Statistical Analysis of the Tensile Strength of Cold Recycled Cement-Treated Materials and Its Influence on Pavement Design

Abstract

The tensile behavior of cold recycled cement-treated mixtures (CRCTMs), typically produced through full-depth reclamation (FDR), is critical for pavement design. Since no universal design method exists, different tests are applied, leading to varying results. In this context, this study aimed (a) to statistically analyze the flexural tensile strength (FTS) and indirect tensile strength (ITS) of CRCTMs incorporating reclaimed asphalt pavement (RAP) and lateritic soil (LS); (b) to evaluate how using FTS or ITS influences the design of CRCTM layers. FTS and ITS tests were conducted with different cement (1–7%) and RAP (7–93%) contents at multiple curing times (3–28 days), and results were used for statistical and mechanistic analyses. Results showed that cement and RAP contents significantly increased FTS and ITS. RAP exhibited the strongest influence on ITS. This indicates that CRCTMs with similar materials benefit from higher RAP contents. Mechanistic analysis revealed that lower RAP contents require thicker pavement structures, suggesting that increasing RAP can reduce costs and environmental impacts. FTS was about 65% higher than ITS, but using ITS in design led to structures 1.7–3.3 times thicker for the same service life. These findings highlight the need for proper CRCTM characterization, with flexural tests recommended for more reliable and cost-effective pavement design.

1. Introduction

The use of chemically stabilized layers is an efficient solution to increase the structural capacity of asphalt pavements. Such materials also enhance pavement resilience against climatic effects, for example, by reducing their sensitivity to water [1,2,3,4,5]. This is particularly important in the context of environmental changes.

In recent years, there has been a growing pursuit of sustainable alternatives in civil construction. The adoption of practices aligned with the principles of the circular economy has driven the valorization of material recycling, with the goal of reducing the extraction of non-renewable natural resources. In this context, asphalt pavement recycling has emerged as a promising solution in the transportation infrastructure sector [6,7,8].

Portland cement can be used as a stabilizing agent in pavement recycling, typically in contents ranging from 2% to 6% [9]. The addition of cement provides the recycled layers with the typical properties of chemically stabilized materials, while the presence of reclaimed asphalt pavement (RAP) provides increased flexibility [10]. The structural design of these layers is generally based on their fatigue performance, considered their main degradation mechanism. Shrinkage is also a relevant phenomenon, as it may induce early cracking. Despite the importance of these factors, studies addressing both fatigue [11,12,13,14,15] and shrinkage [4,5,16,17] on cold recycled cement-treated mixtures are still scarce.

The analysis of fatigue behavior in chemically stabilized layers is often performed using models based on the stress ratio (i.e., the ratio between the acting tensile stress and the tensile strength of the material) [18,19,20]. This approach highlights the need for an accurate determination of the tensile strength of these mixtures in the laboratory. However, since no universally adopted design method exists [21], different testing approaches are employed worldwide, which may yield varying strength values. In addition, correction factors and default values are often adopted. For instance, in France, direct tensile strength (DTS) is used for design purposes. However, some laboratories are not equipped for direct tension testing; instead, they measure indirect tensile strength (ITS) and estimate DTS by applying a factor of 0.8 to the former [22]. This can affect pavement structural design and result in under- or overestimations of service life.

Previous research reported analytical and numerical evaluations of various tests and found that only the biaxial flexural test was able to reproduce the stress path of chemically stabilized subgrades for railway infrastructure. However, the four-point bending (flexural) test and the direct tensile test showed results closer to the stress state than the ITS test [23].

In the case of cold recycled cement-treated mixtures (CRCTMs), there is a lack of a well-defined structural design method [21]. Previous studies reported that the modulus values obtained from four-point bending (flexural) tests are more consistent with those observed in the field [21,24], but no studies have yet assessed the effect of the selected method for determining tensile strength on pavement design, even though some investigations have employed more than one type of test [17,25,26,27,28]. This knowledge gap can affect decision-making in the design process, since distinct laboratory parameters may lead to different estimates. Thus, it is essential to study this topic in order to provide consistent technical guidelines.

