to load it), being also consid-ered as a PR system. PG systems were simulated byexcavating a gap underneath the raft before the tests.

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Figure 11: Arrangement, location and characteristics of the tested foundation systems.

For the purpose of this paper only the tests loadedin the vertical direction will be presented, although lat-erally loaded tests were also performed (see Mendoza2013 [8]).

4.1. Alluvial Anker pile

As previously stated, Alluvial Anker piles were con-structed, and formed the basis of the foundation type inthe loaded systems.

Fig. 12 to Fig. 14 show the general aspects of this par-ticular foundation, as well as a typical drilling hydraulicmachine.

Figure 12: Self-drilling steel tube and open tip-Alluvial Anker pile’s

base and body.

The piles were either executed with a nominal diam-eter of 17 cm and 12 m in length (reaction piles), or 13cm dia. and 8 m in length (tested piles).

The piles are done by continuous drilling with simul-taneous injection of a coolant fluid, which can be wa-ter or a water-cement mixture (the latter was adoptedherein).

The fluid is injected through a rigid hollow steel tubewith an enlarged base (cone shaped cutting edge. SeeFig. 12). The tube itself forms the structural element ofthe pile, and is not withdrawn after soil excavation. Itis totally immersed, and surrounded, by the pressurizedwater-cement fluid injected during self-drilling and postdrilling stages. Once cured, this fluid forms the corru-gated shaft of the pile.

Figure 15 schematically depicts the distinct execu-tion stages of this pile type, from the assemblage in thedrilling machine to the final injection stage.

Perhaps one of the main advantages of the AlluvialAnker is the execution time. Given the fact that it prac-tically has in the same stage both soil excavation andpiles shaft reinforcement & execution, it can be indeeddone in a fast manner.

Fig. 16 and Fig. 17 bring the average execution timesfor each of aforementioned diameters, during drillingand subsequent post-drilling (injection) phases.

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Figure 13: Adopted drilling machine.

Figure 14: Finished top of Alluvial Anker pile.

Figure 15: Schematic phases of the Alluvial Anker pile execution (af-

ter Barbosa [7])

As one can notice, for the (optimum) conditions ofthe Experimental Site, and taking on account that nomajor drawbacks happened during field operations (i.e.,Murphy’s Law did not apply in this case), an averageexecution time of 15 min. was accomplished per pile.This relates to the total time considering all executionphases.

Figure 16: Average time spent for drilling phase.

Figure 17: Average time spent for injection phase.

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4.2. Load test proceduresAll tests were done in accordance to the Brazilian

NBR 12131 (2006) [21] standard for slow maintainedpile load tests.

Therefore, they consisted of equal increments by nomore than 20% of the piles workload, followed by theload stabilization for at least 30 min, during which dis-placement readings (1, 2, 4, 8, 15 and 30 min) are taken.The testing load is raised to a final value equals to twotimes the predicted workload of the pile, when the sys-tem is finally unloaded.

For the load tests a hydraulic jack of 2000 kN capac-ity was adopted, together with a load cell of 1 kN ofinternal resolution. Displacements were measured byfour analogical dial gauges with resolution of 0.01 mmeach, installed all around the base plate of the jack.

Fig. 18 shows the arrangement of the testing elementson top of the superficial rigid raft, while Fig. 19 a typicalset up with reaction frames and reaction piles.

Figure 18: Details of measurement system and rigid raft.

Figure 19: Typical arrangement of the static load test.

4.3. Testing resultsIn total, twelve load tests were carried out in this site,

being seven related to PR systems and 5 to PG ones.

Fig. 20 and Fig. 21 respectively show the obtained re-sults for both systems.

Figure 20: Load test results for PR systems.

Figure 21: Load test results for PG systems.

Both figures contains a linear load x settlement rela-tionship that represents the conventional failure load cri-terion, in accordance to the Brazilian NBR 6122 (2010)[22] standard. It was therefore based on this criterionthat the ultimate load of each system was defined, in theintersection between the standard line and the experi-mental load test result.

