application of the hypoplasticity theory in the concrete ... · application of the hypoplasticity...

2013 IJPC Paper 192-1

© Copyright 2013 IJPC − International Journal of Pavements Conference, São Paulo, Brazil

APPLICATION OF THE HYPOPLASTICITY THEORY IN THE CONCRETE BLOCK

PAVEMENT MODELING – USE OF PLAXIS

Claudia Yaneth Acero Alvarez *

* Instituto Nacional de Vías - INVIAS, Bogotá, Colombia [email protected]

Luis Carlos Leguizamon

Professor of Engineering Faculty, Universidad Pedagógica y Tecnológica de Colombia, Tunja, Colombia. PhD

Engineering Student, Universidad Javeriana, Colombia. [email protected]

ABSTRACT: This paper gives an introduction to hypoplasticity and the modeling results of an interlocking

concrete pavement under a static load. This pavement modeling is composed of a paver layer, a sand layer, a

granular base and a fine soil subgrade. The granular layers were modeled according to the hypoplastic theory.

On the other hand, the concrete block pavement and the subgrade were modeled according to the elastic theory.

We used the algorithm "Plaxis-UMAT-hipoplas-lahey" developed by Masin [1] from the finite element program

PLAXIS version 8.2, in which the hypoplastic parameters of granular materials get involved according to the

constitutive equation of Von Wolffersdorff [2]. It also describes the procedure to determine the hypoplastic

parameters of two kinds of sand (river and rock sand), doing a sensitivity analysis of the influence of the

parameters in the hypoplastic constitutive model. Finally, we show the results of the pavement modeling

quantifying the contribution of the sand layer in its structure.

KEY WORDS: Hypoplasticity, Elasticity Theory, Concrete Block Pavement, Plaxis version 8.2, hypoplastic

parameters, granular layer, sand layer.

1. INTRODUCTION

Generally, the dimensioning of pavement structures is based on rational approaches to control stresses, strains

and admissible deflections; as well as on the relationship of the parameters obtained with the service values

induced by the different stresses on the structure during the design.

Currently, the finite elements method is more and more used for the structural analysis of pavements. This

method allows the inclusion of different constitutive models to predict the behavior of the materials.

Additionally, the finite elements analysis is more precisely used to model the behavior of the load / deflection

relation observed in the structure than the one performed by the elastic multilayer programs [3]. On the other

hand, the constitutive hypoplastic model has proven to be very appropriate to study the behavior of granular soils

[4, 5, 6].

One of the least studied typologies, considered as alternative paving, is the interlocking concrete pavement. This

pavement is used in the Colombian national road network (7.45 Km – Instituto Nacional de Vías, 2011), in

sectors where another type of pavement would be impossible to use because of the type of soil or the presence of

geological faults. Likewise, it has been determined that the potential of paving with these structures represents

29% of the national road network in Colombia (Instituto Nacional de Vías, 2011). That is why the interlocking

concrete pavement behavior should be studied and considered a little more in order to establish a methodology

that allows its design. In this regard, researches have been done to improve, update and systematize the design

procedures, evaluation and construction of the concrete block pavements worldwide.

This article shows the results of the research work done for the implementation of constitutive equations to

predict, as closely as possible, the behavior of each of the materials that the granular layers of an interlocking

concrete pavement contain, quantifying the contribution of the sand layer in the structure under consideration in

order to reproduce the most approximate behavior of those materials through a model developed in a software

(PLAXIS version 8.2).



2. STATE OF KNOWLEDGE

The design of engineering work implies understanding the behavior of materials, which seeks to be described

through constitutive equations based on different theories expressed by mathematical models. Among these

theories, we find the elasticity, plasticity, elastoplasticity; and more recently, viscohipoplasticity and

hipoplasticity. The modeling performed in a structure depends on the variables in the problem, which are defined

by the type of constitutive equations used.

The hypoplastic constitutive model constitutes an alternative model for the elastic and elastoplastic theories,

commonly found in the finite element program [7], including the intergranular strain concept [8].

