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7/25/2019 Prediction of permanent settlements of foundations on Bo Bo sand subjected to high-cyclic loading

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Prediction of permanent settlements

of foundations on Bo Bo sand

subjected to high-cyclic loading

Matas Cuitioa, Mauro Poblete

a,1, Torsten Wichtmann

band Theodoros

Triantafyllidisb

a

Department of Civil Engineering, Universidad Catlica de la SantsimaConcepcin, Concepcin, Chile.

bInstitute of Soil Mechanics and Rock Mechanics, Karlsruhe Institute of

Technology, Karlsruhe, Germany.

Abstract. Permanent deformations of foundations on Bo Bo sand caused by ahigh-cyclic loading are studied by means of finite element calculations. A special

calculation strategy with a combination of the hypoplastic constitutive model withintergranular strain and the high-cycle accumulation (HCA) model proposed by

Niemunis et al. has been applied. The material constants of Bo Bo sand have

been determined from index tests, cone pluviation tests, oedometric tests, drainedmonotonic triaxial compression tests and drained cyclic triaxial tests. A simplified

procedure has been applied for the HCA model parameters, where parts of the

parameters are estimated based on granulometric properties while other ones aredetermined from experimental data. A wind power plant foundation subjected to a

high-cyclic loading due to wind has been studied as a practical example.

Keywords. High-cyclic loading, permanent deformations, accumulation, Bo Bosand, High-cycle accumulation model, hypoplasticity, shallow fundation.

1.Introduction

Concepcin is placed in the middle of Chile, 500 km to the south of Santiago. The city is delimited by Vallede la Mocha and lies on the foothill of the cordillera de la costa mountains, beside the Bo Bo river. The

position of the riverbed of Bo Bo river has changed throughout history. Therefore, parts of Concepcion lieon fluvial deposits formed by ancient branches of the Bo Bo river. In particular, the prosperous and activeurban center of Concepcin is located on these areas. Despite the fact that these zones are highly prone to

flooding [1] residential districts and commercial zones have been built there.

The ground of Concepcin is composed of unconsolidated deposits of black sands and eolic silt [2],mainly composed of volcanic sediments, i.e. basalt fragments and feldspars (as visible in Figure 1). Its origin

seems related to the Antuco volcano. The Bo Bo sand (Figure 1) is a clean uniform sand (

mm,

mm, , ), with angular particle form and generally without fine particles orcementation and in some cases salty. Its colour is dark gray to black brown with fragments of black greyvolcanic rocks and very few granite boulders. In some zones thin layers of grey silt with less than 1 mm

thickness can be found. According to its stratigraphic sequence, in some areas clastic and granitic rock exist[3].

1 Departament of Civil Engeenering, Universidad Catlica de la Santsima Concepcin, Alonso de

Ribera 2850, Concepcin. E-mail: [email protected]

From Fundamentals to Applications in Geotechnics

D. Manzanal and A.O. Sfriso (Eds.)

IOS Press, 2015

2015 The authors and IOS Press. All rights reserved.

doi:10.3233/978-1-61499-603-3-1285

1285


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The present paper deals with the problem of high-cyclic loading and prediction of accumulatedsettlements of foundations on Bo Bo sand. A high-cyclic loading means a loading with a large number of

cycles (N > 1000) of relatively small strain amplitudes (ampl < 10-3). Such cyclic loading is of practical

relevance for example in the case of traffic infrastructure (railways, highways), machine foundations or windpower plant foundations (as studied in Section 3). Coastal structures are also subjected to a high-cyclicloading due to waves. Such cyclic loading causes reorientations of grains leading to an accumulation of

deformation (compaction) in the sand and thus settlements of the foundations. An excessive accumulation of

inhomogeneous settlements, in particular occurring in loosely deposited sands as the Bo Bo sand depositsbelow Concepcion, can lead to a loss of the serviceability of structures. Therefore, the prediction of these

permanent deformations during the design phase of foundations is desirable. However, such prediction is a

challenging issue since the cumulative deformations depend on numerous parameters like amplitude, soildensity, fabric of the grain skeleton, cyclic preloading history, average stress, etc.

Figure 1: Grain size distribution curve of the Bo Bo sand and photo of the grains.