In some few cases where such intersection did notoccur, due to an insu�cient displacement of the testedpile, the results had to be extrapolated by the Van derVeen (1953) technique [23] (red line in Fig. 20 andFig. 21).

Fig. 22 shows the failure loads estimated by afore-mentioned methodology, for both foundation systems.

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It is clearly noticeable that PR systems do have a rea-sonable increase in load given the contact of the raftwith the superficial soil. The average increase was inthe range of ⇠18% of the conventional failure load ofthe PG systems, which is not negligible.

Figure 22: Ultimate (failure) load results.

5. Constitutive models used in FEM

The selected constitutive models to the finite ele-ment simulations were, respectively, the hypoplasticwith structure, the standard elastoplastic one and thesimple elastic model.

5.1. Hypoplastic with structure modelThe first tested model was the hypoplastic with struc-

ture. This model was adopted in the first layer of thestrata (see Table 1), where the soft Braslia porous clayprevails. It was further incorporated into the finite ele-ment simulations, yet to be presented.

In the present paper the proposal made by Masın [24]was chosen given the simplicity required to implement itinto the code, as well as recorded good accuracy. How-ever, a brief discussion of the soils structure and the con-stituent models with structure is presented next.

5.1.1. Introduction in the structured soils and constitu-tive models

The structure models were developed by research ofBurland [25], Leroueil and Vaughan [26], Adachi, etal. [27], Anagnostopoulos, et al. [28], Cuccovillo andCoop [29], Cotecchia and Chandler [30] among others.It has shown the di↵erence in the behavior of recon-stituted and natural soils, explained such di↵erences asthe lack of structure (arrangement of particles and bondsbetween particles) associated to natural soils. Based on

that, some researchers tried to develop constitutive for-mulations that could take on consideration the structurese↵ect. Among them, one can name Gens and Nova [31],Vatsala, et al. [32], Liu and Carter [33], Masın [24], Yanand Li [34]. The majority of formulations change theshape and size of the state boundary surface (SBS) ofthe soil by two state variables (in functions of the stressstate): the first is sensitivity (s) and second is the shift ofthe SBS towards the tensile stresses zone (natural cohe-sion). It means that the stress tensor (�) of the model isthe tensor without structure (�Reconstituted), besides of thestress tensor for the soil structure (�S tructure) (Equation1), with a parallel coupling. This proposal has alreadybeen made by Baudet and Wu [35] and Vatsala, et al.[32], where the stress tensor for soil structure (�S tructure)is a simple linear elastic relation which disappears withthe increasing stress.

� = �Reconstituted + �S tructure (1)

5.1.2. Hypoplastic with structure modelThe theoretical framework of hypoplasticity was de-

veloped by Kolymbas [36] and defined with a contin-uous tangential sti↵ness of the strain rate (Niemunis[37]). Afterwards Kolymbas performs the formulationof its hypoplastic model and since then there have beenseveral modifications as presented by Wu [38], Wolf-fersdor↵ [39] and Niemunis [37] among others. Pre-vious models were proposed for granular soils, never-theless, there have been extensions to represent the be-havior of fine soils as proposed by Niemunis [37] andMasın [24] to natural soils (with structure).

The modification in the hypoplastic with structurewas the incorporation of a structure degradation law bymeans of the proposal made by Baudet and Stallebras[40]. The proposal consists in the incorporation of alarger size swept-out-memory (SOM) surface (this is aclose approximation of the SBS), by altering Hvorslev’sequivalent stress by a scalar (s) value (in a constant vol-ume section through SOM), as illustrated in Fig. 23.

