Category WATER IN ROAD STRUCTURES

In the European project SAMARIS, the predictions obtained with ORNI have been compared with the response of a low traffic pavement tested on the LCPC pavement test track. The pavement consisted of:

• a bituminous concrete wearing course, with an average thickness of 66 mm;

• A 50 cm thick granular base and sub-base (crushed gneiss);

• A clayey sand subgrade (thickness 2.20 m), resting on a rigid concrete slab.

As in the previous example (Section 11.4.5) the pavement was instrumented to measure strains, temperatures and water contents in the various layers. The loading consisted in applying 1.5 million heavy vehicle loads (dual wheels, with a load of 65 kN).

In the modelling of the resilient behaviour (with CVCR), the bituminous concrete and the soil were assumed linear elastic, and the UGM was described using the anisotropic Boyce model (Eq. 9.13). The bituminous concrete moduli (function of temperature and loading frequency) were determined from complex modulus tests, the UGM and soil parameters from repeated load triaxial tests.

In the modelling with ORNI, it was assumed that no permanent deformations occur in the thin bituminous layer. The permanent deformations of the UGM and of the soil were described using the empirical model of Gidel et al. (2001), with model parameters determined from repeated load triaxial tests, at two water contents for the UGM (w = 4% and 5%), and one water content for the soil (w = 11%).

Figure 11.17 shows the finite element meshes used to determine the resilient behaviour with CVCR (in 3D), and then the permanent deformations (in 2D).

The modelling of permanent deformations of pavements is more complex than the modelling of the resilient behaviour because it is necessary to simulate the response of the pavement to large numbers of load cycles (typically 105-106 cycles), with variable loading and environmental conditions.

A programme for the prediction of rutting of low traffic pavements, called ORNI, is also implemented in the finite element code CESAR-LCPC (El Abd et al., 2005; Hornych & El Abd, 2006). To determine the permanent deformations due to large numbers of load cycles, this programme proposes a simplified approach, based on a separate calculation of the elastic response and of the plastic strains. It comprises 3 steps:

i) The first step consists in calculating the resilient response of the pavement, for the different loading conditions considered (different types of loads, different temperature, etc…). The resilient response is calculated in 3D, using the pro­gramme CVCR.

ii) Then, the resilient stress fields are used to calculate the plastic strains pro­duced by the successive application of the different loads. The permanent strains are calculated locally, at different points in the pavement structure, in 2D (in the plane (0,y, z) perpendicular to the direction of displacement of the load).

iii) Finally, the third step consists in calculating the displacements in the pave­ment structure. The plastic strains being calculated locally, at different points, do not derive from a displacement field. It is thus necessary to determine the total strains, ensuring their continuity and integrability, and the corresponding displacements.

Two permanent deformation models are implemented in ORNI: the empirical model of Gidel et al. (2001), and the elasto-plastic model of Chazallon (Chazallon et al., 2006). These models have been described in Chapter 9.

The pavement was modelled in 3D, considering visco-elastic behaviour for the bi­tuminous material, and the non-linear elastic Boyce model (Eq. 9.10) for the un­bound granular material and the soil. The material parameters for the bituminous layer were determined from complex modulus tests and the in-situ temperature of the bituminous layer was taken into account in the modelling. The parameters for the unbound granular material (UGM) and for the subgrade were determined from repeated load triaxial tests. For the UGM, tests were performed at 3 different wa­ter contents: 2.3%, 3.8% and 4.8%, corresponding to the water content variations observed on the site.

11.4.5.1 Modelling of the Pavement Response for Different Water Contents

A series of calculations was performed for the 3 load levels and the 3 moisture contents of the UGM at a constant loading speed of 68 km/h.

Figures 11.12 and 11.13 show comparisons between measured and calculated maximum longitudinal strains at the bottom of the bituminous layer (exx BB), and maximum vertical strains at the top of the UGM layer (ezz GNT), for the 3 load levels. The results show that:

The model predicts relatively well the strains in the granular layer (ezz GNT), and their non-linear increase with load level. The strains in the bituminous layer (exx BB) are slightly over-predicted.

The water content of the granular layer has a strong influence on the vertical strains in the UGM layer. Increasing w from 2.3 to 4.8% increases the strains by about 60%. The calculations with w = 3.8% lead to the best predictions, close to the mean of the experimental measurements.

The calculations with the 3 water contents led to a range of variation of the verti­cal strains in the UGM layer similar to the scatter of the experimental measurements.