The high-cycle accumulation (HCA) model of Niemunis et al. [4] can be applied for a prediction of

these permanent deformations by means of the finite element method. The HCA model is used in theframework of a special calculation scheme. The first two cycles are calculated with a conventionalconstitutive model (see Figure 2). The authors use hypoplasticity (Kolymbas [5], von Wolffersdorff [6],

Niemunis [7]) with the extension by the intergranular strain concept of Niemunis and Herle [8] for that

purpose. A severe problem of the original hypoplastic model is the prediction of excessive permanent strainaccumulation in case of small loading and unloading cycles. The intergranular strain concept solves this

problem. During the second cycle of the hypoplastic calculation, the strain path is recorded in each

integration point. The strain amplitude ampl is determined from this strain path, which is one of the mostimportant input parameters of the HCA model. During the following explicit calculation (see Figure 2), the

HCA model predicts the cumulative deformations due to the cyclic loading directly, without following the

stress or strain path during the individual cycles. The structure of the HCA model is similar to a viscoplasticmodel, replacing time t by the number of cycles N. Therefore, the HCA model predicts the accumulation of

permanent strains in sand due to a high-cyclic loading in a similar manner as viscoplastic models predictcreep in cohesive soils under constant load.

The basic equation of the HCA model reads:

(1)

with stress rate , elastic stiffness E, strain rate , rate of strain accumulation and plastic strain

rate . The plastic strain rate is necessary in order to keep the average stress possibly evolving during high-cyclic loading within the yield surface.

M. Cuitio et al. / Prediction of Permanent Settlements of Foundations on Bo Bo Sand1286


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The rate of strain accumulation is calculated as the product of a scalar cumulative intensity ,

and a tensorial direction of accumulation(flow rule):

(2)

The intensity of accumulation is obtained as the product of six functions, each considering a separate

influencing parameter, i.e. strain amplitude ( ), cyclic preloading (), void ratio (), average mean

pressurepav(), normalized average stress ratio () and polarization changes ( ).

Figure 2. Procedure of a calculation with the high-cycle accumulation model

Using the combination of the hypoplastic model with intergranular strain and the HCA model, 23material constants have to be determined from laboratory tests. The procedure is explained for Bo Bo sand

in the following. Finally, a FE calculation of a shallow foundation subjected to a high-cyclic loading ispresented as an example.

2.Determination of the constitutive parameters for Bo Bo sand

2.1 Hypoplasticity

The basic hypoplastic model [5, 6] is generally described by a single tensorial equation (3) with a linear (L)and a nonlinear (N) stiffness tensor. The model needs eight material constants. Its determination is explained

in the following.

(3)

Critical friction angle

:The critical state is characterized by large shear deformations without any

changes of shear stress and volume. The shear stress mobilized in the critical state is determined by the

critical friction angle cof the material. This constant can be determined from undrained monotonic triaxial

tests or from cone pluviation tests. In the present study the latter test method has been used (Figure 3). is

the inclination of the cone.

Limit void ratios , , :These parameters correspond

to the critical, the minimum and the maximum void ratio,

respectively, at zero effective mean stress ( [8]. FollowingHerle [9], these limit void ratios for Bo Bo sand have been

estimated from the relationships , , and

with eminand emaxbeing the minimum and maximumvoid ratios determined from standard laboratory procedures (see

Table 1).

Granular hardness and exponent : These constants

describe the decrease of the void ratios , , with increasingmean effective stress according to

(4)

These parameters can be determined from the compression curves measured in oedometric tests

beginning from the loosest possible state [8]. The granular hardness and the exponent were determined

from the curves from fourteen oedometric compression tests performed on dry Bo Bo sand. For

Figure 3:Cone pluviation test on

Bo Bo Sand.

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comparison purpose two different specimen geometries were used: a diameter of 100 mm with a height of 18mm and a diameter of 150 mm with a height of 30 mm. Seven tests have been performed with the smaller

sample geometry while seven other ones were conducted with the larger diameter. The measured curves

for the loose sand are given on the left-hand side of Fig. 4 (dashed curves). The oedometric stiffness of thesmaller samples has been found somewhat lower than that of the larger ones. This is probably due to

boundary effects that are more significant in the case of the smaller samples. Eq. (4) was fitted to each curve

resulting in the constants and . Afterwards the oedometric tests have been simulated using the

element test program IncrementalDriver of A. Niemunis (solid curves in Fig. 4). During an iterativeprocedure, the parameters hsand n have been optimized until the best approximation of the test data has beenachieved. The optimum parameters are summarized in Table 1. Due to the larger stiffness measured for the

samples with diameter 150 mm, the corresponding granular hardness is larger and the exponent n is smaller(Table 1).