The modification done by Masın [24] basically adds3 new parameters (s0, k, A). The first (s0) is the ini-tial value of the state variable of the structure factor orsensitivity (s), shown in Equation 3 (law of degrada-tion). The other factors in the equation are the (s f ) fac-tor, which is the limit to a stable state with a value of 1(Fig. 23); the (k) factor, which is a parameter that con-trols the degradation of the structure; �⇤ which is theslope of the virgin isotropic compressibility line, in adouble natural logarithm chart; (✏d) (Equation 4) whichis a damage strain that depends on the volumetric andshear strain rates; and the (A) factor which controls the

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importance of the shear strain, with values in the range0 < A < 0.5. A complete mathematical formulation ofthe model is given in appendix A.

Figure 23: Isotropic compression behavior of natural and reconsti-

tuted soil (after Mas´ın [24]).

The model is represented by Equation .1, where�T

isan objective stress rate, D is the Eulers stretching ten-sor, L and N are fourth and second order (Masın [24])invariants. The model is written as a nonlinear increas-ing function of time to correlate stresses and strains.

�T

= L : D + N k D k (2)

s = � ⇤

�⇤(s � s f )✏d (3)

✏d =

r✏2

v +A

1 � A✏2

s (4)

The other five variables of the model can be obtainedfrom a natural or a reconstituted sample, tested in a tri-axial isotropic consolidated chamber.

The variables (�⇤, ⇤, N) are similar to those inthe Cam-Clay (CC) model, and can be assessed in adouble logarithm chart. The variable (r) is obtainedfrom undrained triaxial tests as the ratio between theundrained bulk and the shear moduli. The (�c) angleis analogous to the (M) parameter, i.e., the slope of thecritical state line on the CC model.

The hypoplastic model with structure was then im-plemented, and validated, with the incremental driverprogram (Niemunis [41]). This is the program to imple-ment constitutive models to the level of a Gauss point.This program follows the same methodology of mate-rials in the Abaqus software. It was written in Fortrancode, and inputs increases of strains and returns stressincrements.

Given the previously mentioned (Section 3)anisotropic consolidations, CID and CIU triaxialdata, it was possible in this stage to directly comparenumerical and experimental results. Fig. 24 to Fig. 26show such comparisons, illustrating a reasonably goodagreement of all trajectories, in the spaces e x p0, qx p0 and q x ✏a. Table 2 specifies the derived modelparameters, from aforementioned calibrations.

The first tested model was the hypoplastic with struc-ture. This model was adopted in the first layer of thestrata (see Table 1), where the soft Braslia porous clayprevails. It was further incorporated into the finite ele-ment simulations, yet to be presented.

(a)

(b)

(c)

Figure 24: Comparison to triaxial results: a. Compression test with⌘=0.0-0.5; b. Compression test with ⌘=0.3; c. Compression test with⌘=0.5.

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Figure 25: Comparison of stress paths for CID and CIU triaxial tests.

Figure 26: Left: Comparison of stress paths in drained conditions;

Right: Similar for undrained conditions.

Table 2: Model parameters with simulations

⇤ �⇤ N �c r A s k

0.0022 0.060 2.13 31 0.35 0.4 1.5 2.5

5.2. Elasto-plastic model

The second model tested herein was a simple, stan-dard, elastoplastic model that responds to the knownMohr Coulomb failure criteria. This model has beenimplemented for the finite element simulation. Due tofact that this model has only four parameters and dueto the fact that all of them have a physical explanation,it has a great popularity in the geotechnical practices(Johnson et al. [42]). Given its simplicity (and lack ofdata from a deeper profile), this model was adopted inthe remaining 3 layers of the strata (see parameters inTable 1). It was also further incorporated into finiteelement simulations, yet to be presented.

In the elastic range, the relationship between stressand strain tensor is linear, with two parameters: Young’smodulus (E) and Poisson’s ratio (µ). This behavior isvalid until the stress-path reaches the yield envelope, at

which time plastic deformation starts. The yield enve-lope is of a Mohr Coulomb type and there are with ittwo soil parameters (�= friction angle of the soil and c=cohesion) associated.