The design methods also suppose that the permanent deformation occur only in the subgrade. However,

researches done [9, 10, 11, 12, 13, 14, 15] cited by Rondón [6], provide experimental and theorical evidence that

the granular layers also support the applied stress, and the magnitude of such stress can generate high values of

permanent deformation. Experiments developed under hypoplastic theories have shown that in the different

constitutive layers of the pavement there are equal stress and greater strain than in those calculated by traditional

methods [6].

2.1 Hypoplasticity

The hypoplasticity constitutes a non-linear constitutive model [16], which doesn’t distinguish plastic from elastic

deformation, allowing initial deformations to occur from the beginning of the load process. The hypoplastic

theory models the non linear stiffness and strength of the soil in terms of void ratio, the state of stress and strain

or load path, as observed in laboratory tests [17]. In the same manner, it lacks complex mathematical

formulations to describe the mechanical behavior of granular soils and sands in particular, which makes the

equation simple and easy to implement computationally, using a single equation for both load and download.

The hypoplasticity theory was developed independently during the last two decades at the universities of

Karlsruhe and Grenoble [18]. Tamagnini et al. [19] presented a comparison of the two kinds of hypoplastic

constitutive models. The first kind (K – hypoplasticity) was developed in Karlsruhe, with Kolymbas [20] as the

pioneer, followed by Kolymbas & Wu [16], Kolymbas [21], Wu & Bauer [22], Gudehus [23], Bauer [24], Von

Wolffersdorff [2], Niemunis [25, 26, 8, 27], Herle & Kolymbas [28], and Masin [18]. The second kind was

developed in Grenoble by Chambon et al. [29] under the name of CLoE- hypoplasticity (Consistency and

Explicit Localization Analysis).

There are several versions of hypoplasticity, that is why there is a framework of constitutive equations [30, 31].

The hypoplastic model described by Von Wolffersdorff [2] can be considered as a synthesis of researches done

on the subject in Karlsruhe, represented in the following general expression:

( ̂ ){ ( ̂) ̂ [ ̂ ̂

]‖ ‖} (1)

Here the stress tensor T is replaced by the normalized stress tensor T̂ , (cited by [5]) where:

trT

TT ˆ ; Normalized stress tensor (2)

332211 TTTtrT ; Tensor trace T (3)

TtrTtr

TT ˆ

3

1

ˆ

ˆˆ * ; Deviator tensor of normalized stress (4)

With:

√ ( )

√ (5)

F is the function of ̂ :

√

√

√ (6)



With:

√ ‖ ̂ ‖ (7)

√ ( ̂ )

[ ( ̂ )] ⁄ (8)

The voids ratio functions are described by Gudehus [23], as expressed in the equation:

io

do

i

d

io

co

i

c

e

e

e

e

e

e

e

e ; (9)

The pycnotropy functions are:

(

)

(10)

(

)

(11)

The barotropy function is:

(

) (

) (

)

[ √ (

) ]

(12)

The hypoplastic equation for the hypoplastic constitutive law given by Wolffersdorff [2] includes eight material

constants (c, n, hs, eco, edo, eio, , ), which are:

c Critical friction angle

n Exponent of compression law

hs Granular stiffness

eco Critical void ratio when ps=0

edo Void ratio at maximum density when ps=0

eio Void ratio at minimum density when ps= 0

Pycnotropy exponent

Barotropy exponent

2.2 Interlocking concrete pavement

The interlocking concrete pavements, also known as pavers or concrete block pavement (CBP), have taken force

in the last years as an alternative of paving given its extensive advantages over other types of pavements.

Globally, there have been researches done ([32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42], among others) tending to

improve, update and systematize the design procedures, evaluation and construction of the pavers.

