To support the growing demands of pavement maintenance engineering, this study focused on the strength characterization of a high-performance asphalt mixture specifically designed for ultra-thin overlays. The mixture adopted a gap-graded SMA-8 gradation and incorporated a chemically toughened modified asphalt binder, developed by Prof. Jianlong Zheng’s team at the School of Transportation Engineering, Changsha University of Science and Technology. Basalt was selected as the aggregate material.

Comprehensive strength tests including direct tension, indirect tension, and unconfined compression—were conducted to capture the material’s mechanical behavior under various stress modes. A unified strength model was established to evaluate the performance consistency across these loading conditions.

Key material properties and mixture proportions are summarized in Tables 1–5, including the physical characteristics of the modified binder (Table 1), bulk densities of the aggregates (Table 2), performance indices of lignin fibers (Table 3), gradation design for the SMA-8 mixture (Table 4), and Marshall test results for determining the optimal asphalt content (Table 5).

To establish the optimum asphalt–aggregate ratio (OAR), a Marshall mix design was performed. Five trial asphalt contents—5.4, 5.7, 6.0, 6.3, and 6.6 wt% of the total mixture—were prepared and tested in triplicate for stability, flow, air voids, voids in mineral aggregate (VMA), and voids filled with asphalt (VFA). Statistical evaluation showed that 6.1 wt% simultaneously satisfied all JTG E20-2011 design requirements while offering the greatest stability reserve. Therefore, 6.1 wt% was selected as the optimum asphalt content for subsequent specimen preparation (Table 5).

Direct tensile strength tests were conducted at loading rates of 10, 15, 20, 25, 30, 50, 60, 80, 100, and 110 MPa/s. The test results are summarized in Table 6, and the relationship between tensile strength and loading rate is shown in Figure 2.

The results indicate a clear trend: the direct tensile strength of the asphalt mixture increases progressively with the loading rate, following a power-law relationship. The fitted regression model for this trend is shown in Equation 1: R D = 5.401986 v 0.14149 , R 2 = 0.97144 (1) where R _D is the direct tensile strength (MPa), and v is the loading rate (MPa/s). The coefficient of determination (R ² = 0.97144) confirms the reliability of the fitting.

This rate-dependent strengthening behavior can be attributed to the viscoelastic nature of asphalt mixtures. At higher loading rates, the time available for crack nucleation and propagation is reduced, resulting in a delayed failure process and thus a higher apparent strength. This phenomenon is analogous to the stiffening observed at low temperatures, where increased stiffness inhibits microcrack growth. As the loading rate continues to increase, the strength enhancement gradually plateaus, indicating a saturation effect in the rate sensitivity of the material.

The uniaxial compressive strength of the asphalt mixture was evaluated at loading rates of 1, 5, 10, 15, 20 and 25 MPa/s. Due to equipment limitations, direct measurements at higher loading rates were not feasible using the MTS Landmark testing system. Therefore, a delayed loading extrapolation method (Xia et al, 2019) was employed to estimate compressive strength values beyond 25 MPa/s. The extrapolated strengths for higher loading rates (30–110 MPa/s) are also included in the analysis.

The test results are summarized in Table 7, and the corresponding strength-loading rate relationship is illustrated in Figure 3.

The fitted power-law model describing the relationship between compressive strength and loading rate is demonstrated by Equation 2: R C = 18.23685 v 0.16183 , R 2 = 0.99852 (2) where R _C is the unconfined compressive strength (MPa), and v is the loading rate (MPa/s). The high coefficient of determination (R ² = 0.98825) confirms the accuracy and reliability of the fitted curve.

The fitting results demonstrate that the compressive strength of the asphalt mixture increases significantly with loading rate, following a nonlinear trend. This behavior is attributed to the viscoelastic response of the material under rapid loading, which suppresses microcrack development and enhances aggregate interlock. As the loading rate increases, the deformation time shortens, resulting in stiffer material behavior and greater resistance to compressive failure.