5.3. Elastic model

The third model is an elastic model. This is a verysimple model where the relationship between the stressand strain tensor is linear by means of a elastic modu-lus, which is function of the Young’s modulus (E) andPoisson’s ratio (µ) (Desai and Siriwardane, [43]). Thismodel is used in FEM analyses of pile foundations un-der assumptions that the piled raft is infinitely rigid incomparison with the soil (therefore the soil deforms firstand to a larger extent).

6. Finite Element Analyses

Finite element (FEM) analyses of all foundationsystems were carried out in order to verify the geotech-nical parameters and adopted layering (from previoussections), and the suitability of the rheological modelsto properly simulate the physical phenomena. Besides,the FEM analyses were used to further calibrate theparameters (allowing slightly value changes) in orderto use this technique to predict testing scenarios ina subsequent future stage (which, by the way, is notcovered here given space limitations).

The initial simulation steps and the final calibra-tion have also expanded the knowledge on the shearingmechanisms, generated stresses, displacement fields,load share, pile e�ciency, and on the contribution ofthe supporting raft to the overall system’s performanceto be presented in this Section.

6.1. FEM environment

Abaqus environment was used to enable the 3D anal-yses of the systems. In all cases, boundary e↵ects wereavoided by placing the center of the raft 30 (individualpile) diameters away from lateral frontiers. Likewise,a distance of 1/2 pile length was left between pile tipsand the lower end. Fig. 27 schematically depicts the ge-ometry for the 6-pile (PG and PR) cases.

Given aforementioned aspects of the geometry, thenext stage was the generation of the 3D mesh. In orderto reach a final, optimum, condition in terms of sim-ulation time, stability and quality of response, severalelements were tested in terms of type, size, distributionand number (see Mendoza 2013).

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Figure 27: Boundaries for analyses of 6-pile systems.

Hence, C3D8 (continuous and 8 nodes), C3D8R(continuous, 8 nodes, and reduced integration) andC3D8P (continuous, 8 nodes with pore pressure mea-surement) were respectively selected for the dry soil /pile elements and the saturated soil. Fig. 28 shows thegeometry for the 1-pile (PG and PR) cases, and delin-eates contour conditions that were similarly adopted forall analyses.

Figure 28: Mesh for analyses of 1-pile systems.

Once the geometry was created, loads in the modelwere applied in three sequential stages, as follows: Geo-static initial overburden stresses; individual pile excava-

tions (via element extraction); and system loading (viaconstant strain rate till a total vertical displacement of15 cm).

The latter stage was carried out in drained mode, onceraft elements were inserted into analyses (with gap, PG,or without, PR, to superficial soil). The water level anda naturally consolidated K0 were also considered for thesoil layers.

Figure 29 depicts the initial conditions adoptedthroughout the analyses.

Figure 29: Initial conditions of FEM analyses.

6.2. FEM simulations

Comparisons between the numerical predictions af-ter initial adjustments and calibrations, and experimen-tal data, are presented in Fig. 30 and Fig. 31 in terms ofthe overall load versus settlement curve.

Figure 30: Comparison of results for PR systems.

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Figure 31: Comparison of results for PG systems.

The results clearly show that the FEM simulation wasable to grasp the overall physical behavior obtained inthe field, at least in terms of the generated external dis-placements. Assuming that this outcome su�ces to as-sure a reasonable understanding on the other aspects ofthe shearing mechanism, some extra (numerical) resultswill be presented and discussed next.

Fig. 32 for instance depicts the vertical displacementsand stresses generated in the surrounding soil of the 5pile PR system. Although not shown here (but presentedin Mendoza 2013 [8]) this result is somehow similar tothose from the other PR systems. It was noticed that, ingeneral, the stress bulb (influence of up to 10% of ap-plied stresses on raft) and the displacement bulb (like-wise for raft displacement) can stretch vertically andhorizontally around the raft. A practical average num-ber would be 4 times the shorter dimension of the raft inthe vertical direction, and 2 times in the horizontal one.

Besides, the bulbs also extend vertically from the tipof the piles to a dimension of around 2 to 3 times thepiles diameter.