The design methods have included equivalent design concepts [40], design catalogs, methods based on

researches and mechanistic analysis, empirical methods calibrated from observations of the behavior of

structures and track tests [43], analysis of the slab modified [44, 45]), the elastic analysis of layers [46, 34] and

analysis using the finite elements method [33, 32, 47, 38, 32, 41, 43, 42]. In most cases, the layer sand is

considered as a simple support of the block elements placed without structural contribution to the mechanical

behavior of the pavement. Research in the Netherlands [38] have shown that sand can be treated as structural

layer, being frequently used as a replacement of the base in interlocking concrete pavements placed on subgrade

poor quality.

The finite elements analysis of a CBP pavement consider the concrete block with an elastic behavior; the layer of

sand, base, sub base and subgrade with elastoplastic behavior, using the Druker Prager model as failure criteria

[41].

The equations to define the properties of the materials refer to the relationship between the elastic modulus and

the concrete strength; elastic modulus of the soils, and the relationship between the shear modulus and the elastic

modulus [42]. It is proposed, as failure criteria, the gradual accumulation of permanent deformation by rutting

[41], and the strain by tensile on top of the base layer [41].



3. HYPOPLASTIC PARAMETERS DETERMINATION IN GRANULAR MATERIALS

The parameters of the hypoplastic model of Wolffersdorf [2] were determined experimentally for the sand layer;

and for the granular base were taken from the research of Rondón [6].

3.1 Parameters researched

For the sand layer, we studied the parameters of two granular materials (rock sand – river sand: Guamo’s sand),

from the development of simple laboratory tests. The river sand used corresponds to sand of Guamo (Tolima).

Two types of sand (rock sand and river sand) were tested, with the objective to analyze their behavior and, under

technical criteria, confirm or deny that its performance is adequate in its use as a support layer of pavers.

The experimental phase includes granulometric classification test, specific gravity, maximum and minimum void

ratio, critical friction angle, oedometric test on a loose sample (maximum void ratio), and drained triaxial test on

a dense sample (minimum void ratio). With the parameters obtained, the behavior stress-strain was simulated

using the hypoplastic constitutive model of Von Wolffersdorf [2].

The materials characterize from the construction of the grain size distribution curve, with the objective to adjust

the grain size distribution of sands tests to the “General Specifications for Highway Construction”, of the

National Highways Institute 2007 (Article 510-07), so that the triaxial and oedometric tests performed were

made on adjusted samples. The grain size distribution curves present coincidences in order to compare the

behavior of the sands tested.

The characterization procedures and determination of granular material parameters have been taken from

researches of Rondón [7], Arias [5], Patiño [4], Fuentes [48], Solaque [49], Leguizamón [50] and Anaraki [51],

which are based on the approach exposed by Bauer [24], Gudehus [23], Herle and Gudehus [52], Kolymbas and

Herle [53]. The validity ranges for each hypoplastic parameter determined correspond to those described in the

research of Fuentes [48].

Critical friction angle c: This parameter was determined from drained triaxial test. Considering the

assumption validated by Solaque [49] that states that the critical friction angle (c) is equal to the angle of repose

(p) [52, 4, 54, 51], this parameter was obtained also by the method of Santamarina y Cho [55, 56, 49] and from

the funnel method [52].

Using a sensitivity analysis on the results of applying the three methodologies over tested sands, it was verified

the written by Solaque [49] and other authors, referred to simplifying p = c, and therefore it can be used

anyone of the methodologies described for determining this parameter since the variability encountered is low.

Void relation of reference eio, eco, edo: Three of the eight hypoplastic parameters are directly related to the void

ratio of the sample, called maximum void ratio for a free stress state (eio), minimum void ratio for a free stress

state (edo) and the critical void ratio for a free stress state (eco). Herle and Gudehus [52] establish, experimentally,

formulations to determine the reference void ratios, from the minimum void ratio (emín) and maximum void ratio

(emáx), so from these equivalences and traditional tests were obtained the eio, eco and edo parameters.

Granular stiffness (hs) and exponent of compression law (n): This parameters were determined from a

traditional oedometric test with stepwise load [51], considering the availability of equipment. The test was

reproduced on dry sand samples (rock sand and river sand) under conditions of the material in loose state (emax).