Furthermore, lateritic soils (LSs) are often used as pavement materials in some regions [29,30,31], especially in tropical countries with restricted availability of high-quality granular materials, and may therefore be incorporated into CRCTMs. However, studies on cement-treated mixtures of RAP and LS are still limited, particularly regarding their flexural tensile behavior [32,33]. Previous research on these mixtures has predominantly focused on unconfined compressive and indirect tensile strengths [34,35,36].

In this context, the main objectives of this study are as follows: (a) to statistically analyze the effect of cement content, RAP content, and curing time on the tensile strength of CRCTMs of RAP and LS; (b) to evaluate how tensile strength values determined by different test methods (flexural or indirect tensile tests) influence the structural design of cold recycled cement-treated pavement layers.

2. Experimental Program

This section presents the materials and methods used in the experimental part of the study.

2.1. Materials

Laboratory tests were conducted on mixtures composed of cement, lateritic soil (LS), recycled base course, and RAP. Figure 1 illustrates the LS and RAP materials used in this study. LS was classified as a clayey lateritic soil (LG’) according to the MCT (Miniature, Compacted, Tropical) methodology [37]. Its liquid limit and plasticity index were 44% and 12%, respectively. Considering the classical classification systems, the soil is classified as a low-plasticity inorganic silt (ML) according to the Unified Soil Classification System (USCS) and as a plastic silt (A-7-5) according to the AASHTO Soil Classification System. It is important to note that, although the soil’s plasticity index is relatively high, the technical literature indicates that values up to 20% are acceptable for cement stabilization [38], whereas the limit should be restricted to 10% for asphalt stabilization [9]. The RAP contained 5.3% asphalt binder (6.0% in the fine fraction and 4.6% in the coarse fraction). LS and RAP were collected during a full-depth reclamation project from the base layer and wearing course of an actual pavement, respectively. Portland cement with ground-granulated blast-furnace slag addition (Brazilian type CP II E 32) was used.

2.2. Methods

The test methods employed in the present study are described in this section.

2.2.1. Compaction Tests

Modified Proctor compaction tests were performed to establish the optimum moisture content (OMC) and maximum dry unit weight (MDUW) of the studied mixtures, which served as the basis for specimen preparation. The procedure followed Method D of AASHTO T180-01 [39]. Mixtures were compacted in five layers within a mold with a diameter of 152.40 ± 0.70 mm and a height of 116.40 ± 0.50 mm, with 56 blows per layer applied using a 4.54 kg hammer dropped from a height of 457 mm. Not all mixtures were tested, since in some cases the cement contents (1.17% and 2%) or the RAP contents (70% and 80%) were very close to each other. Thus, the number of tests was reduced without compromising the quality of the data obtained. The mixtures that were not tested are highlighted in the following sections.

2.2.2. Flexural Tensile Strength Tests

A full factorial design with three levels (3k) for each factor k (cement and RAP contents) was considered, as presented in

Table 1. Experimental matrix of the flexural tensile strength tests.

Cement, C (%) 1	RAP (%) 1	Mixture Code	OMC (%)	MDUW (kN/m3)
2 (−1)	20 (−1)	2 C-20 RAP	14.2	17.10
2 (−1)	50 (0.2)	2 C-50 RAP 2	8.6	19.30
2 (−1)	70 (+1)	2 C-70 RAP 2	7.1	20.73
4 (0)	20 (−1)	4 C-20 RAP	14.2	17.41
4 (0)	50 (0.2)	4 C-50 RAP	10.9	19.59
4 (0)	70 (+1)	4 C-70 RAP	10.1	20.10
6 (+1)	20 (−1)	6 C-20 RAP	12.7	18.11
6 (+1)	50 (0.2)	6 C-50 RAP 2	12.8	19.43
6 (+1)	70 (+1)	6 C-70 RAP 2	8.2	21.03

¹ Coded units are presented in parentheses. ² Mixtures that were not tested and the used values are from similar mixtures presented in Table 2.

