Issue 74

B Budzi ń ski et alii, Fracture and Structural Integrity, 74 (2025) 165-170; DOI: 10.3221/IGF-ESIS.74.11

Cracked state

Uncracked state

RC Class [MPa]

Large blocks Small blocks E [MPa]  [-] E [MPa]  [-] E [MPa]  [-]

C5/6 C3/4

7 200 4 800

0.25 0.25

2 500 2 000

0.3 0.3

500 400

0.3

0.3 Table 2: Stiffness moduli and Poisson's ratios of HBM adopted for the 2014 Catalogue design [7]

C OMPARISON OF THE SELECTED FATIGUE CRITERIA FOR CBGM LAYERS

T

he fatigue criterion for hydraulically bound layers refers to the number of equivalent single axle loads (ESALs) after which cracking occurs at the bottom of the layer. A comprehensive review of commonly used fatigue criteria for hydraulically bound layers in pavement design was carried out by Pe ł czy ń ska and Gajewski in 2018 [8]. Most of these criteria define fatigue life using parameters indirectly related to material fatigue behavior, such as tensile strength or ultimate tensile strain. In the case of hydraulically bound materials, there is also a relatively poorly understood phenomenon known as "mortar training," which refers to the temporary increase in strength during the early life of the material [9,10]. The analysis of fatigue criteria revealed that for low traffic loads, the Dempsey criterion yields the lowest fatigue life values. This criterion has been used in the fatigue life calculations of semi-rigid pavement structures in Poland. Dempsey and his team recommended using a modified formula originally proposed by the Portland Cement Association (PCA) in 1966 for the design of concrete pavements [11]. This approach takes into account the tensile strength of the hydraulically bound layer Rf and the tensile stress at the bottom of the layer σ t. In the absence of direct test data, Dempsey proposed assuming a tensile strength value equal to one-fifth of the compressive strength RC.

t 



11.782 12.1212 



(1)

logN

f

R

f

Among the fatigue criteria that provide significantly higher fatigue life estimates for hydraulically bound layers under low traffic loads—and which have been calibrated through field testing—is the criterion developed by De Beer [12]. He calibrated his fatigue life formula based on test sections loaded using the Heavy Vehicle Simulator (HVS). This criterion considers the ratio of tensile strain ε t at the bottom of the hydraulically bound layer to the failure strain ε b , along with the influence of shrinkage-induced cracking, represented by a coefficient d. The value of d ranges from 1.1 for materials of lower strength and thicknesses below 20 cm, to 1.4 for higher-strength materials and thicknesses above 20 cm.

7.19 1           8 b  d  

logN

(2)

f

M ATERIALS AND METHODS

T

o calculate strains and stresses in the layers of the pavement structure (Fig. 3), the BISAR 3.0 software was used [13]. This program, based on the theory of multilayer elastic half-space, is designed for mechanistic pavement design. It has been and continues to be widely used in pavement structure dimensioning, including for the structures presented in the 2014 Polish Pavement Design Catalogue [7]. The calculations were performed for a CBGM C1.5/2 layer with a compressive strength R C =2.4 MPa and varying thickness, placed on subgrades with bearing capacities of 80 MPa and 25 MPa, and a Poisson's ratio ν =0.35. For fatigue life calculations corresponding to the first (uncracked) working phase, the following parameters were assumed for the CBGM layer: stiffness modulus E=2500 MPa and ν =0.3. In practical applications, it is common to place an unbound aggregate layer (with E=400 MPa and ν =0.3) on freshly laid CBGM. This is primarily for technological reasons: to ensure proper curing by preventing moisture loss and to protect the layer from construction traffic. The latter is particularly critical, as heavy construction traffic may cause premature cracking of the

168