Obtaining the hs and n parameters is performed through a numerical simulation of elementary test (oedometric

and triaxial) for which we used the Excel spreadsheet developed by Arias [5]. Alternatively, the hs and n

parameters were estimated directly from diagrams that relate with the grain size distribution properties of the

material and the method proposed by Patiño [4] and it is validated in the research work of Arias [5].

From the results obtained, it was found that the application of Patiño’s Figures [4], for determining hs and n

parameters, require care in its use since with this methodology was obtained the same value of parameters for the



sands tested, which contradicts the calculated and adjusted numerical simulation based on real tests conducted on

the samples. The sensitivity of this method is high. The figures proposed by Patiño [4] and validated by Arias [5]

require the definition of a confidence interval and the inclusion of the standard error of the regression or the

adjustment made for its use.

Exponent The parameter was introduced as an exponent in the definition of density factor that controls the

evolution of soil behavior of the critical state [51]. For its determination were conducted drained triaxial tests on

dense samples, for which the sample was prepared to the minimum void ratio (e=0.58 for rock sand and e=0.69

for river sand). The triaxial test was developed to three confining pressures (50, 75 and 300 KPa). From the

curves resulting of triaxial test and the application of the equation defined by Herle and Gudehus [52] was

determined the parameter. Equally, the parameter was calculated from numerical simulations of elementary

tests using the Excel spreadsheet developed by Arias [5].

Exponent The exponent influences the compression stiffness of the material when it is in states denser

than critic. The value of this factor can be determined by two triaxial or oedometric compression tests in drained

conditions, one in dense state and one in loose state. Arias [5] mentions that the parameter for Guamo sand is

1.0, as well as for other sands cited by Rondón [6]. The typical value for Colombian sands is 1.0 [5] and, in

general, a good approximation is =1 [52, 6].

3.2 Parameters determined on the materials tested (rock sand – river sand)

The hypoplastic parameters for the sands tested are summarized in Table 1.

Table 1. Hypoplastic parameters on sands tested

MATERIAL TESTED c

[º]

eio

[-]

eco

[-]

edo

[-]

hs

[MPa]

n

[-] [-]

[-]

River sand 31 0.94 0.82 0.58 730 0.33 0.22 1.0

Rock sand 32 0.99 0.86 0.69 600 0.35 0.14 1.0

The consistency of the determined parameters is verified by a numerical simulation of the oedometric and

drained triaxial tests, from the use of an Excel spreadsheet developed by Arias [5] so as to coincide the real

curves obtained of the tests with the modeled ones.

3.3 Analysis of sensitivity of the researched parameters

We evaluated the sensitivity of each parameter from the simulation tests and comparison with real results from

experimentation in order to determine the individual contribution of hypoplastic parameters on the response

variability of a drained triaxial and oedometric test. In this way the influence of the parameters for each type of

sample are listed in Table 2. The results show coincidence with the analyzed and described by Anaraki [51].

Table 2. Sensitivity of the variables analyzed RIVER SAND

TYPE OF TEST c hs n edo eco eio [º] [MPa] [-] [-] [-] [-] [-] [-]

OEDOMETRIC LOW MEDIUM HIGH HIGH HIGH HIGH LOW LOW

DRAINED TRIAXIAL HIGH MEDIUM HIGH HIGH HIGH HIGH HIGH HIGH

ROCK SAND

TYPE OF TEST c hs n edo eco eio [º] [MPa] [-] [-] [-] [-] [-] [-]

OEDOMETRIC LOW HIGH HIGH HIGH HIGH HIGH LOW LOW

DRAINED TRIAXIAL HIGH MEDIUM HIGH HIGH HIGH HIGH HIGH LOW

In general terms, the oedometric test response is controlled by exponent n, the granular stiffness hs and the

exponent. The individual variation of these parameters in the hypoplastic model has a high incidence in the

oedometer compression response curve. The drained triaxial test response is controlled by the critical friction



angle, the exponent, and the critical void ratio (eco). The n parameter presents a high influence on the response

curves of the oedometric and drained triaxial tests, therefore its determination must be done carefully.