The main results from the numerical analyses interms of the direct comparison, and individual assess-ment, of the distinct PG and PR systems are given next.

(a) Vertical displacements gener-ated in the simulation.

(b) Vertical stress generated in thesimulation.

Figure 32: Soil displacements and stresses around 5 pile PR systemand along depth.

6.3. Main results from FEM analyses

6.3.1. Pile E�ciencyE�ciency factor (⌘⇤) was calculated in accordance to

the definition expressed in Equation 5. It is basically arelationship between the ultimate capacity of the groupover the ultimate capacity of a single pile similar tothose in the group, without inclusion of any e↵ect ofthe raft. Group e�ciency (Ge) on the other hand wascalculated in accordance to Equation 6. This variableexpresses the relationship of the average (pile) load inthe group divided by the load of a (similar) single pileat the same vertical displacement of the group. Bothequations are solely valid for the PG systems.

PPG = ⌘⇤

npX

i=1

PP (5)

Where PPG=ultimate load capacity of the group; ⌘⇤=e�ciency factor; np= number of piles; and PP= ultimatecapacity of a similar single pile.

Ge =

Pwrknp

Psng(6)

13

Where Ge= group e�ciency; Pwrk= working load ofPG system (equal to ultimate / 1.5); np= number ofpiles; and Psng= load of a similar single pile at samegroup displacement.

Given the fact that the single pile had a contact of theraft with the soil (being considered as a PR), its experi-mental value could not be employed in Equations Equa-tion 5 and Equation 6. Hence, Table 3 solely presentsthe results from the numerical simulations.

An average e�ciency factor of 0.97, i.e., approxi-mately one, was obtained indicating that with the givengeometric disposition of the systems (pile to pile dis-tances), there were almost zero detrimental e↵ects givenby the superposition of individual stress and displace-ment (pile) bulbs. It also means that pile group failurerather than block failure did happen (taking on accountnomenclature given by Mandolini et al. [44]), thus con-firming the pseudo-independent behavior from each ofthe piles of the group.

Moreover, an average group e�ciency of 92% wasobtained, indicating that under similar displacements, apile within the group had a slight smaller load than theequivalent one of a similar single pile. It points out to asmall, but existing, interaction between the piles of thegroup.Table 3: E�ciency factors from numerical simulations from PG sys-tems

System Ultimate ⌘⇤ Ge

Load [kN] [-] [-]

1pile-PG 419 - -2piles-PG 850 1.01 913piles-PG 1100 0.88 974piles-PG 1800 1.07 885piles-PG 1900 0.90 906piles-PG 2520 1.00 93

6.3.2. Load ShareLoad share between each element of the PR founda-

tion system, i.e., piles and raft, was also derived withthe numerical simulations. These individual loads werethen divided by the systems ultimate loads (capacity)and by their working loads (ultimate / 2.0), as respec-tively presented in Fig. 33 and Fig. 34.

In both cases similar tendencies were noticed. Thatmeans, the higher is the number of piles in the system,the lower is the (percentage) load share taken by eachpile individually. For instance, note that for the single1pile-PR, the pile contributed with more than 80% ofboth ultimate and working loads of the system, whereasfor the 6piles-PR the individual contribution has de-creased to values lower than 20%.

Figure 33: Load share between components of the PR system, in re-

lation to the ultimate loads.

Figure 34: Load share between components of the PR system, in re-

lation to the working loads.

Besides, in terms of the load absorbed by the raft andby the group itself (sum of each pile’s contribution),it is also clearly seen that the higher is the number ofpiles, the higher will also be the importance of the raftto the overall system’s capacity (with the exception ofthe larger 6piles-PR system). For instance, note againthat for the single 1pile-PR, the relative weight of theraft to the overall (ultimate and working) capacity isvery low compared to the piles importance. Neverthe-less, although still small, as one move towards higher(pile) number PR systems, the relative contribution andweight of the raft slightly increases.

