# Evaluation of anti-rutting capacity of road structures

Rutting is a popular kind of road distress in Vietnam in recent years. This phenomenon is due to the permanent deformation of asphalt concrete under repeated loading of vehicles. Rutting is divided into 3 types: rutting at the asphalt layers, rutting at the foundation and rutting at both asphalt layers and foundation. Among these types, the first and the third ones are most popular. There are three mechanisms forming rutting: post compaction consolidation, creep flow and shear defomation where shear deformation mechanism is dominant. Shear deformation limitation is the key to control rutting phenomenon.

Empirical method is usually used to evaluate anti-rutting capacity of road structures by simulating the in situ behavior of road structures. Two typical types of experiments are fullscale test and scale model test. Scale model test with Hamburg Wheel Tracking Device is the most used.

In comparison with empirical method, mechanistic method has much advantage and is the subject of research of many scientists. With aid of this method, one can estimate rutting depth of the whole road structures rather than of an asphalt concrete layer as estimated with Hamburg Wheel Tracking Device. The BMT R&D and Testing Departement is working on a finite defomation elasto-plastic model to estimate anti-rutting capacity of road structure.

Asphalt concrete is a kind of cohesive geomaterial. Its shear strength is made of cohesion c and internal friction angle $\varphi$. The BMT R&D and Testing Departement applies a method of [Christensen et al., 2002] to determine c, $\varphi$ of asphalt concrete. The method is as follow. Let $\sigma$uni be the uniaxial compression strength and pidt is applied (distributed) force at failure of indirect tensile test.

The cohesion c and internal friction angle j are the solution of two following equations

With these two parameters in hand, one can make a first step evaluation of anti-rutting capacity of road structures by calculating elasticity limit and bearing capacity using c-$\varphi$

model of Morh-Coulomb or Drucker-Prager. If the applied pressure is less than elasticity  limit, the whole road structures is in elastic region and rutting does not happen. If the applied pressure is greater than the bearing capacity, rutting is happening in the short term. Ortherwise, rutting will happen in the long term. In this case, rutting depth is a function of climate, applied load, material properties as well as numbers of axles. Rutting depth is defined as irreversible displacement of road surface. Estimation of rutting depth has important meanings as discussed below.

(i) direct problem: Let road structure cross section, applied load, materials properties, number of axles be known. In estimating rutting depth and consulting rutting severity level, one can answer the question “Is rutting happens?” and  “When does rutting happen?”.

(ii) inverse problem: One must chose road structure cross section, applied load, material so that rutting depth were less than an allowable value. This means that rutting will not happen.

In order to estimate rutting depth in function of exploitation time, one needs to determine plastic deformation modulus H(N) of asphalt concrete. This modulus decays with exploitation time and is modeled as a logarithm function

[Ben-Naim 1998, Karrech 2011].

In this model, three parameters  describe rutting law of material and are determined by experiments. With the problem described below, there exists an analytical solution of permanent deformation

The applied pressure – displacement curve and rutting depth in function of number of axles are represented in figure 1 and 2.

Fig 1. Applied pressure – displacement curve

Fig 2. Rutting depth in function of number of cycles

Rutting depth increases rapidly within the first 1000 cycles and then increases slowly. This result is in accordance with the result obtained with Hamburg Wheel Tracking Test and with field observation.

Nguyễn H T Tài
R&D and Testing Departement, BMT Investment Construction JS Company