3.4 Hypoplastic parameters of granular base

We considered the hypoplastic parameters defined in Rondón’s research [6] for a Granular Base Material Type

BG-2 (Article 330-07, [57]), according to Table 3.

Table 3. Hypoplastic parameters of granular base BG-2

MATERIAL c

[º]

eio

[-]

eco

[-]

edo

[-]

hs

[MPa]

n

[-] [-]

[-]

Granular Base Type BG-2 38 0.51 0.44 0.225 97 0.24 0.14 3.2

Source: Table 3.4. Hypoplastic parameters of material tested [6].

4. MODELING OF CONCRETE BLOCK PAVEMENT

We analyzed a structure of concrete block pavement calculated from elastic theory and hypoplastic theory. These

results allow comparing the values of deflection, vertical stress and vertical strain on the subgrade obtained from

the modeling in PLAXIS version 8.2. Subsequently, we simulated the concrete block pavement structure in

which the thickness of the sand layer is varied to determine whether this layer has significant structural

contribution to the model analysis. Additionally, we consider two types of sand (river sand and rock sand) in

order to compare the influence of using materials in which the source is alluvial or a sedimentary deposit.

4.1 Comparison of calculating concrete block pavement with elastic theory and hypoplastic theory

The concrete block pavement modeling is basically composed by pavers of 10 cm thick, a sand layer of 5cm, a

granular layer (base granular) of 30 cm and a poor subgrade (CBR=4%). The pavers layer and the subgrade are

considered with elastic behavior. Granular layers (sand and granular base) will be modeled with elastic behavior

(Model 1) and hypoplastic behavior (Model 2).

In the case of using elastic theory, the properties of granular materials were evaluated using the formulations

proposed in the literature (Shell) for the calculation of the elastic modulus of each layer and the recommended

values of Poisson’s ratio. In the case of the hypoplastic theory, we take the values found experimentally for the

river sand registered in the Table 3, and the values referenced by Rondón [6] for the granular base type BG-2.

The results obtained are presented in Table 4, referring to deflection, stress and vertical strain on the subgrade.

Table 4. Results of modeling in PLAXIS

s x10-6

Change Dissip

(%) SENSITIVITY

s Change Dissip

(%) SENSITIVITY

s Change

Dissip (%)

SENSITIVITY [m] [KN/m2] x10-3%

MODEL 1 791.54 0 0.00 LOW

9.04 1.23 15.75 HIGH

8.19 0.02 0.24 HIGH

MODEL 2 791.54 7.81 8.17

From the results it can be concluded:

In Model 1, there are greater stresses and strains on the subgrade that in the Model 2. On deflections both

models are the same, which makes sense when you consider that generally this is assumed from the surface

layer and in lesser proportion by subgrade.

The graphs of behavior exhibited by the modeled structure with hypoplasticity present a quantitative trend

similar to those generated in elastic models, affirmation that had been proposed by Rondón [7].

It is possible that the modeling under elastic theory or hypoplastic theory of the granular materials in a concrete

block pavement present a similar response of behavior; therefore either one of the two methodologies can be

employed. However, if we considered that the characteristics of the materials of different layers, modeled with

elastic theory, referred principally to the Elastic Modulus (E) and the Poisson’s ratio (), are determined from

formulations and correlations in function of the CBR, proposed in the literature [58, 6]; uncertainty in structural



behavior of supposed properties is generated, and therefore it is preferable to model under hypoplastic theory

because the parameters defined for the model are of simple determination and characterized adequately granular

materials which translates in a behavior of the structure more approximated to reality.

4.2 Application of the hypoplastic theory in modeling of block pavement concrete

In general, the modeled pavement structure is composed by a surface layer (concrete pavers), modeled with the

elastic theory; a sand layer modeled with the hypoplastic theory; a granular base layer, modeled with the

hypoplastic theory and a poor subgrade modeled with the elastic theory.

