Category WATER IN ROAD STRUCTURES

9.4.1.1 Routine Pavement Analysis

In practice much routine pavement design is carried out as catalogue-based design. Nevertheless, routine structural analysis and design methods are used as supple­mental design methods where the pavement is considered as a multi-layered elastic system (Amadeus Project, 2000). The layers are characterised by Young’s modulus, Poisson ratio and thickness. The simplest model for the stress-strain behaviour of isotropic materials is based on linear elasticity, which is described by Hooke’s law. In two or three dimensions, the model is written:

°ij = Ejr (9.1)

where oij, ей, Eeijkl are respectively members of the stress, strain and stiffness tensors а, є and Ee.

A symmetric stiffness matrix is used to describe the constitutive equations in those cases. As a road pavement is a layered structure, the material behaviour might be non-isotropic, with different stiffnesses in horizontal and vertical direc­tions. Thus, the constitutive matrix is described with more independent parameters, which are also difficult to determine in a laboratory test. Hence, materials are usu­ally considered isotropic. If the layers are not too thin, this might be a reasonable simplification.

The purpose of this section is to introduce some of the constitutive models devoted to routine, as well as advanced, pavement analysis and design. For all these models, moisture or water pressure are not taken into account. They are written, here, in terms of total stresses – i. e. the effects of pore water pressure and/or pore suction are subsumed into the mechanical response of the materials and are not explicitly described.

Nowadays, models for subgrade in pavement engineering have been split in two categories dealing with the main mechanical behaviour which needs to be taken into account:

• resilient behaviour (see Fig. 9.3); and

• long term elasto-plastic behaviour.

With the use of numerical modelling, engineers aim to obtain the displacement fields as well as the stress values (effective stress, pore pressure and suction) in the road and earthworks sub-structure. The numerical modelling allows the understanding of the behaviour of the geostructure and the analysis of an optimal design. In order to be successful, the computational tool should, then, include the main physical processes of the rheology of the materials that make up the structure.

The behaviour of granular media is mainly dependant on an inter-granular fric­tion as well as on the applied stress which modifies the rigidity and the strength of the material. It is highly non-linear and irreversible. Figure 9.2 summarizes the main stress-strain aspects.

Fig. 9.2 The main stress-strain aspects of a granular medium

The materials that comprise the lower parts of the road and which form the subgrade are all geomaterials – particulate solids with pore spaces occupied by a combina­tion of water and air in varying proportions. The solid particles are, for the most part, crystalline. They are derived, ultimately, from geological sources. Individually the grains have considerable strength which means that the mechanical response (strength, stiffness, resistance to development of rutting) of an assembly of parti­cles is a primarily a consequence of the way the individual grains interact with one another and not of their own properties.

The primary contribution to mechanical property derives from the ease or diffi­culty with which one particle can be moved adjacent to another particle. This ease or difficulty is controlled by many factors which can, broadly, be grouped into three: physical characteristics of the grains, arrangement of the grains and the fluid condi­tions in the pores. The list of factors under each heading would be very long, but the following aims to highlight some of the more important:

• Physical characteristics of the grains:

о Particle shape; о Particle mineralogy; and о Particle roughness.

• Arrangement of the grains:

о Size and size distribution of the grains; and о Packing of the grains.

• Fluid conditions in the pores: о Fluid pressure in the pores;

о Surface tension effects in the pores between fluids; and о Water adsorption to mineral surfaces.

When a stress is applied to a granular or soil material, the stress has to be carried across the assemblage of grains via the inter-particle contact points. These contacts will be subjected to both normal and shear stresses. Both can cause compression that is recoverable and slippage between the particles at the contact or damage and wear to the contact. Recoverable compression of the contacts will contribute to the stiffness behaviour of the whole material while slip and damage will contribute to plastic deformation. In addition the assembly of particles will re-arrange itself by sliding and rolling of particles – also contributing to the stiffness and plastic de­formation behaviour of the whole. Changing the shape and nature of the contacts and changing the packing of particles will all, therefore, have an impact on strength, stiffness and resistance to plastic deformation.

As the force carried at an inter-particle contact point increases, the laws of fric­tion dictate that (unless the contact point fails in some way) there will be greater resistance to shear loading. Thus a greater compressive stress applied to an assem­bly of grains allows the whole material to gain shear strength and resistance to shear deformation which is characterised by the apparent angle of frictional resistance, ф’ . The greater compression of the particle contacts also makes further compression more difficult leading to the phenomenon of a non-linear stress-dependent modulus, so often observed in granular materials. Section 9.4 introduces some of the models of mechanical behaviour that are used to replicate these behaviours.