6.4. Main experimental results

6.4.1. Raft’s PerformanceA direct comparison between PG and PR systems

yields a quantitative (and indirect) measurement of theperformance of the raft to the overall systems behavior,or, in other words, how much the system improves byhaving a close contact between the raft and the superfi-cial soil.

Thus, a practical result gathered from previous nu-merical analyses would be the average value of the raft

14

contribution (in percentage) to either ultimate or work-ing loads of the systems. In both cases, and for all sys-tems, an average raft load of 12% was calculated withsuch analyses.

Perhaps this performance is related to the (poor) su-perficial characteristics of the porous Braslia clay. In-deed, Janda et al. [9] have already noticed similarbehavior from numerical analyses of CFA (continuousflight auger) pile-PR systems founded in the UnB Ex-perimental site. In this particular case, the raft had theability to increase the bearing capacity by only ⇠15%for the simulated systems.

Another way of checking this performance is givenby the bearing capacity coe�cient ⇣PR, as defined byEquation 6.

⇣PR =PPR

PGP(7)

Where ⇣PR= capacity coe�cient; PPR= load capacityof the PR system; and PGP= similar capacity of the PGsystem.

According to Mandolini et al. [44] ⇣PR may be as-sumed as a measure of the increase of bearing capacitydue to raft-soil contact. It was calculated and presentedin Table 4 with experimental, rather than numerical, re-sults.

Table 4: Experimental bearing capacity coe�cients using data fromboth PG and PR systems

System Ultimate Load ⇣PR

PPR [kN] PPG [kN] [-]

2piles-PG 1000 650 1.533piles-PG 1200 1100 1.094piles-PG 2000 1780 1.125piles-PG 2190 1950 1.126piles-PG 2700 2520 1.07

Results from Table 4 clearly indicate the small, butbeneficial e↵ect of the raft (in average 18%, as noticedfor Fig. 22 too). Besides, it agrees with Mandolini et al.[44] accounts that such factor should decrease with anincreasing no. of piles.

Also according to these authors, there is a criticalspacing ratio (scrit/d) for a PR system above which thefailure changes from block failure to a pile group one.This latter case is related to an almost (pseudo) inde-pendent pile behavior, that fails without much of inter-action with adjacent piles, or with the systems compo-nents (raft and soil around). Moreover, PR systems thatfail as a pile group tend to have ⇣PR greater than one.

Taking on account results from Table 4, and the factthat spacing ratios above 4 are noticed for the systems ofFig. 11, one can conclude that they indeed failed as pilegroup ones (which by the way has already been noted inthe section of load share).

6.4.2. Displacements at capacity loadCunha and Sales [45] report a field investigation on

the behavior of piled raft foundations in the UnB Ex-perimental Site, where four PR systems were loaded atdistinct conditions of soil’s water content and individ-ual geometries. The settlements attained during the testsranged between ⇠20 to ⇠45 mm, and in any case, the PRsystems did not reach a settlement larger than 3% of B(systems breadth) at the maximum load.

Using the available data for the experimental PR sys-tems, it was also possible to construct Table 5. This ta-ble presents the values of load (PPR) and displacement(�) at ultimate conditions (in accordance to the Brazil-ian conventional failure load criterion). It also bringsthe breadth of each of the systems and the relationship�/B.

As noticed, the systems reached an average settle-ment around 2.6% of B, the shortest raft’s dimension.This value agrees with aforementioned results for simi-lar soil conditions. Similarly as other (previously given)numbers in this paper, this relationship can be adoptedas a practical design number in a first rough assessment.

Table 5: Experimental results using data from the PR systems

System Ultimate Values BreadthPPR [kN] � [mm] B [mm] �/B [%]

2piles-PG 480 6.8 500 1.362piles-PG 1000 10.0 350 2.853piles-PG 1200 10.8 350 3.084piles-PG 2000 14.8 580 2.555piles-PG 2190 15.9 580 2.746piles-PG 2700 19.1 580 3.29

7. Conclusions

This paper focused on the experimental and numer-ical behavior of standard groups and piled rafts con-structed with helical screw piles (a novel feature in theregion), founded in the typical soil of the Federal Dis-trict of Brazil. This is a particular tropical and laterizedsoil, which characteristics that can be somehow foundin other deposits of the Midwest region of this country.