The pavers are concrete blocks, it is recommended not to use other materials for interlocking pavement in

vehicular roads, and if used, their resistance and physical properties must be determined experimentally. The

thickness of the pavers for vehicular roads is 100 mm, that is the reason why we didn’t modify this variable in

the modeling. The characteristics of the Elastic Modulus and Poisson’s ratio were taken from data sheets

provided by suppliers of concrete blocks. In PLAXIS version 8.2, the pavers were simulated by rectangular

blocks of 200 mm x 100 mm x 100 mm. At each node of the drawn element, we generated a hinge that allows

considering the element attached to the continuous member with the possibility of displacement and rotation. At

the edges, we guarantee the confinement by placing an embedment of the pavers.

There will be two types of sand layer, depending on the material that defines it, referred to rock sand or river

sand. This layer is taken as support of the concrete element (when its thickness is 5 cm), or in replacement of the

material of the granular base layer. The thickness of the sand layer begins from 5cm until 30 cm. The granular

base layer is reduced every 5 cm, until reaching a minimum value of 20 cm thick. We adopted a subgrade layer

where the CBR is 4%. To eliminate the edge effect, we considered a subgrade depth of 20m.

Fort the hypoplastic modeling of the granular materials, we used UMAT, proposed by Masin [1], available at

http://web.natur.cuni.cz/uhigug/masin/plaxumat/.

Modeling results: For the different analyzed typologies (9), it can be deduced that:

We obtained lower values of the parameters of deflections, vertical stress and vertical strain on the subgrade

if we use river sand. This implies that under the application of load, the granular structure is rearranged and

this presents more resistance since the change in the void ratio is much smaller than in the rock sand, which

gives a better performance of the structure.

Regarding the preceding paragraph, the reduction value is low, there is a variation between 1% and 7%. This

means that from this point of view, it is feasible to use rock sand in the construction of interlocking concrete

pavement. We highlight the fact that by applying the load, the larger grains are comminuted and undergo a

size reduction; therefore, the sand of the layer is fine enough, which produces output of material by

infiltration phenomena through the joints, and this generates the washing of the layer. This does not happen

if you use alluvial materials, so this is better choice than the rock sand. If you guarantee impermeability of

the surface, the rock sand behaves similarly to the river sand.

Regarding the deflection parameter, this increases when increasing the thickness of the sand layer in the

structure, which is reasonable if one considers that the constant thickness of the granular base has been left.

An opposite trend is observed for the deformation and the vertical stress on the subgrade.

When we leave the total thickness of the constant structure, and we begin to vary the thickness of the granular

layer, we observe that there is a decrease of the values of deflection, stress and strain, in clearer way than in

the previous case, visualizing that the three parameters exhibit this behavior, unlike what is recorded when we

vary the total thickness of the structures.

Stress states of the pavement: To determine the structural contribution of the sand layer in the pavement

analyzed, we performed an analysis of stress states of the pavement, considering the values of service of stress

(vertical stress on the subgrade - yy), strains (vertical strain on the subgrade -yy) and deflections (yy) of the

structure considered.

http://web.natur.cuni.cz/uhigug/masin/plaxumat/



For the sensitivity analysis, we evaluated the dissipation rate of the variable considered in the analyzed layer,

taking, as rating scale, the recommendation given by Higuera [59]. In the Table 5, there is a summary of the

sensitivity of the variables analyzed in function of depth, for each of the layers in each model performed.

Table 5. Sensitivity of the variables

LAYER DEPTH (cm) RIVER SAND ROCK SAND

VERTICAL STRESS DEFLECTION VERTICAL STRAIN VERTICAL STRESS DEFLECTION VERTICAL STRAIN

PAVERS 0

HIGH MEDIUM HIGH HIGH MEDIUM HIGH 10

SAND LAYER 10

HIGH LOW HIGH HIGH LOW HIGH 30

GRANULAR BASE

30 HIGH LOW HIGH HIGH LOW HIGH

55

SUBGRADE 55

LOW HIGH HIGH BAJA HIGH HIGH 100

In general, it appears that there are similarities in the overall sensitivity of the variables, whether the model uses

rock sand or river sand. It follows that the deflection variable is assumed by the subgrade and the pavers, not by

the granular layers. Whereas the vertical load and vertical strain of the subgrade are assumed by all the layers of

the structure, particularly by the granular layers.