In contrast to the tensile strength discussed in Section 3.1, the compressive strength exhibits both higher absolute values and greater rate sensitivity. This difference arises from the fundamental mechanics of failure: compressive loading activates the full structural capacity of the aggregate skeleton, while tensile loading primarily challenges the adhesive and cohesive properties of the asphalt binder.

The extrapolated compressive strengths under higher loading rates—obtained through the fitted model serve as a critical dataset for strength comparison across stress modes and provide the basis for constructing the unified strength model described in Section 3.5.

The indirect tensile strength of the asphalt mixture was evaluated at loading rates of 10, 15, 20, 25, 30, 50, 60, 80, 100, and 110 MPa/s, consistent with the rates used in the direct tension tests. Test results are summarized in Table 8, and the corresponding relationship between strength and loading rate is illustrated in Figure 4.

The variation of indirect tensile strength with loading rate can be described by the power-law function in Equation 3: R T = 4.11121 v 0.17620 , R 2 = 0.98489 (3) where R _T is the indirect tensile strength (MPa), and v represents the loading rate (MPa/s). The coefficient of determination for this regression model is 0.98489, indicating strong consistency between experimental data and the fitted trend.

An increase in loading rate leads to a nonlinear increase in indirect tensile strength. This trend is attributed to the viscoelastic characteristics of the asphalt mixture, which become more pronounced under rapid loading conditions. At higher loading rates, the time available for crack nucleation and propagation is reduced, resulting in enhanced apparent strength. The increase in strength tends to slow down as the loading rate approaches higher values, suggesting that the material reaches a threshold of rate sensitivity beyond which further strength gains are limited.

Compared with the other loading modes, the indirect tensile strength shows the highest sensitivity to changes in loading rate, as indicated by the exponent value of 0.17620. The direct tensile strength exhibits the lowest rate sensitivity, with an exponent of 0.14149, while the compressive strength shows intermediate sensitivity with an exponent of 0.16183.

In terms of strength magnitude, unconfined compressive strength remains significantly higher than both tensile modes due to the dominant role of aggregate interlock under compressive loading. However, the rate-dependent behavior under indirect tension reflects a more prominent influence of crack formation and propagation mechanisms, which are particularly sensitive to time-dependent loading conditions.

These results confirm that asphalt mixtures exhibit distinct mechanical responses under different stress states. Both the magnitude of strength and its sensitivity to loading rate vary across testing methods. This variation reinforces the necessity of developing a unified strength evaluation framework capable of bridging different loading conditions, which is addressed in Section 3.5.

Asphalt mixtures are composed primarily of asphalt binder and mineral aggregates. The mechanical behavior of the material is governed by the interaction between these two phases. The binder provides cohesive strength, while contact and interlock among aggregate particles contribute to internal friction. These two parameters—cohesion and internal friction angle—are fundamental components of the shear strength and are typically described using the Mohr Coulomb failure criterion.

Triaxial shear testing is conventionally regarded as the standard method for determining these strength parameters, due to its ability to replicate complex stress states encountered in the field. However, the high cost, operational complexity, and strict requirements for sample preparation and test execution often limit its application in routine engineering evaluations.

To simplify the testing process and improve practical applicability, this study employed an alternative method using direct tension and unconfined compression tests to estimate cohesion and internal friction angle. Based on the assumption that material properties remain consistent across test modes and that principal stresses can be represented by the measured strengths, the Mohr Coulomb envelope can be constructed using results from unconfined compression and direct tension.

In direct tension, the stress condition corresponds to σ ₁ = R _D and σ ₃ = 0, while in unconfined compression, it corresponds to σ ₁ = 0 and σ ₃ = −R _C . By constructing the Mohr circle under these two stress conditions, cohesion C and internal friction angle φ can be back-calculated using geometric principles. The relationship between the two is defined as shown in Equations 4, 5: tan ⁡ φ = R C − R D 2 R C R D = C l + R D (4) C = R C R D 2 (5)

By substituting the strength values from Table 6 (direct tensile strength) and Table 7 (unconfined compressive strength) into the above equations, the corresponding values of cohesion and internal friction angle under various loading rates were calculated. The results are summarized in Table 9, and their variation trends with loading rate are illustrated in Figure 5.