Figures 11.14, 11.15 and 11.16 present additional examples of prediction of sig­nals of longitudinal and transversal strains at the bottom of the bituminous layer

(exx and eyy), and vertical strains at the top of the UGM layer (ezz), for the load of 65kN. The results show that CVCR (with w = 3.8% for the UGM) predicts well the strain signals (strain variations when the load moves in the x direction). The experimental curves of exx and eyy at the bottom of the bituminous concrete are non-symmetrical, due to the viscosity of the material, and this is well predicted by the visco-elastic model.

The experimental pavement structure is presented in Fig. 11.11. It had a length of 28 m, a width of 6 m and consisted of:

• a bituminous concrete wearing course, with an average thickness of 85 mm;

• a granular base (0/20 mm crushed gneiss) with an average thickness of 430 mm;

• a subgrade soil consisting of 2.5 m of mica-schist with a low modulus (around 30 MPa).

Asphalt concrete (85 mm)

Fig. 11.11 Structure of the LCPC experimental pavement

The instrumentation installed in this experimental structure included:

• strain gauges to measure longitudinal and transversal strains at the bottom of the asphalt layer;

• displacement transducers to measure vertical strains in the top 100 mm of the granular layer and of the subgrade;

• vertical pressure transducers at the top of the subgrade;

• thermocouples in the asphalt layer; and

• tensiometers, to measure suction in the granular base and in the subgrade.

The pavement was subjected to dual wheel loads. Different load levels (45, 65 and 75kN), and different loading speeds (3.4-68km/h) were applied during the experiment.

To model the resilient behaviour of pavements, the French pavement laboratory, LCPC, has developed a finite element program called CVCR, which is a part of the finite element code CESAR-LCPC (Heck et al., 1998; Heck, 2001a, b). This program allows the modelling of the response of pavements in 3D, under moving wheel loads, and incorporates the following material models:

• Linear elasticity

• The Huet-Sayegh visco-elastic model for bituminous materials.

• Two non-linear elastic models for unbound granular materials: the Boyce model, modified to take into account anisotropy (Hornych et al., 1998) and the well known k-0 model (Hicks & Monismith, 1971). These models have been de­scribed in Chapter 9, Section 9.4.1.

The example below (Hornych et al., 2002) presents an application of CVCR to the modelling of a low traffic pavement with a granular base, tested on the LCPC pave­ment test track. In this study, the objective was, in particular, to evaluate the ability of the model to simulate experimental pavement response for different load levels and different water contents of the unbound granular material.

Erlingsson (2007) describes two thin pavement structures that were tested in ac­celerated testing by using a Heavy Vehicle Simulator. Both were surface dressed structures, one with 20 cm thick unbound base course layer and the other with the base course divided into a 10 cm bitumen stabilized base over 10 cm unbound base. Both structures were instrumented to estimate deflections, strains and stresses in various locations inside the structure. A numerical analysis was also carried out to simulate the response behaviour of the structure that could be compared with the actual measurements. The simulation was performed using different techniques: 3D and 2D axi-symmetric analyses, finite element and multi layer elastic theory, linear elastic and non-linear elastic base behaviour. The results were further used to model the permanent deformation development in each layer. A cross section of the two structures is shown in Fig. 11.8.

Figure 11.9 shows the induced vertical stress under the centre of a single tyre load for both structures where the axle load is 120 kN, or close to one conventional axle load (11.5 ton in the EU), and the tyre pressures is 800 kPa.

Fig. 11.8 Two test pavement structures: (a) IS02 is an unbound structure and (b) IS03 is a bitumen stabilized structure

Note: The instrumentation used for the response measurements is shown as well.

One can see in Fig. 11.9a the importance of taking into account the non-linear base behaviour for the unbound structure IS02. The linear analyses overestimate the stresses in the upper part of the structure, compared with the two non-linear analyses. In the structure with the bitumen-stabilized base, Fig. 11.9b, this is not as prevalent and both the linear as well as the non-liner analyses capture the overall response of the structure quite reasonably.

Finally Fig. 11.10 shows the results of the predicted as well as the measured accumulated permanent deformation for the base, sub-base and the subgrade layer as a function of load repetition for both pavement structures. The response over the first 300 000 load repetitions are shown.

A simple power law assumption was used in calculating the permanent deforma­tion. This seems to give a satisfactory agreement between the numerical simulations and the measurements for both structures. The largest deviation took place during the early part of the test but, thereafter, the rate of increased permanent deformation was quite similar between the analyses and the actual measurements.