Several structures of concrete block pavement were modeled under two typologies: thickness variation of the

sand layer, keeping the thickness of the granular layer constant (Type 1) and the variation of both the thickness

of the sand layer and the granular base (Type 2). In each case we used a hypoplastic constitutive model

implemented in PLAXIS version 8.2, from the inclusion of one UMAT proposed by Masin [1]. From the

modeling was calculated the average, the structural contribution of the sand layer in the pavement structure

modeled under hypoplastic theory, which results are displayed in Table 6, for the two typologies proposed.

Table 6. Structural contribution of the sand layer of concrete block pavement

RIVER SAND. GENERAL SUMMARY. TYPE 1 ROCK SAND. GENERAL SUMMARY. TYPE 1

LAYER DEPTH (cm) VERTICAL

STRESS DEFLECTION VERTICAL STRAIN



CONTRIBUTION IN THE STRUCTURE % CONTRIBUTION IN THE STRUCTURE %

PAVERS 0

22.10 73.98 10.50 PAVERS 0

13.24 0.58 3.11 10 10

GUAMO’S SAND

10 32.32 1.15 21.59

GUAMO’S SAND

10 39.54 4.03 13.61

30 30

GRANULAR BASE

30 37.48 0.75 37.52

GRANULAR BASE

30 42.68 1.89 38.59

55 55

SUBGRADE 55

8.10 24.12 30.39 SUBGRADE 55

4.54 93.51 44.69 100 100

RIVER SAND. GENERAL SUMMARY. TYPE 2 ROCK SAND. GENERAL SUMMARY. TYPE 2





CONTRIBUTION IN THE STRUCTURE % CONTRIBUTION IN THE STRUCTURE %

PAVERS 0

18.10 19.67 5.05 PAVERS 0

18.75 2.66 5.48 10 10

GUAMO’S SAND

10 19.01 1.74 5.57

GUAMO’S SAND

10 26.63 0.99 7.47

30 30

GRANULAR BASE

30 58.13 5.93 34.65

GRANULAR BASE

30 52.43 0.43 30.19

55 55

SUBGRADE 55 4.77 72.67 54.74 SUBGRADE 55 2.18 65.52 56.86

4.3 Sensitivity analysis of hypoplastic parameters in the response of concrete block pavement

Several simulations were performed in which the hypoplastic parameters of the layers of granular materials are

changed to display their sensitivity in the behavior of the pavement structure. The sand layer is composed of

river sand since this material showed better resistance characteristics and thus better performance. The obtained

results concerning sensitivity ranking [59] is recorded in Table 7.



Table 7. Sensitivity of the variables analyzed

LAYER VARIABLE c hs n edo eco eio

[º] [MPa] [-] [-] [-] [-] [-]

SAND LAYER

LOW LOW LOW LOW LOW LOW LOW

yy LOW LOW LOW LOW LOW LOW LOW

yy MEDIUM MEDIUM MEDIUM LOW LOW LOW MEDIUM

BASE

GRANULAR

LAYER

MEDIUM MEDIUM MEDIUM LOW LOW LOW MEDIUM

yy HIGH HIGH HIGH MEDIA MEDIUM MEDIUM HIGH

yy HIGH HIGH HIGH MEDIA MEDIUM MEDIUM HIGH

From these results, it follows:

The hypoplastic parameter variation has a significant influence on the base layer, being very low influence on

the sand layer. This is because the granular base is the one that has a greater contribution to the structure of a

concrete block pavement. This shows that for the good behavior of an interlocking concrete pavement, a

granular base is necessarily required. It is not convenient to replace totally the granular base layer for a layer

of sand.

In the granular, the incidence of hypoplastic parameters on the behavior of the structure is more clear, so c,

hs, n y , have a high influence in the behavior of the layer; and therefore, in the hypoplastic model.