Figure 4: Oedometric compression tests on loose (left-hand side) and dense (right-hand side) Bo Bosand using samples of 100 mm or 150 mm diameter. The dashed curves are the results from the experiments.

The solid curves have been obtained from the element test simulations.

Exponent :This constant controls the influence of the material density on the peak friction angle. In order

to determine , a test with triaxial compression may be performed on an initially dense specimen. Based onthe measured peak shear strength, can be determined from the following equation:

(5)

The factors (peak stress ratio) and (dilatancy angle) are defined as:

(6)

and

(7)

(8)

and are the axial and radial stress components in the peak state. re = (e-ed)/(ec-ed) is thepressure-dependent relative density. The factor a in Eq. (5) depends on the critical friction angle:

(9)

Four drained monotonic triaxial tests with different initial densities (ID0= (emax e)/(emax emin) = 0.17, 0.62,

0.77 and 0.90 have been performed. The samples measured 100 mm in diameter and 100 mm in height. They



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were prepared by air pluviation. The effective confining pressure was kPa in all tests. The

measured curves of deviatoric stress and volumetric strain versus axial strain are given in Figure 5 (dashedcurves). Obviously, the shear strength and the dilatancy increases with increasing density (pyknotropy) [10].

Two more tests have been performed on medium dense samples with effective confining pressures of 200

and 400 kPa. The curves q(1) and v(1) for all three medium dense samples (ID0= 0.61 0.65) are provided

as dashed curves in Figure 6, demonstrating the barotropy of the material.

Figure 5: Drained monotonictriaxial tests with variation of initial relative density. The dashed curves are the

results from the experiments. The solid curves have been obtained from the element test simulations.

Figure 6:Drained monotonictriaxial tests with variation of effective confining pressure. The dashed curves

are the results from the experiments. The solid curves have been obtained from the element test simulations.

The parameter has been calibrated from Eq. (5) based on the test performed on the sample with the

largest initial density (ID0= 0.90). Afterwards, all triaxial compression tests have been simulated by means of

IncrementalDriver. The parameter was slightly adjusted to deliver a perfect agreement between the

measured peak strength and that predicted by hypoplasticity (Figure 4). The parameter is also slightly

affected by the parameters hsand n which differ for the two tested geometries in the oedometric tests (see

Table 1). The results from the simulations with the optimum -value are given as solid curves in Figures 4

and 5. Obviously, some aspects of the experimental data are reproduced well by the constitutive model (e.g.the stress strain and dilatancy curves in the test with 3 = 200 kPa) while in some other cases there are larger

deviations between the experiments and the prediction (e.g. some of the v(1) curves)

Exponent : The constant effects an increase of the stress rate with increasing density at D =constant. It can be obtained from oedometric tests on specimens with different initial densities. For that

purpose additional oedometric compression tests on dense sand have been performed. The resulting curves

e(p) are shown on the right-hand side of Figure 4. From the tests on the loose and the dense samples, the

oedometric stiffness(loose) and(dense) have been determined for the same effective mean stress .The parameter can then be obtained from:

(10)

with

and

(11)

and (Eq. 10) are the pyknotropy factors for loose and dense sand respectively, with and

evaluated at the p value under consideration. After has been determined from Eq. (10) it has been

optimized by recalculations of the dense oedometer tests (solid curves in Figure 4). The optimum parameters

for the two different sample geometries are summarized in Table 1. Note, that a negative value was

necessary to reproduce the stiffness measured in the oedometric tests on dense samples in the case of thediameter 100 mm (see Table 1). This negative value is necessary because the density-dependence expressed

by the hypoplastic equations without feis too large, i.e. the negative value of must counteract.