It is also interesting to compare the measured and calculated permanent defor­mation of the two structures. Adding the three curves of Fig. 11.10 together gives the total permanent deformation, i. e. rutting, in the unbound part of the structure.

Number of passes, N Number of passes, N

Fig. 11.10 Prediction versus measurements of permanent deformation development for the three unbound layers as a function of load repetition for both pavement structures IS02 and IS03

The one with the upper part of the base stabilized with bitumen shows a total of about 14 mm of deformation after ca. 300 000 passes, but the other with un­bound base shows almost a 40 mm deformation after the same number of passes. This indicates quite a different “lifetime” of the two structures. This difference in “lifetime” does not prevail in the measurement and calculation of vertical stresses, where stresses at the top of the subgrade are almost the same for both structures (see Fig. 11.9).

The significance of the coupling between heat and water transport will be illustrated using a freezing experiment performed by Mizoguchi (1990). He packed four iden­tical cylinders with Kanagawa sandy loam. Each cylinder was 20 cm long and had an internal diameter of 8 cm. The samples were prepared for the freezing test by bringing them to the same initial state involving a uniform temperature of 6.7 °C and a close to uniform volumetric water content of 0.33 throughout the cylinders. Water and soil in each cylinder was subjected to freezing from the top down, since their top covers were exposed to a circulating fluid with a temperature of -6 °C. One cylinder was used to obtain initial values, and the other three were removed from freezing after 12, 24 and 50 hours respectively. The cylinders were then cut into 1 cm thick slices for which the total water content (ice + liquid water) was

Fig. 11.6 The simulated volumetric water content, 9, in a model road (a) after a light rainfall event (top), (b) after a heavy rainfall event (middle), (c) after a moderate rainfall event using small fracture-zone permeability (bottom) The particles illustrate the flow paths of the infiltrated rainwater. The vertical scale is exaggerated for clarity

determined. The experimental procedure thus described was then reproduced in a computer model in order to test the model.

As described in Chapter 4, Section 4.6, water flows towards freezing fronts where it changes phase from liquid to solid. This process is clearly evident in Fig. 11.7 where the total water content in the upper half of the cylinder increases as the col­umn freezes (Hansson et al., 2004). Since freezing is a relatively quick process, extremely high hydraulic gradients emerge and can lead to sometimes very rapid upward flow of water. The freezing front is clearly visible in Fig. 11.7 as the depth interval where the total water content decreases rapidly. The calculated results are in fair agreement with the measured values. Specifically, the rapid decrease in the total water content at, or immediately below, the freezing front and the gradual recovery deeper in the columns is well predicted.

It is the dramatic redistribution of water caused by the freezing that causes frost heaving, which may damage roads even though the largest problems occur in con­nection with thaw weakening. It should, however, be pointed out that the computer

model used here neglects effects of frost heave. If the conditions for frost heave had been met during the simulation, the result had been different since the liquid pressure head would have changed as an effect of a relative ice pressure not equal to zero.

Hansson et al. (2005) made an attempt to illustrate the effect of a rain shower and fracture zone permeability on the subsurface flow pattern using a two-dimensional computer model; thus making the simulation domain more like reality (Fig. 11.6). The properties of the materials used in the various layers of the model road fulfil the requirements of the Swedish road design guide. In addition, it was assumed that the asphalt layer of the road had plenty of fractures over a relatively short distance, “a fracture zone”, which thus enabled the use of an equivalent homogeneous porous media model. More details about material properties, driving data etc. can be found in Hansson (2005).

Notice (Fig. 11.6) that the fracture zone captures most, if not all, of the upstream surface runoff for the light rainfall event. The heavier rainfall causes a significantly larger infiltration in the road shoulder since the infiltration capacity of the fracture zone, or the granular base layer beneath it, was exceeded. As a consequence, a larger fraction of the total surface runoff reached the road shoulder, and the region of the roadside where both rainfall and surface runoff infiltrated was considerably ex­panded laterally. This result is qualitatively supported by the findings of Flyhammar and Bendz (2003) who measured concentrations of various solutes in the shoulder and beneath the asphalt cover in a Swedish road partly built with alternative materi­als, generated from waste and residuals. These materials contained plenty of solutes, and the leaching pattern is similar to the simulated water flow pattern, although the leaching patterns exhibited a large variability between solutes.