The hypoplastic parameters highly control the vertical strain and stress on the subgrade. These parameters

should be appropriately defined and based on experimental researches of materials. It is not suitable to

assume values for these since the response of the pavement structure is different.

5. PROPOSAL OF AN ANALYSIS PROCEDURE FOR THE DESIGN OF CONCRETE BLOCK

PAVEMENTS

The analysis proposal procedure for concrete block pavement design is performed through the use of finite

elements that allow to find the service values for stress, strain and deflections generated in the structure, so that

they can be compared with the admissible values to optimize the pavement structure. The proposed methodology

is summarized in general terms in the steps outlined in Figure 1.

6. CONCLUSION

The sand layer in a concrete block pavement shows significant structural contribution when its thickness is

greater than 5cm, so it is correct to say that for lower thickness values it can be considered as a simple layer of

support. The river sand (alluvial) is more competent to be used in a concrete block pavement structure due to the

grain characteristics. If you use rock sand as granular material layer, waterproofing of the surface layer should be

guaranteed to prevent the output of the material forming the layer.



Figure 1. General scheme of the proposed procedure for analysis of concrete block pavement design

REFERENCES:

[1] D. Masin, 2010. [On line]. Available: http://web.natur.cuni.cz/uhigug/masin/plaxumat/. [Last access: 01 04

201].

Sv = Admissible vertical strain on the subgrade [mstrain] N = Number of Equivalent Single Axles Load of 8.2 Ton in the lane design during design period

SUBGRADE

Determination of the CBR.

Determination of specificgravity saturated andunsaturated.

VERTICAL STRAIN ADMISSIBLE

STRAIN FOR TENSION IN TOP LAYER OF GRANULAR BASE LAYER

CALCULATION OF ADMISSIBLE VALUES

CALCULATION OF SERVICE VALUES(Modelling in a finite element software e.g. PLAXIS)

GRANULAR LAYERS

Characterization of grain size distribution that fulfill with

the INVIAS's Especifications 2007, determination fo uniformcoefficiente and Cu y del d50.

Determination of specific gravity saturated and

unsaturated.

Determination of hypoplastic parameters:

Critical friction Anglec (Funnel Method, Method of

Santamarina and/or drained triaxial test).Exponent n y Granular Stiffness hs (Oedometric Test).Critical void ratio eco and void ratio at maximum density edo.

Picnotropy exponent (Drained triaxial test).

Barotropy exponent.

ELASTIC MODEL HYPOPLASTIC MODEL

PAVERS: To consult in catalogsof supplier the Technical Data

Sheet (E, )

GRANULAR LAYER

Calculation of Elastic Module

(E) from different correlationsgiven in Literature (Rondónand Reyes, 2007).Definition of Poisson's Module

().

Characterization of grain sizedistribution that fulfill with theINVIAS's Especifications 2007.Determination of specific

gravity saturated andunsaturated.

CHARACTERIZATION OF MATERIALS FOR EACH LAYER OF PAVEMENT

DEFINITION OF THE CONSTITUTIVE MODEL TO APPLY

ELASTIC MODEL(Pavers, granular layers,

subgrade)

HYPOPLASTIC MODEL(Granular layers, subgrade)

DEFINING THE PERIOD OF DESIGN(Recommended value of 10 years for interlocking concrete pavement)

TRAFFIC DESIGN DEFINITION(8.2 Ton Equivalents Single Axles Load on lane design during the design

STUDY AND CHARACTERIZATION OF THE SUBGRADE(Determination of the CBR)

DEFINITION OF THE INITIAL STRUCTURE MODELLING

STRUCTURE OPTIMIZATION(Service values ≤ Admissible values)

St = Tensile strain on the top base granular layer [strain] f’c = Compressive strength of the base material [MPa] Eb = Vertical strain of tension on the top of base granular layer N = Number of Equivalent Single Axles Load of 8.2 Ton in the lane design during

design period

25.0

2800

NSv

0502.0022.1

'993500

NE

fSt

b

c



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