Adding water under pressure to a pore will cause all the particles around the pore to become loaded so that some of the force that previously was carried across the adjacent inter-particle contact points will now be carried by the pore fluid (Fig. 9.1).

This is the reason behind the effective stress equation, Eq. 1.1, which is further de­scribed in this chapter at Eq. 9.19 and following. Because some force is now carried through the pores, the inter-particle forces acting at the contacts are reduced and, therefore, due to the frictional effects, the shear strength, stiffness and resistance to permanent deformation are also reduced.

If water is retained in the pores due to surface tension effects, then the opposite will occur with a suction being applied to the adjacent particles. This causes the inter-particle contact forces to increase and the shear strength, stiffness and resis­tance to permanent deformation will all rise. These influences of water on mechan­ical performance are the subject of Section 9.5 and the required models are given in Section 9.6.

Lyesse Laloui[22], Robert Charlier, Cyrille Chazallon, SigurOur Erlingsson, Pierre Hornych, Primoz Pavsic and Mate Srsen

Abstract This chapter deals with the effects of water on the mechanical behaviour of pavements. The analysis is based on constitutive considerations. Constitutive models devoted to both routine and advanced pavement analysis and design are introduced and both the resilient behaviour as well as the long term elasto-plastic approaches are presented. As soon as the approach considers the material as a two phase (solid matrix and a fluid), the introduction of the effective stress concept is required. In the last section an analysis is made on the extension of the constitutive models to the characterisation of partially saturated materials.

Keywords Constitutive models ■ resilient behaviour ■ elasto-plastic models ■ effective stress ■ suction effects

9.1 Introduction

Road structures and the underlying soil are subjected to traffic loading. Their me­chanical behaviour depends on their initial state, the hydraulic conditions and the temperature. The numerical prediction of the behaviour of such material under such conditions is not a simple matter and the user needs, therefore, to make use of com­prehensive constitutive models that include a coupling of the mechanical, hydraulic and thermal aspects. The aim of the present chapter is to present an overview for such constitutive modelling, in particular covering the modelling of effects of water on the mechanical behaviour of pavements.

After first summarising the underlying reasons for the type of mechanical behaviour observed, this chapter presents a consideration of the constitutive rela­tionships of the materials that comprise the pavement and embankment layers. It provides an introduction to the following constitutive models that may be employed in routine and advanced pavement analysis and design:

• Resilient models: the k-0 model and the Boyce model and their derivatives; and

• Long term elasto-plastic models. These models are split in four categories:

о Analytical models; о Plasticity theory based models; о Visco-plastic equivalent models; and о Shakedown models.

Routine pavement design is mostly based on an elastic calculation, using a re­silient modulus and Poisson’s ratio for each layer. The design criterion is usually limited to the maximum vertical strain for a given loading condition. More elabo­rate models take into account the irreversible behaviour, e. g. the Chazallon-Hornych model, the Suiker model and the Mayoraz elasto-visco-plastic model. References to each of these models is given at the appropriate place in the text.

The final part of the chapter discusses how these models can be adapted to take into account and replicate the effects of variations in suction that occur in partially saturated soils and aggregates. Some suggested research topics are presented to­wards the end of this chapter.

Tjal2004, developed by VTI, monitors temperature at every 50 mm down to a depth of 2 m. Temperatures are collected twice an hour and distributed via the Internet. The temperature sensors are calibrated to give highest possible accuracy close to 0°C where freezing starts. Trucks, having mobile Internet, pick up the current freezing situation from the installed Tjal2004 along the intended roads to travel. Road own­ers give truckers allowance to use roads as long as the upper part of the pavement is frozen down to a certain depth. This means that in spring, load restrictions are imposed and removed automatically and very frequently. During periods in spring with clear weather the situation might change daily. In the daytime the solar ra­diation thaws the upper layers, which is followed by re-freezing during the clear and cold night. This means that the heavy loading of trucks is allowed in the early morning but prohibited in the afternoon. Figure 8.13 shows typical repeated freezing and thawing during the period March 4 – April 22 of the year 2008 monitored by one of the Tjal2004 installed in Sweden. The total frost depth is close to 1.5 m.