The paper investigated and characterized a new Ex-perimental Site, presenting an overview of the main

15

geotechnical parameters for a simple elasto-plasticmodel via laboratory and in situ tests. Specific pointload (lab) tests were coupled to numerical FEM analy-ses to calibrate a new (modified) hypoplastic model thatcan incorporate the soils structure. This model was fur-ther adopted into numerical simulations to include someof the complex features of the superficial porous claystrata of the site.

The calibrated numerical tool aimed the expansion ofthe knowledge on the behavior of the tested foundationsystems, in terms of traditional (piled raft) variables, de-sign considerations, and overall (shearing and displace-ment) mechanisms. Practical and academic conclu-sions of real added value for professionals of the studiedregion or elsewhere are given, as follows:

1. Hipoplasticity with the modifications proposed inthe present paper has proved to grasp reasonablywell the main, complex, geotechnical character-istics of the superficial tropical soil of the Fed-eral District of Brazil. This rheological model candefinitively be used into numerical simulations asthose presented herein, to acquire knowledge onthe approximate behavior of common engineeringstructures founded on this particular strata;

2. For (pile group) systems under similar conditionsas those studied herein, the average e�ciency fac-tor is close to unity, indicating that detrimentale↵ects given by the superposition of individualstress and displacement bulbs are negligible. It alsomeans, and confirms, that individual pile failures,rather than block failures, are the main shearingmechanisms that takes place underneath the sys-tems during soil plastification;

3. Besides, at identical displacement levels, a pilewithin the (pile group) system has a slight smallerload than the equivalent one of a similar single pile.This feature leads to a conclusion that, althoughsmall, there is indeed some interaction between thepiles of the group;

4. For (piled raft) systems under similar conditionsas those studied herein, the region of influence(stress and strain bulbs) around the raft can stretchto around 4 times the raft’s breadth in the verticaldirection, and 2 times in the horizontal one. Thisbulb also extends downwards below the pile tips,within a zone of around 2 to 3 times the piles di-ameter;

5. Besides, for such (piled raft) systems, there is aload share between the elements that compose thesystem, i.e., raft, piles and surrounding soil. Thecontribution of the raft to the total load is not

high, but nevertheless not insignificant. It has beenshown that the raft was able to absorb a value inthe range of 12% of the total (ultimate or work-ing) load. As one move towards systems withhigher number of piles, hence with larger raft di-mensions, the relative importance of the raft to thetotal systems capacity slightly increases, as it alsodecreases the percentage of load share taken byeach pile individually;

6. Finally, it is clearly noticeable that (piled raft) sys-tems do have a reasonable increase in load giventhe contact of the raft with the superficial soil. Ithas been shown an average increase in the rangeof 18% of the conventional failure load of standard(pile group) systems, which is by no means negli-gible. Moreover, at such ultimate conditions, it hasalso been shown that (piled raft) systems do notdisplace more than around 3% of the rafts breadthin the vertical direction;

7. Helical screw piles have shown to be feasible to beemployed in the region under certain constructioncharacteristics (viaducts, soil reinforcement, smallstructures, and so on), where the fast speed of exe-cution (15 min) and field behavior (slender frictionpiles for compression or tension loads), add a strik-ing competitiveness to this pile when compared toother solutions.

Although the range of the numerical analyses of thepresent paper was limited in scope and dimension, gen-eralized conclusions have been drawn, and knowledgewas undoubtedly generated. The provided informationcan of course be referenced as an initial guideline in thedesign of similar foundation systems for the region, orperhaps in others that equal conditions apply. It alsoserves as a rough insight in the complex soil-structureproblem that is related to particular foundation systemsconstructed in regions of structured, laterized and tropi-cal soil deposits.