. The used cement and RAP levels were based on previous studies [4,10,33]. Flexural tensile strength (FTS) tests were carried out in triplicate and the results were evaluated through regression using Minitab^® 22.4.0 software. Analysis of Variance (ANOVA) was used to assess the significance of each model and its individual factors, and the significance level (α) adopted was 0.05. Table 1 also presents the compaction characteristics of the mixtures (OMC and MDUW), while their grain size distributions are shown in Figure 2. The same figure also presents the LS and RAP grain size distributions. The grain size distributions of the mixtures were defined exclusively from those of the LS and RAP materials, without considering the cement. Although some standards specify gradation envelopes [38] and some of the studied mixtures may fall outside those limits, it was decided not to modify the materials by adding virgin aggregates for correction. This approach aimed to accurately assess the influence of the soil–RAP proportion on the mixture, without altering its original composition. It is important to highlight that the mixtures with 2% and 4% of cement were also studied by Fedrigo et al. [33], which evaluated their resilient and fatigue behavior.

Prismatic beams (100 mm × 100 mm × 400 mm) were produced from LS + RAP mixtures containing the specified amounts of cement and water at OMC (calculated considering the dry mass of solids). The RAP and LS were air-dried until reaching constant mass. After weighing RAP, LS, cement, and water, the solids were first blended, and then water was gradually incorporated while mixing continued. The mixtures were statically compacted in three equal layers to reach the MDUW using a hydraulic press, based on previous studies [10,33]. To enhance interlayer bonding, the surface of each compacted layer was carefully scarified. The specimens were cured for 28 days at room temperature in sealed plastic bags to preserve the mixtures’ moisture content.

Tests were carried out using a four-point bending configuration, following the experience of the National Cooperative Highway Research Program [18,19,20]. A testing machine with a 250 kN capacity was employed. As in the methodology of Castañeda López et al. [10], the testing temperature and relative humidity were kept at 24 ± 3 °C and 55 ± 15%, respectively. Tests were carried out under controlled-stress conditions, with stress increasing monotonically at a rate of 0.69 MPa/min. The flexural tensile stress was calculated using Equation (1). The flexural tensile strength is defined as the maximum flexural stress that the material can withstand.

$${\sigma }_i={\displaystyle \frac{P_i\ast L}{{w\ast h}^2}}$$

(1)

where σ_i (MPa) is the flexural tensile stress corresponding to force P_i (N); L is the length between supporting rollers (300 mm); w and h are the average width and height of the specimen (mm), respectively.

2.2.3. Indirect Tensile Strength Tests

Indirect tensile strength (ITS) test specimens are easier to prepare than those used for flexural tests; therefore, this test was selected to analyze more levels of cement and RAP contents, as well as to include curing time as a factor. In this case, Design of Experiments (DoE) was used to define the experimental matrix. The Central Composite Design (CCD) was selected because it allows accurate estimation of the response while avoiding the large number of tests required in a full factorial design. CCD and other statistical techniques have been employed for mix design evaluation and optimization of chemically stabilized materials [40,41]. A concise description of the CCD is provided based on the literature [42,43,44,45].

The CCD is structured on a two-level factorial design (2k), supplemented with 2 * k axial (star) points positioned along the coordinate axes, plus replicated runs at the centroid (0, 0). The 2k factorial points (−1, +1) enable the estimation of first-order effects (linear terms and interactions), while the axial points (−α, +α) provide information on second-order effects. The error estimated at the center point (in this study, six replicates of mixture 4 C-50 RAP) offers a reliable measure of experimental variability.

Table 2. Experimental matrix of the indirect tensile strength tests.