11.4.1 Modelling of Moisture Movements

Alonso (1998) presents, on the basis of in-situ measurements, relevant aspects of the water content development of pavement layers and its effect on the mechanical characteristics of granular bases and subgrades. A general model for the coupled analysis of transfer processes (water, heat) and stress-strain behaviour of unsatu­rated compacted soils is then presented. A review of some representative properties of compacted soils has been carried out from the perspective of modern concepts of unsaturated soil mechanics. As an application of the methods described a full simulation of a modern pavement structure under the effects of a Mediterranean cli­mate has been developed. The last section of Alonso’s paper is devoted to collapse and swelling phenomena of subgrades. Collapse is found in some natural lightly cemented soils but it is more common in embankments compacted on the dry side of the optimum water content. A real case involving severe collapse deformations and the role of described models to analyse the problem is presented. Finally, the available techniques to design and analyse the behaviour of highways on expansive soils are presented.

1

0.9

0.8

0.7 ro

0.6 IS

0.5 о

0.4

0.2 0.1 0

Alonso et al. (2002) also presented an analysis of the optimum position and depth of longitudinal drains in pavements. An analysis of different climates on the over­all pavement behaviour is then given. Three climates have been defined: Tropical, Mediterranean and Sub-alpine (see Chapter 1, Section 1.11), which were defined on the basis of actual data involving rainfall, temperature and relative humidity records. Five years of climate were simulated and the reaction of the selected pavement struc­ture and drainage position were computed and discussed. Figure 11.4 shows some of the computed results. It can be seen that the addition of longitudinal drains has a profound effect on the granular base and sub-base saturation over time, whereas their effect on the subgrade, Fig. 11.5, was found to be more limited. Longitudinal

b)

0 2 4 6 8 10 12 14

m

Fig. 11.5 Distribution of degree of saturation for a pavement in a Mediterranean climate. Evapora­tion through pavement allowed. (a) 1st July, (b) 1st December, adapted from Alonso et al. (2002)
drains are capable of maintaining a fairly well drained subgrade platform under a Mediterranean climate (as illustrated) whereas their effect was found to be more limited under sub-alpine or tropical climates.

The monolithic approach of coupled phenomena implies identical space and time meshes for each phenomenon. This is not always possible, for various reasons. The coupled problems may have different numerical convergence properties, generally associated with different physical scales or non-linearities. For example, a coupled hydro-mechanical problem may need large time steps for the fluid diffusion prob­lem, in order to allow, in each step, fluid diffusion over a long distance (of the order of magnitude of the finite elements). At the same time, strong non-linearities may occur in solid mechanics behaviour (strong elasto-plasticity changes, interface be­haviour, strain localisation…) and then the numerical convergence will need short time-loading steps, which should be adapted automatically to the rate of conver­gence. Then, it is quite impossible to obtain numerical convergence for identical time and space meshes.

Research teams of different physical and numerical culture have progressively developed different modelling problems. As an example, fluid flow has been largely
developed using the finite difference method for hydrogeology problems including pollutant transport, and for oil reservoir engineering (see Section 11.2.3) taking mul­tiphase fluid flow (oil, gas, condensate, water,…) into account. Coupling such fluid flow with geomechanics in a monolithical approach would imply implementation of all the physical features already developed respectively in finite elements and finite differences codes. The global human effort would be very large!

Coupled problems generally present a higher non-linearity level then uncoupled ones. Thus, inaccuracy in parameters or in the problem idealisation may cause degradations of the convergence performance. How can we solve such problems and obtain a convincing solution? First of all, a good strategy would be to start with the uncoupled modelling of the leading process, and to try to obtain a reasonable first approximation. Then, one can add a first level of coupling and complexity, followed by a second one… until the full solution is obtained.

However such a “trick” is not always sufficient. Staggered approaches may then give an interesting solution. In a staggered scheme, the different problems to be coupled are solved separately, with (depending on the cases) different space or time mesh, or different numerical codes. However, the coupling is ensured thanks to transfer of information between the separated models at regular meeting points. This concept is summarised in Fig. 11.3. It allows, theoretically, coupling of any models.

When using different spatial meshes, or when coupling finite elements and finite differences codes, the transfer of information often needs an interpolation proce­dure, as the information to be exchanged is not defined at the same points in the different meshes.

The accuracy of the coupling scheme will mainly depend on the information exchange frequency (which is limited by the lowest time step that can be used) and by the type of information exchanged. The stability and accuracy of the process has been checked by different authors (Turska & Schrefler, 1993; Zienkiewicz et al., 1988). It has been shown that a good choice of the information exchange may highly improve the procedure efficiency.

Time