As illustrated in Figure 5, the cohesion of the asphalt mixture increases significantly with loading rate, showing a rapid rise followed by a gradual leveling off. This trend indicates enhanced interfacial adhesion between asphalt and aggregates under rapid loading conditions, which can be attributed to reduced molecular mobility and improved stiffness. The calculated cohesion values are influenced simultaneously by compressive and tensile strength, reflecting the combined effect of aggregate structure and binder adhesion.

In contrast, the internal friction angle exhibits a fluctuating trend rather than a clear monotonic change with loading rate. The variation in internal friction angle may result from differences in failure mechanisms, local stress distributions, or microstructural inconsistencies. Unlike cohesion, which is primarily governed by asphalt–aggregate interaction, the internal friction angle is more sensitive to aggregate morphology, compaction quality, and crack propagation paths—all of which may vary across test conditions.

These observations suggest that cohesion is a more stable and reliable indicator of rate-dependent strength enhancement, while the internal friction angle is more prone to experimental fluctuations. Further investigation at the microscale is necessary to clarify the mechanisms driving the evolution of internal friction with loading rate.

To establish a consistent strength characterization framework across different loading modes, the average strength values obtained from direct tensile, indirect tensile, and unconfined compression tests were compiled for a loading rate range of 10–110 MPa/s. These results, including extrapolated values for compressive strength using the delayed loading method, are presented in Table 10.

Table 10 clearly shows the progressive increase in strength with loading rate for each stress mode. Among the three, unconfined compressive strength reaches the highest magnitude, while direct and indirect tensile strengths remain comparatively lower but still exhibit notable rate sensitivity.

To further visualize and compare these trends, Figure 6 presents the fitted strength–loading rate relationships for the three loading modes.

As shown in Figure 6, all strength values increase with loading rate and conform to power-law trends. However, their growth patterns differ significantly. The compressive strength exhibits the steepest increase, reflecting enhanced aggregate interlock and greater resistance under compression as loading rate increases. In contrast, direct and indirect tensile strengths demonstrate more moderate increases and follow nearly parallel trajectories, suggesting similar viscoelastic responses under tensile loading.

To quantify these differences, the regression parameters for each stress mode are listed in Table 11.

As shown in Table 11, the fitted models for all three modes yield high coefficients of determination (R ² >0.97), confirming the strong correlation between strength and loading rate. However, the considerable variation in both α and β values indicates that direct conversion of strength values across different loading modes is unreliable without further normalization.

To address this issue, a dimensionless normalization approach was adopted. For each loading mode, the strength at 110 MPa/s was designated as the reference value S ₀, and both strength and loading rate were normalized to obtain strength ratios S/S ₀ and rate ratios v/v ₀. The normalized data for all three loading modes are provided in Table 12.

Figure 7 plots the normalized strength ratio against the normalized loading rate ratio.

Figure 7 plots the normalized strength ratio against the normalized loading rate ratio. As shown in Figure 7, the normalized data from all three loading modes collapse onto a single unified curve. This trend can be well represented by the following power-law relationship: S / S 0 = 0.98347 v / v 0 0.16389 , R 2 = 0.92641 (6)

The fitting result achieves a high correlation coefficient (R ² = 0.92641), demonstrating the feasibility of using a unified strength model to describe rate-dependent mechanical behavior across different stress states.

This normalization-based approach enables reliable interconversion of strength values among direct tension, indirect tension, and unconfined compression modes. It also offers practical benefits, such as reducing the number of required strength tests by allowing estimation of unmeasured strength values based on a known test result under another mode. Furthermore, the model facilitates unified material characterization and design parameter selection in performance-based mixture design and mechanistic-empirical pavement analysis frameworks.