Cement, C (%) 1	RAP (%) 1	Mixture Code	OMC (%)	MDUW (kN/m3)
1.17 (−α = −1.414)	50 (0)	1.17 C-50 RAP	8.6	19.30
2 (−1)	20 (−1)	2 C-20 RAP	14.2	17.10
2 (−1)	80 (+1)	2 C-80 RAP	7.1	20.73
4 (0)	7.57 (−α = −1.414)	4 C-7.57 RAP	18.0	17.57
4 (0)	50 (0)	4 C-50 RAP	10.9	19.59
4 (0)	92.43 (+α = + 1.414)	4 C-92.43 RAP	5.8	21.64
6 (+1)	20 (−1)	6 C-20 RAP	12.7	18.11
6 (+1)	80 (+1)	6 C-80 RAP	8.2	21.03
6.83 (+α = +1.414)	50 (0)	6.83 C-50 RAP	12.8	19.43

¹ Symbols/coded units in parentheses: −1 and +1 represent the 2k factorial points, −α and +α represent the axial points, which coded values are −1.414 and +1.414, respectively, and 0 represents the center point.

presents the experimental matrix of the ITS tests. Minitab^® 22.4.0 software randomized the run order to reduce systematic bias. It should be emphasized that curing time was not included as a factor in the CCD; instead, separate CCDs were conducted for each curing period. Once the DoE was completed, regression analysis was applied to the results. ANOVA with a significance level of 0.05 was used. Additional details on the CCD employed can be found in Kleinert et al. [46]. Table 2 also summarizes the compaction properties of the mixtures, while Figure 3 shows their grain size distributions. The same considerations made for the grain size distributions of the mixtures tested for FTS also apply to those tested for ITS.

Mixtures were prepared following the same procedures as in the flexural tests. Cylindrical specimens, 102 mm in diameter and 65 mm in height (Marshall mold), were compacted by applying blows of the Marshall hammer to both faces and then cured for 3, 7, 14, and 28 days under the same conditions as the flexural specimens. The testing procedures followed ASTM D6931 [47]. Tests were carried out under controlled-strain/displacement conditions, with displacement increasing at a rate of 50 mm/min until specimen failure. Equation (2) was used to calculate the indirect tensile strength (MPa).

$$ITS={\displaystyle \frac{2P}{\pi Dh}}$$

(2)

where P is the peak load (N); D is the diameter of the specimen (mm); h is the height of the specimen (mm).

3. Mechanistic Pavement Design

The hypothetic pavement structure shown in

Table 3. Analyzed pavement structure.

Layer	Material	Thickness (mm)	Modulus (MPa)	Poisson’s ratio
Wearing course	Asphalt concrete (Asphalt PEN 30/45 #12.5 mm Sepetiba) 1	150	9000	0.30
Base	Stabilized (studied CRCTMs)	200	Table 4	0.25
Subbase	Granular (Graded crushed stone—Gneiss C5) 1	200	381	0.35
Subgrade	Silty soil (Brazilian MCT classification NS’) 1,2	-	189	0.45

¹ Used data were the default present in the MeDiNa 2.0 software, which are based in laboratory tests on each material; ² NS’ denotes non-lateritic silty soil.

was initially used in the mechanistic analyses. The studied CRCTMs were considered as base layer material. The initial thickness of the base layer was set to 200 mm and the Poisson’s ratio was assumed to be 0.25, following research on CRCTMs by Kleinert [48]. Since the focus of the study was the cold recycled cement-treated layers, the Brazilian National Design Method (MeDiNa) default materials were used for the other layers [49]. However, it is important to note that all MeDiNa database is derived from previous experimental research on the default materials. The AEMC (Multiple layer elastic analysis), a linear elastic analysis program from the MeDiNa package, was used, and full-adhesion condition was assumed between the pavement layers.

Table 4. CRCTM data used in the mechanistic analysis.