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2.2 Intergranular strain

The extension of hypoplasticity by intergranular strain needs five more constants , , , ,.

and are constants that represent the increases of stiffness due to changes of the strain path direction

by 90 or 180, respectively. is the strain range for which the stiffness is constant and at its maximum

value. The parameters anddescribe the degradation of the stiffness with continued monotonic loading

after the change of the strain path direction. These five parameter can be obtained from resonant column tests

and triaxial tests with changes of the direction of loading. In the case of Bo Bo sand the parameters havebeen determined from a drained cyclic triaxial test performed on a medium dense sample (ID0= 0,65) with an

average stress of pav= 200 kPa, av= qav/pav= 0.75 and a deviatoric stress amplitude of qampl= 60 kPa. The

following assumptions have been made: R = 10-4, r= 0.1, = 6 and mT= mR/2 1. The chosen values of r

and render the material response during the cycles nearly perfectly elastic, i.e. the undesired ratcheting

effect is prevented. This is appropriate in the present case because the accumulation of deformations is

predicted during the subsequent calculation using the HCA model. In order to calibrate the constant mR, fivecycles of the cyclic triaxial test were simulated with IncrementalDriver. The constant m R has been varied

until the strain amplitude amplmeasured in the test could be reproduced in the simulations. The optimum

constants are summarized in Table 1. Note that the obtained mR-values are relatively small, owing to therelatively large values of the granular hardness hs. It has to be kept in mind that mR increases the basic

stiffness predicted by the hypoplastic model, i.e. mR is coupled with the hs and n values previouslydetermined. Therefore, the mR and mTvalues also depend on the sample geometry used in the oedometrictests.

2.3 HCA model

For the calibration of the HCA model usually at least 11 drained cyclic triaxial tests with different stressamplitudes, initial densities, average mean pressures and average stress ratios are necessary. A simplified

procedure has been proposed by Wichtmann et al. [11]. Following this procedure, the HCA model parameters

can be fully or partly estimated from correlations with granulometry (mean grain size d 50, uniformitycoefficient Cu) or index quantities (minimum void ratio emin). These correlations have been developed based

on approximately 350 cyclic triaxial tests on clean sands with and [11]. In the present study on Bo Bo sand, the four constants C ampl, Ce, Cpand CYhave been estimated from

the correlations provided in [11], using d50= 0.73 m and Cu= 2.15, while the parameters CN1, CN2and CN3

have been determined from the strain accumulation curve acc(N) (see Figure 7) measured in the drained

cyclic triaxial test mentioned in Section 2.2. The constants CN1, CN2 and CN3 determine the shape of theaccumulation curves predicted by the HCA model. Table 1 summarizes the HCA model parameters obtained

for Bo Bo sand.

Table 1:Constants of hypoplasticity with intergranular strain and of the HCA model for Bo Bo sand. The

different stiffness measured in the oedometric tests with different diameters (100 or 150 mm) leads todifferent sets of material constants.



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Figure 7. Strain accumulation and strain amplitude curves measured in the drained cyclic triaxial test

3.Finite element calculations

The FE calculations have been performed using the program Abaqus. The hypoplastic model with

intergranular strain and the HCA model were available as UMAT subroutines written by A. Niemunis. Awind power plant under its high-cyclic loading due to wind action has been studied. For simplicity, a 2D(plane strain) model has been used, see Figure 8. The foundation has a width of 23 m and the tower of thewind power plant measures 44 meters in height. A horizontal load acts at the top of the tower. The mesh

shown in Figure 8 has been built with 1009 quadrilateral elements CPE4R with four nodes and reducedintegration. Elements with reduced integration are advantageous in calculations with the HCA model becausethey significantly reduce the occurrence of undesired self-stresses [8]. The material parameters of Bo Bo

sand given in Table 1 have been assigned to the soil. A initial relative density of I D0= 0,63 has been set intoapproach. The first four steps are calculated with hypoplasticity with intergranular strain:

Step 1: Application of the own weight of the soil without deformations (geostatic equilibrium)

Step 2: Application of the own weight of the foundation and the tower of the wind power plant(V = 3,625 kN/m)

Step 3: Calculation of the first cycle of loading (amplitude Hcyc= 200 kN/m).