8. Acknowledgements

This study was made possible through an existingjoint technical co-operation research program from thePilot and Los Andes Universities in Colombia and theUniversity of Braslia in Brazil, where students and pro-fessors from both institutions were able to correspondand interact.

The authors also thank the Brazilian sponsorship or-ganizations CNPq and CAPES for all related support inthis and in all other studies carried out by the second au-

16

thor, either in terms of personal research grants, or viasabbatical & student scholarships.

One of such scholarships allowed the first author topursue his Doctorate in Brazil, strengthening the coop-eration links between this country and his homeland.

The first author to pursue his Doctorate in Brazil,strengthening the cooperation links between this coun-try and his homeland.

The first author thanks to the project ”Study of themechanical behavior of bases for pavements constructedwith soil-cement mixes” for the financial support.

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Appendix A

The equations needed to implement the model in aUMAT (used material) for Abaqus program are givenbelow:

The basic equation is shown in Equation .1.�T

= fsL : D + fs fdN k D k (.1)

Defining (�T

) as the change rate of the Cauchy stresstensor in time, (D) as the rate of change of strain intime, the fourth-order tensor (L) (Equation .2) and thesecond-order tensor (N) (Equation .9).

L =1

ˆ

T : ˆ

T

⇣c1F2I + c2a⇤2 ˆ

T ⌦ ˆ

T

⌘(.2)

(L) is a constitutive fourth order tensor which is func-tion of the stress tensor ( ˆ

T) (the Cauchy stress tensor(T) divided by the trace tensor) and the criterion of thecritical state of Matsuoka-Nakai (F) (Equation .3), (a⇤)(Equation .4), as well as scalars of the factor (c1) (Equa-tion .5) and (c2) (Equation .6), and finally (I) is a fourthorder tensor unit.

F =

s18

tan2 +2 � tan2

2 +p

2 tan cos 3✓� 1

2p

2tan (.3)

a⇤ =

p3(3 � sin �c)2p

2 sin �c(.4)

Factors (c1) and (c2) relate to the material compres-sion law in (↵) (Equation .7) and (r) is a constant ofthe ratio between bulk modulus and the undrained shearmodulus. Also, it is already taken into account the in-fluence of the structure factor (S i) (Equation .8).

c1 =

0BBBB@

2(3 + a⇤2 � 2↵p

3a⇤)9rS i

1CCCCA (.5)

c2 = 1 + (1 � c1)3

a⇤2(.6)

↵ =1

ln 2ln

"�⇤ � ⇤S i

�⇤ + ⇤S i

3 + a⇤2

a⇤p

3

!#(.7)

S i =s � (s � s f )

s(.8)

Tensor (m) (Equation .10) and function (Y) (Equa-tion .11) can be used to obtain the tensor (N) (Equation.9) with the materials flow rule. Function (Y) (Equa-tion .11) relates the critical stress with the stress tensorinvariant’s function.

N = L : �Y

m

k m k

!(.9)

m = �a⇤

F

2666666664

ˆ

T + ˆ

T

⇤ �ˆ

T

3

0BBBBBBBB@

6 ˆ

T : ˆ

T � 1⇣

a⇤F

⌘2+ ˆ

T : ˆ

T

1CCCCCCCCA

3777777775 (.10)

Y =0BBBB@p

3a⇤

3 + a⇤2� 1

1CCCCA"(I1I2 + 9I3)(1 � sin2 'c)

8I3 sin2 'c

#(.11)

To complete the components of the equation there arethe scalar factors ( fs) (Equation .12) and ( fd) (Equation.13) representing picnotropy and barotropy factors ofthe material. They are a↵ected by the soils structure( fsr) factor (factor unstructured model fs) multiplied bya (S i) factor. In the ( fd) factor the Hvorslev stress ismultiplied by a scalar (s) with the addition of the struc-ture.

fs = S itrT

�⇤⇣3 + a⇤2 � 2↵a⇤

p3⌘�1

(.12)

fd =

2psp⇤e

!↵(.13)

18