Mixture	Resilient Modulus (MPa)	FTS (MPa) 1	ITS (MPa) 1	Fatigue Model 2
				k1	k2	R 2
4 C-20 RAP	2041	0.65	0.26	9.8504	−40.028	0.90
4 C-50 RAP	3505	0.96	0.52	10.527	−43.446	0.78
4 C-70 RAP	4163	0.93	0.70	9.0449	−28.538	0.69

¹ FTS and ITS values used in the mechanistic analysis are presented and analyzed in Section 4. ITS values for mixtures 4 C-20 RAP and 4 C-70 RAP were estimated using the prediction model presented in Table 8 (Section 4.2). ² Fatigue models reported by Fedrigo et al. [33].

presents the data for the CRCTMs. The resilient modulus values and the coefficients of the fatigue models were obtained by Fedrigo et al. [33] through flexural tests conducted after 28 days of curing. The authors investigated the same mixtures with 4% of cement as those used in the present study, which were considered in the mechanistic design. The fatigue models are expressed by Equation (3). It is important to note that the fatigue models were derived from laboratory tests and were not calibrated to field condition.

$$N={10}^{k_1+k_2.SR}$$

(3)

where N is the number of cycles to failure; SR is the stress ratio, that is, the ratio between applied tensile stress and tensile strength (in decimal); k₁ and k₂ are regression coefficients.

Although a thickness of 200 mm was initially defined for the CRCTM layers, the appropriate thicknesses of the mixtures presented in Table 4 were designed based on the fatigue models, first using the FTS values obtained in the present study and assuming a fatigue life of one million load cycles (maximum failure criterion considered for the laboratory tests). Subsequently, the analyses were repeated using the ITS values obtained in the present study in the fatigue models instead of the FTS. In this case, as later presented in the results section, the structure designed using the FTS was not sufficient. Since the CRCTM layers obtained in the first design stage were already too thick, they were limited to those values. Therefore, the thickness of the asphalt wearing course was increased until it ensured the same one million load cycles.

4. Results and Discussion

This section presents the experimental results and the outcomes from the mechanistic pavement design.

4.1. Flexural Tensile Strength

Table 5. Flexural tensile strength results.

Mixture	FTS (MPa)	Standard Deviation (MPa)
2 C-20 RAP	0.28	0.05
2 C-50 RAP	0.49	0.03
2 C-70 RAP	0.75	0.20
4 C-20 RAP	0.65	0.06
4 C-50 RAP	0.96	0.05
4 C-70 RAP	0.93	0.09
6 C-20 RAP	0.61	0.07
6 C-50 RAP	0.90	0.11
6 C-70 RAP	1.43	- 1

¹ Due to testing issues, it was only possible to test one specimen of mixture 6 C-70 RAP.

presents the 28-day FTS results. It is important to note the high standard deviation shown by mixture 2 C-70 RAP. This mixture contains the highest RAP content and the lowest cement content simultaneously. Since RAP is a highly heterogeneous material, it is possible that one of the specimens of this mixture contained chunks or a higher amount of a certain RAP fraction, which caused greater variability. In addition, the lower cement content may have been insufficient to make the mixture more homogeneous in terms of mechanical behavior. In this regard, mixture 4 C-70 RAP also shows higher standard deviation compared to the others with the same cement content.

Table 6. FTS statistical analysis results.

Term	Coefficient	p-Value
Constant	−0.118	2.2 × 10−14
Cement (%)	0.1068	2.0 × 10−5
RAP (%)	0.00948	4.7 × 10−5

summarizes the outcomes of the statistical analysis, showing the coefficients of the significant terms and their corresponding p-values. The interactions were evaluated but were not found to be statistically significant. The coefficient of determination (R²) of the regression model was 77.56%. The levels of the independent variables were standardized between −1 and +1; therefore, the model is presented using coded units (as presented in Table 1).

Figure 4 illustrates the main effects of the significant independent variables on the mean FTS. It is important to note that the main effects plots depict how each factor individually influences the response.

