# TIRE/PAVEMENT STRAIN TENSOR MEASUREMENT WITH AN INFRASTRUCTURE-BASED APPROACH

**A. L. Coiret**

Lab. Central des Ponts et Chaussees
Infrastructure and Road Safety Unit
BP 4129-Bouguenais, France 44341
Email: alex.coiret@lcpc.fr

**M.-L. V. Gallenne**

Lab. Central des Ponts et Chaussees
Technical Direction for
Road Safety and Management
marie-line.gallenne@lcpc.fr

**P.-Y. M. Texier**

Lab. Central des Ponts et Chaussees
Technical Direction for
Road Safety and Management
pierre-yves.texier@lcpc.fr

## ABSTRACT

Studies are conducted at the LCPC for investigating the role of infrastructures in road safety. In this context, tire/pavement contact characterization is a key point for both vehicle and road surface optimization. For this purpose, car industry usually instruments dedicated cars with wheel dynamometers but this procedure doesn't offer the possibility to observe a large set of vehicles in practice. Regarding road management, it has been chosen to use the infrastructure itself as an instrument for acquiring the complete 6-components stress tensor. In this paper, a new test apparatus allowing this is shown, using a mechanically isolated part of the pavement. Validations are presented on a variety of situations such as emergency braking and constant speed driving. Correlations with inboard vehicle sensors measurements and numerical models have been worked out.

## INTRODUCTION

To know road characteristics effects on vehicle controlability it is necessary to evaluate the stress tensor developed at the tire to road contact patch. Indeed the relationship between slips and forces needs to be more defined to predict road effects. The stress tensor can be estimated [1] meanwhile laboratory tests are often performed. 3D rotating wheel dynamometers mounted on vehicles provide forces which require corrections to take in account unsprung mass and wheel/tire inertia (method presented in [2]). Furthermore, as a general rule, it is difficult to use vehicle instrumentation when facing a large set of vehicles (as experienced in [3]). Then, we have chosen to instrument the infrastructure

itself for acquiring those forces. Three approaches have been envisaged : road-embedded strain gages, arrays of instrumented pins, and the instrumentation of a mechanicaly isolated part of the road. Embedded strain gages lead to Dirac-like and temperature sensitive outputs of which interpretation is risky [4]. Arrays of instrumented pins [5] mask the pavement surface. For freeing from these limitations, the third approach has been chosen and tested by means of a system called MEVI<fnref n="1" />.

## EXPERIMENTAL SET-UP

A surface layer pavement tile has been extracted, instrumented at its lower face with a 6 components force transducer (Figure 1, pavement surface element not showed), and placed at its original location to preserve the pavement surface characteristics. Its dimensions have been fixed in order to ensure the whole contact patch measurement, meanwhile limiting moments to non-hazardous levels for the sensor unit. A high frequency (2.5 kHz) measurement chain and a rigid sensor, with high natural frequency, allow the time-stabilized signals acquisition (forces and moments), and moreover their spatial evolutions as the tire moves on the tile area.

## MEASUREMENT ASSESSMENT

### Assessment Facing an Instrumented Vehicle

For safety considerations and better identification, emergency braking tests are often realized with disconnected rear

<footnote n="1">¹Measure of force applied to vehicles, by the Infrastructure</footnote>
<figure><img src="image_1.png" /><figcaption>Figure 1. SYSTEM INTEGRATION IN THE INFRASTRUCTURE.</figcaption></figure>

brakes, as described in the LCPC frontal braking procedure [6]. While braking, a loading transfer occurs from the rear to the front axle. The mean front-tire longitudinal road friction coefficient is given by equation 1 (with α and β free-rolling term coefficients ; M global mass, Z<sub>fr</sub> front load, h gravity center height, L wheel-base and d distance needed to brake from V<sub>1</sub> velocity to V<sub>2</sub>).

$$
\mu_{\text{mean}} = \frac{M \left( \left[ \frac{V_1^2 - V_2^2}{2 \cdot d} \right] - \left[ \alpha + \beta \frac{(V_1 + V_2)^2}{2} \right] \right)}{Z_{fr} + M \left( \frac{V_1^2 - V_2^2}{2 \cdot d} \right) \frac{h}{L}} \quad (1)
$$

Measurements have been realized with the "MEVI" system in frontal or full (but moderate) braking situations, with or without anti-locking system, for initial speed between 8 to 28 m/s, with dry or wet conditions. Figure 2 presents measurements while braking only the front wheels for the front and the rear tires (respectively left and right parts of the graph). Loading transfers and longitudinal forces measured by MEVI comply with inboard measurements and with results from equation 1, after taking into account estimated aerodynamic strains. Tests realized at constant speed and freewheel have both shown the possibility to reach such low forces as aerodynamic stress or transversal corrections applied by the driver to compensate banking.

Assessment Facing a Detailed Numerical Model

The global inertial force exerted on a vehicle cornering at
a steady speed is centrifugal. MEVI has shown that this force
measured under the front inner tire is centripetal (Figure 3) which
is in accordance (less than 10%) with results given by a complete
dynamical model as Callas. This experiment shows the interest
of disaggregated measurements facing a global vehicle approach.

In conclusion, strain tensor measurements have been per-
formed with an infrastructure-based approach, allowing to study
the safety offer by a given road facing of varied vehicles, without
needing to instrument all of them. First order reliability has been
verified with a testing vehicle and a full numerical model.

<figure><img src="image_2.png" /><figcaption>Figure 2. DRY EMERGENCY BRAKING FROM 20 M/S.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 3. MANEUVER AT LOW SPEED AND LOW TURNING RADIUS.</figcaption></figure>

REFERENCES

1. Gustafsson, F., 1997. "Slip-based tyre-road friction estimation". *Automatica*, **33**(606), pp. 1087-1099.

2. Minakawa, M., Nakahara, J., and Nimomiya, J., 1999. "Method for measuring force transmitted from road surface to tires and its applications". *JSAE, 20*, pp. 479-485.

3. Coiret, A., and Delanne, Y., 2003. "Modelisation of accident risks links to the heterogeneity of grouped vehicles". *Tech. Innovation Land and Transportation, 1*(302), pp. 365-373.

4. Vijayanath, B., Wu, Z., Hossain, M., and Gisi, A., 1999. "Instrumentation of the superpave test sections...". *Int. Conf. on Accelerated Pavement Testing, Reno, Nevada, 1999*.

5. DeBeer, M., Fisher, C., and Jooste, F., 2002. "Evaluation of non-uniforme tyre contact stresses...". *ISAP 2002, Denmark*.

6. LCPC, 2002. *Determination de l'adherence a partir d'essais de freinage frontal*. LCPC, Centre de Nantes, France.