Step 4: Calculation of the second cycle of loading (amplitude Hcyc= 200 kN/m). During this step thestrain path is recorded in each integration point

Figure 8: Eolic turbine model in Abaqus

0,0

0,2

0,4

0,6

0,8

1,0

Bleibend

eDehnungacc[

%]

100

101

102

103

104

105

Zyklenanzahl N

0

1

2

3

4

5

Dehnungsa

mplitudeampl [10-4]

100

101

102

103

104

105

Zyklenanzahl NNumber of Cycles [-] Number of Cycles [-]

Strainacc

umulation

Strainamplitude

200

150

q [kPa]

p [kPa]

60



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The next step is calculated with the HCA model:

Step 5: Calculation of 1,000,000 cycles with the HCA model. All loads are kept on their average

values during this step (Fcyc= 0). The HCA model predicts the increase of the cumulative deformations. Atthe beginning of this step the strain amplitude is determined from the strain path recorded during Step 4.

The results of the calculation, i.e. the settlements of both corners A and B of the foundation after 1,000,000cycles are summarized in Table 2. The settlement obviously slightly varies depending on the set of

parameters (100 or 150 mm diameter) applied in the calculations.

Table 2: Settlements obtained from the FE calculations after 1,000,000 cycles of horizontal load

4.Summary and conclusions

The permanent deformations of a wind power plant founded on a shallow foundation and subjected to a

cyclic loading with 1,000,000 cycles has been studied by means of finite element calculations. The high-cycle accumulation (HCA) model of Niemunis et al. [8] has been applied, in combination with thehypoplastic model with intergranular strain. The latter conventional constitutive model has been used for the

monotonic loading and the first two cycles. The material constants of the various constitutive models havebeen determined for Bo Bo sand, a sand of volcanic origin from Concepcion in Chile. Index tests, conepluviation tests, oedometric compression tests, drained monotonic triaxial tests and drained cyclic triaxial

tests have been performed for that purpose. The oedometric tests have been conducted with two different

sample geometries (100 and 150 mm diameter). A higher stiffness was observed in the tests with the largersample geometry. Therefore, two different sets of hypoplastic parameters have been derived and compared in

the FE calculations. The parameters of the HCA model have been partly estimated from correlations withgranulometry and partly determined from a single drained cyclic triaxial test. The FE calculations applyingthese parameters revealed that a significant accumulation of settlement can occur for foundations on Bo Bo

sand subjected to a high-cyclic loading. The influence of the different sets of parameters, belonging todifferent sample geometries in the oedometric tests, was rather negligible. In future, the constitutive

parameters determined for Bo Bo sand can be used to model any type of foundation on strata of Bo Bo

sand subject to cyclic loads.

5. References

[1]

Mardones M. & Vidal C,La zonificacin y evaluacin de los riesgos naturales de tipo geomorfolgico: un instrumentopara la planificacin urbana en la ciudad de Concepcin. EURE (Santiago) v.27 n.81 Santiago set.2001.

[2]

Quezada J, Geologa urbana y ambiental de la ciudad de Concepcin. Memoria para optar al ttulo de Gelogo,Universidad de Concepcin, 1996.

[3] Puga P, Estudio experimental de coef icientes de permeabilidad en arenas. Memoria para optar al ttulo de ingenierocivil, Universidad Catlica de la Santsima Concepcin, 2012.

[4]

Niemunis A, Wichtmann T, Triantafyllidis T.A high-cycle accumulation model for sand. Comput Geotech, 32(4): 245-63, 2005.

[5]

Kolymbas D, A rate-dependent constitutive equation for soils, Mechanics Research communications, 1(4):367-372,

1997.[6]

Wolffersdorff P. A hypoplastic relation for granular materials with a predefined limit state surface. Mechanics ofCohesive Frictional Materials 1996,1:251 -271.

[7]

Niemunis A,Extended hipoplastic models for soils, Dissertation submitted for habilitation. Bochum, January 2003

[8]Niemunis A., Herle I. Hypoplastic model for cohesionless soils with elastic strain range. Mechanics of Cohesive-Frictional Materials 2:1997, 279 - 299 pp.

[9]

Herle I. & Gudehus G. Determination of parameters of a hypoplastic constitutive model from properties of grain

assemblies. Mech. Choes. Frict., 4,461-486

[10]

Villalobos F.A. Mecnica de suelos. Editorial Universidad Catlica de la Santsima Concepcin, Chile. 2014.

[11]

Wichtmann T, Niemunis A, Triantafyllidis T. Improved simplified calibration procedure for a high-cycleaccumulation model. Soil Dynamics and Earthquake Engineering 70 (2015):118-132.


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