Figure 4 shows that FTS increases with both higher cement content and higher RAP content. The magnitude of these effects is also similar, with values ranging approximately from 0.5 MPa to 1.0 MPa. Although it is well known that FTS of CRCTMs increases with cement content [10,21,24,28,50], the increase in FTS with RAP content diverges from the findings reported in the literature, which indicate that cement-treated recycled pavement materials tend to lose strength with RAP addition [10,17,21,24,25,26,28,50], or may even present FTS values similar to those of conventional cement-treated materials [51]. As reported by Fedrigo et al. [33], this behavior may be attributed to the increase in LS percentage, which raised the finer fraction (clay) of the mixtures and consequently their specific surface area. The higher the specific surface area, the greater the cement demand required to bond the particles together. In addition, increasing RAP percentages resulted in well-graded grain size distributions, thereby enhancing strength.

4.2. Indirect Tensile Strength

Table 7. Indirect tensile strength results.

Mixture	3-Day ITS (MPa)	7-Day ITS (MPa)	14-Day ITS (MPa)	28-Day ITS (MPa)
1.17 C-50 RAP	0.22	0.17	0.10	0.05
2 C-20 RAP	0.34	0.26	0.18	0.16
2 C-80 RAP	0.44	0.52	0.47	0.58
4 C-7.57 RAP	0.38	0.42	0.26	0.42
4 C-50 RAP	0.56 [0.09]	0.64 [0.09]	0.42 [0.04]	0.50 [0.05]
4 C-92.43 RAP	0.48	0.72	0.85	0.86
6 C-20 RAP	0.37	0.24	0.21	0.22
6 C-80 RAP	0.71	0.81	0.98	0.84
6.83 C-50 RAP	0.57	0.63	0.70	0.84

presents the ITS results obtained at different curing times. The standard deviation of mixture 4 C-50 RAP, which was used to determine the experimental error, is presented in brackets. The coefficients of the significant terms and their corresponding p-values are shown in

Table 8. ITS statistical analysis results.

Term	Coefficient	p-Value
Constant	0.5234	0.000
Cement (%)	0.1990	1.5 × 10−14
RAP (%)	0.2627	4.4 × 10−12
Cement (%) * Cement (%)	−0.1148	0.002
Cement (%) * RAP (%)	0.1648	0.001
RAP (%) * Curing time (days)	0.1083	0.006

. The resulting regression model yielded a R² of 65.06%. Although the R² value was lower than that obtained for FTS, it is still considered acceptable for this type of material, as mixtures composed of RAP and soil exhibit inherent heterogeneity and variability. Nevertheless, the model was statistically significant (p-value < 0.05), and the residual analysis confirmed that the regression adequately represents the experimental data within the studied range. The levels of the independent variables were standardized between −1 and +1; therefore, the model is presented using coded units (as presented in Table 2).

Table 8 shows that cement and RAP contents had a significant effect on ITS, as did their interaction. Furthermore, cement exhibited a quadratic effect on ITS. The interaction between RAP content and curing time was also significant, although curing time alone was not. This can be observed in Table 7, where no clear pattern is seen across different curing times. The non-significant effect of curing time on ITS may be linked to variations in OMC during specimen preparation. After molding, the actual moisture content was verified using part of the same material, but these variations were not considered in the statistical analysis.

Figure 5 presents the Pareto chart, in which the red value (1.986) represents the critical t value from Student’s t-distribution, calculated for a 95% confidence level (α = 0.05) based on the residual degrees of freedom. This threshold is used to identify statistically significant effects in the Pareto chart, where factors with absolute t values exceeding 1.986 are considered significant. From the chart, it can be inferred that RAP content had the most significant effect, closely followed by cement content, while the least significant effect was the interaction between RAP content and curing time.

Figure 6 illustrates the main effects of the significant independent variables on the mean ITS. Confirming the outcomes of the Pareto chart, the mean ITS varies from 0.2 MPa to 0.8 MPa with RAP content, a wider range than that produced by cement content (0.2 MPa to 0.6 MPa). Moreover, the quadratic effect of cement content can be observed graphically, with the mean ITS stabilizing at 6% cement and then tending to decrease. As with FTS, ITS increased with cement content and RAP content; the former agrees with the literature [21,24,28,36,52,53,54,55,56,57,58], while the latter contrasts with previous findings on the ITS of CRCTMs [17,21,24,25,26,28,52,53,54,55,58,59], for which possible explanations were provided in Section 4.1.