8.2 Conclusions, Implications, Recommendations

Field observations indicate clear and significant variations of moisture in subgrades. This is true both for moderate climates as well as for cold regions where it is related to temperature. In particular, thawing may induce strong increases in moisture lev­els. The mechanical behaviour as observed in-situ is strongly affected by moisture variations: the wetter the state the lower the stiffness (up to a factor 2 or more), the lower the stiffness then the higher the deflection.

Therefore one may conclude that an efficient drainage system is crucial in order to reduce the road structure’s ageing. An analytical assessment of this relationship between moisture and mechanical performance will be undertaken in the following two chapters.

8.3.5.1 Introduction

Spring-thaw load restrictions are often imposed to avoid severe pavement deteriora­tion during periods of reduced bearing capacity. Equipment that enables monitoring of the pavement strength situation is very important for a road’s traffic carrying capacity, as restrictions could be lifted as soon as the pavement regains its capacity. There are projects with this aim being run in both Sweden and Finland. In Finland the Percostation is used to monitor dielectric value, electrical conductivity and tem­perature with depth. The Swedish approach is to monitor temperature profile only and to distribute this via the Internet enabling direct access from trucks to frost depth readings that are updated twice an hour. Both approaches are now described.

8.3.5.2 The Finnish Percostation

The Percostation monitors dielectric value, electrical conductivity and temperature at different depths through a maximum of eight channels. Both dielectric value and electrical conductivity are sensitive to the amount of unfrozen water, that is, it is clearly indicated when water freezes and when ice melts. Temperature is, of course, also related to freezing and thawing. Figure 8.12 shows dielectric values at depths 0.15 and 0.30 m together with air temperature during the thawing period of the year 2000 at the Koskenkyla Percostation. From the figure it is clear that the dielectric value approximately equals 5 at both depths when the soil is frozen and that it in­creases at thawing.

The increase starts at depth 0.15 m and is somewhat delayed at the lower depth as thawing takes place from the surface and downwards. In late spring the dielectric value is highest at the greater depth indicating higher frost susceptibility and higher amount of ice lenses melting. Around April 10-12 the dielectric values show a peak followed by a continuously ongoing decrease when surplus water drains and bearing capacity recovers. The data monitored by the Percostation is of great value when imposing and removing spring-thaw load restrictions.

Figure 8.10 and Table 8.1 show the weakening of a road structure after spring thaw. The stiffness modulus E2 of the whole pavement structure measured by the FWD is, on average, 13% lower in the spring time than it is before the next freezing period. According to the FWD indices, the reason is the weakening of the up­per structure. This is shown since the BCI-indices (which are a representation of deflection in the subsoil) remain about the same, but the upper structure is weak­ened: the SCI (which is a representation of near-surface deflections) rises by 22%. The reason for this is that there must be more moisture in the structure after the thawing than in late autumn. The temperature of the pavement has been taken into account in the calculation on the indices. The data is from a 5.5 km long old high­way section of highway #6 in Finland with an AADT of 6500, before rehabilitation measures.

Figure 8.11 shows an example of a poor quality aggregate base layer in the mid­dle of the above section. In the central length of the road the SCI is very high, indicating that there are a lot of fines in the base layer.

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SCI300, BCI (pm)

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SCI300, BCI (pm)

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Figure 8.9 shows the air temperature together with the volumetric water content at Dyrastadir in Nordurardalur in SW Iceland during spring thaw, monitored through an environmental program run by the Public Roads Administration in Iceland. One can clearly see that as the thawing period starts in early March the water content increases, initially close to the surface and later at greater depth, before it slowly reverts back to normal values. As the water content affects the stiffness of the struc­ture as well as the permanent deformation characteristics, increased deterioration or damage is expected at the high water content if no axle load limitations are applied.

In cold climates, and with frost susceptible materials, freeze thaw phenomena play a major role in pavement deterioration. Figure 8.8 shows examples of measurements of deflection development, and of water content in the subgrade, performed in a full scale experiment, carried out in Quebec (Savard et al., 2005). The pavement structure consists of 18 cm of bituminous materials over a granular base (40 cm) and a 40 cm thick sand frost-protection layer. The pavement is subjected to frost indices exceeding 1000°C. days. The deep frost penetration (up to 1.5 m during severe win­ters) leads to large water content variations in the silty, frost susceptible subgrade,

which considerably affect the pavement deflections. The period of reduced bearing capacity lasts about 2 months (thaw period, followed by a recovery period, where the excess moisture dissipates).