Figure 7 shows the interaction effects on the mean of ITS. It can be observed that for RAP contents lower than 30%, 4% cement results in a higher ITS than 6.83% cement. Conversely, for RAP contents greater than 30%, the higher cement content yields higher ITS. This behavior may be related to the fact that at lower RAP contents (i.e., higher LS content), cement levels even above 6.83% would be required due to the greater quantity of fines present in the mixture. The effect of curing time also depends on RAP content. For RAP contents below 50%, shorter curing times lead to higher ITS, while the opposite trend is observed for higher RAP contents. A possible explanation is that, although the mixtures were cured in sealed conditions, they still lost some water due to hydration reactions. At shorter curing times, specimens with higher LS content would retain more water than mixtures with higher RAP content, possibly generating suction effects during testing. At longer curing times, more water would be consumed by hydration, reducing suction and consequently lowering ITS; an effect even more pronounced in mixtures with lower LS content. However, it is also important to note that, due to possible variations in OMC during specimen preparation, as previously mentioned, the OMC might not have been constant, and some mixtures may have contained more water in the matrix, affecting the curing process.

The Brazilian technical specification for full-depth reclamation with Portland cement (FDR-PC) [60] states that the 7-day ITS range for such materials should be between 0.25 MPa and 0.35 MPa. Figure 8 presents a contour plot showing that, when recycling an LS base layer, achieving these limits would require maximizing the use of RAP; otherwise, the cement content would need to be increased. However, since the specification limits RAP content to 50%, it would then be necessary to incorporate natural aggregates to stabilize the mixture, in contradiction with the principles of the circular economy. It should be noted that the specification does not establish any recommended or maximum value for the cement content.

4.3. Comparison Between Flexural and Indirect Tensile Strengths

Figure 9a,b present the contour plots for the 28-day results of FTS and ITS, respectively. Although the contour plots present the cement and RAP contents in uncoded levels, the software used the coded models presented in Table 6 and Table 8 to generate them. The graphs facilitate the determination of tensile strength as a function of cement and RAP contents. They may also be useful in the preliminary mix design phase for mixtures composed of similar materials. Furthermore, the minimum limit of the tensile strength ranges shown in the graphs confirms that FTS values (0.4 MPa) are generally higher than those of ITS (0.2 MPa).

The relationship between FTS and ITS is presented in Figure 10. The 28-day ITS of the mixtures that were not experimentally obtained were estimated using the ITS model, whose coefficients are shown in Table 8. This was necessary because the experimental matrix for ITS differed from that of FTS. The model presented in Figure 10 allows one to obtain the 28-day FTS based on the 28-day ITS with high predictive power (R² of approximately 98%). The model also confirms that FTS is generally higher than ITS, by a factor of approximately 65%. It is important to highlight that, although such a model is presented, the relationship between FTS and ITS is not constant (ranging from 1.3 to 2.5), possibly due to mix design variables. This variability is illustrated in Figure 11, where the isoline corresponding to the 1.65 ratio is highlighted (color changing from red to green). Another important aspect to be considered is that, by isolating the load in Equations (1) and (2) and equating them in terms of stress, an FTS/ITS ratio of 2.83 is obtained. Therefore, when considering only the geometry and not the material type, the ratio between the two tensile stresses is even higher.

It also is important to point out that controlled-stress tests (FTS) are more aggressive than controlled-strain/displacement tests (ITS), as also observed in cyclic testing [61]. Nevertheless, the FTS results were still higher. Another relevant observation is that, based on the tensile strength models (Table 6 and Table 8), the coefficients associated with cement and RAP are higher for ITS, suggesting a stronger influence on ITS compared to FTS.

4.4. Mechanistic Pavement Design Results

Table 9. Mechanistic design of the pavements with CRCTM base layers.

Mixture	Initially Defined Structure		Structure Designed Using FTS		Structure Designed Using ITS
	WC (mm)	BL (mm)	WC (mm)	BL (mm)	WC (mm)	BL (mm)
4 C-20 RAP	150	200	150	450	500	450
4 C-50 RAP	150	200	150	400	380	400
4 C-70 RAP	150	200	150	430	260	430

WC = wearing course; BL = base layer.

shows the results of the mechanistic design for pavement structures with CRCTM base layers. It can be observed that using FTS in the fatigue model to predict a service life of one million cycles resulted in CRCTM base layers 400–450 mm thick, depending on the RAP content. When ITS was used in the fatigue model, in addition to the base layer thickness, the asphalt concrete wearing course had to be increased from 150 mm to 260–500 mm, also depending on the RAP content. This increase in the wearing course thickness corresponds to a factor of 1.7 to 3.3, whereas the ratio between the used FTS and ITS values ranges from 1.3 to 2.5, as shown in Figure 11. This indicates that the impact of using ITS on the pavement design is approximately 30–40% greater than its difference relative to FTS.

It is important to note that the lower RAP content (20%) resulted in the thickest wearing course and base layer. This is controversial because, as previously stated, according to the Brazilian specification for FDR-PC [60], this would be the only adequate mixture, with RAP content lower than 50% and ITS within the range of 0.25–0.35 MPa. It is also worth noting that the designed pavement structures are quite thick. Such results are related to the fatigue model used in the design process, which was derived solely from laboratory flexural fatigue tests, known to be more severe than field conditions.

5. Conclusions

This paper presented a statistical analysis of the flexural tensile strength (FTS) and indirect tensile strength (ITS) of cold recycled cement-treated mixtures (CRCTMs) incorporating lateritic soil (LS) and reclaimed asphalt pavement (RAP). The paper also investigated the influence of using FTS or ITS on the structural design of CRCTM layers, similar to those obtained using full-depth reclamation. Based on the analysis, the following conclusions can be drawn:

• The effects of cement and RAP contents on tensile strength were significant, with both contributing to its increase. This suggests that CRCTMs incorporating similar materials may benefit from higher RAP contents, in contrast to much of the academic and industry experience. Furthermore, mechanistic analysis showed that a lower RAP content leads to the necessity for thicker pavement structures. Such findings suggest that optimizing RAP content could help reduce costs and environmental impacts.
• For ITS, both cement content and curing time showed significant interactions with RAP content. Moreover, RAP content had the most significant effect on the ITS. These outcomes demonstrate the key role of RAP in achieving an adequate mix design of CRCTMs.
• FTS is, on average, about 65% higher than ITS. However, when ITS is used in pavement design, the resulting structures are 1.7 to 3.3 times thicker than those designed with FTS for the same service life. This emphasizes the importance of properly characterizing CRCTMs for design purposes. In this regard, flexural tests are recommended, as they not only provide a closer simulation of field behavior but also appear to result in more cost-effective pavement structures.

Further research on CRCTMs should focus on evaluating their static and cyclic behavior through different testing methods and on comparing the outcomes both across laboratory procedures and against field performance. This could support the development of a calibrated mechanistic–empirical structural design method. The influence of RAP content also needs continued investigation, including through full-scale experiments, particularly accelerated pavement testing, to provide more reliable results within shorter periods.

It is also important to acknowledge some limitations and potential concerns of this study. The results are based on CRCTMs produced with a single source of base material (LS) and RAP. Different types of soils could lead to different results and conclusions due to their interaction with cement. In addition, the laboratory fatigue models were not calibrated against field conditions, and the mechanistic analysis focused only on the CRCTM layers’ behavior. As mentioned above, further studies are required, encompassing a wider range of materials and additional tests. Moreover, it is important to highlight that, although using FTS for pavement design may lead to thinner structures compared to using ITS, the layer thicknesses obtained in the present study are already considerable even when using FTS, which mitigates concerns about a possible underestimation.