Three-mechanism synergistic constraint cement stabilized macadam anti-cracking grading design method

Abstract

The application discloses a three-mechanism synergistic constraint cement stabilized macadam anti-cracking grading design method, and relates to the technical field of base material design of road engineering. The method comprises the following steps: obtaining basic data of raw materials; generating a candidate grading; calculating a skeleton embedding and extruding coefficient Ksk; calculating a pore connectivity coefficient Kvc; calculating a shrinkage energy coefficient Kse; calculating an anti-cracking risk index Rcr and sorting and screening; verifying through indoor tests; and feeding back and correcting in the construction process. The cement stabilized macadam cracking risk is converted from empirical control to a calculable synergistic constraint by the Ksk constraint of coarse aggregate bearing skeleton, the Kvc control of connected pores, and the Kse control of shrinkage energy accumulation. The potential cracking risk can be identified in the pre-design stage, the method does not depend on special additives, is suitable for raw materials from different sources, the dry shrinkage strain can be reduced by more than 25%, and the water permeability coefficient can be reduced by more than 36%.

Description

Technical Field

[0001] This invention relates to the field of road engineering base material design technology, specifically a three-mechanism synergistic constraint cement-stabilized crushed stone crack-resistant gradation design method. Background Technology

[0002] Cement-stabilized crushed stone is a widely used load-bearing material in semi-rigid base and subbase courses of roads, with advantages such as rapid strength formation, mature construction systems, and good economy. Its main drawback is that it is prone to drying shrinkage cracks, thermal shrinkage cracks, and subsequent reflective cracks when combined with cement hydration shrinkage, drying water loss, temperature cycling, and base course constraints. Once these cracks penetrate, they provide pathways for moisture migration and freeze-thaw damage, weakening the overall durability of the pavement structure.

[0003] Traditional aggregate gradation design typically revolves around parameters such as standard sieve pass rate, maximum dry density, optimum moisture content, unconfined compressive strength, and compaction degree. While these methods can meet basic load-bearing requirements, they struggle to directly address three crucial questions related to crack resistance: whether the coarse aggregate force chain forms a stable interlocking skeleton; whether the pores create continuous moisture migration channels; and whether there is an energy imbalance between shrinkage strain, elastic modulus, and tensile reserve. Consequently, in engineering projects, it is common to encounter situations where the unconfined compressive strength meets requirements, yet early cracking remains significant.

[0004] According to publicly available information, existing technologies cover areas such as cement-stabilized crushed stone with strong interlocking skeleton, crack-resistant mix design, maximum nominal particle size mechanical analysis, admixture crack resistance, and recycled asphalt-stabilized crushed stone. These technologies typically focus on gradation envelope, strength testing, the influence of maximum particle size, or admixture modification, and can improve the load-bearing or crack-resistant performance of base course materials from different perspectives.

[0005] However, existing technologies have not yet incorporated skeleton interlocking, pore connectivity, and shrinkage energy as three parallel and calculable gradation design constraints, nor have they established a closed-loop method for adjusting the proportions of coarse aggregate, transition aggregate, fine aggregate, and powder based on feedback from deviations of these three indicators. Therefore, a cement-stabilized crushed stone crack-resistant gradation design method is still needed that can simultaneously constrain the load-bearing skeleton, pore channels, and shrinkage energy accumulation before trial mixing and during construction. Summary of the Invention

[0006] The purpose of this invention is to provide a cement-stabilized crushed stone crack-resistant gradation design method based on the synergistic constraint of three mechanisms: skeleton interlocking, pore connectivity, and shrinkage energy. This method aims to solve the problem that existing cement-stabilized crushed stone gradation designs rely too much on specification envelope, maximum dry density, or compressive strength, making it difficult to identify cracking risks caused by skeleton instability, excessively high interconnected pores, and excessive shrinkage energy in advance.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows:

[0008] A three-mechanism synergistic constraint method for the crack-resistant gradation design of cement-stabilized crushed stone includes the following steps:

[0009] S1. Obtain the screening data and physical parameters of the aggregate, including apparent density, needle-like and flaky content, crushing value, water absorption rate, mud content, vibratory density, and coarse aggregate skeleton porosity.

[0010] S2. Generate several candidate gradations within the standard gradation range;

[0011] S3. Calculate the skeleton interlocking coefficient Ksk of the candidate gradation, whereby Ksk is used to characterize the ability of coarse aggregate to form a stable load-bearing skeleton;

[0012] S4. Calculate the pore connectivity coefficient Kvc of the candidate gradation, whereby Kvc is used to characterize the trend of pores developing from a closed state to a connected channel.

[0013] S5. Calculate the shrinkage energy coefficient Kse of the candidate gradation, where Kse is used to characterize the degree to which shrinkage deformation is converted into cracking driving force under material stiffness constraints.

[0014] S6. Calculate the crack resistance risk index Rcr based on Ksk, Kvc, and Kse, and sort and screen the candidate gradations from low to high according to Rcr to obtain the preliminary gradation.

[0015] S7. Conduct indoor tests to verify the initial gradation. If it meets the design requirements, it is determined as the target gradation. If it does not meet the requirements, the particle size is adjusted and recalculated.

[0016] S8. During construction, Ksk, Kvc, Kse and Rcr are recalculated based on the fluctuation of aggregate screening, and the proportions of each particle size are adjusted.

[0017] Furthermore, the skeleton interlocking coefficient Ksk mentioned in step S3 is calculated according to equation (1):

[0018] Ksk=(Mc / 100)×Ac×Dc (1)

[0019] Wherein, Mc is the cumulative sieve residue percentage of the coarse aggregate skeleton phase, in %; Ac is the coarse aggregate morphology correction coefficient, which is graded according to the needle-like and flaky content or crushing value; Dc is the coarse aggregate contact density correction coefficient, which is graded according to the coarse aggregate skeleton porosity under vibration condition; Ksk is controlled within the range of 0.42 to 0.58.

[0020] Furthermore, Ac is valued according to the following rules: Ac=1.10 when needle-like and flaky content is ≤8%, Ac=1.05 when >8% and ≤12%, Ac=1.00 when >12% and ≤16%, Ac=0.95 when >16% and ≤20%, and Ac=0.90 when >20%.

[0021] The Dc value is determined according to the following rules: Dc = 1.15 when the coarse aggregate skeleton porosity is ≤38%, Dc = 1.10 when it is >38% and ≤40%, Dc = 1.05 when it is >40% and ≤42%, Dc = 1.00 when it is >42% and ≤44%, Dc = 0.95 when it is >44% and ≤46%, Dc = 0.90 when it is >46% and ≤48%, and Dc = 0.85 when it is >48%.

[0022] Furthermore, the pore connectivity coefficient Kvc mentioned in step S4 is calculated according to equation (2):

[0023] Kvc=(Vcon / Vt)×(k / k0) 0.25 (2)

[0024] Where Vcon / Vt is the ratio of the volume of the connected pores to the total volume, k is the measured permeability coefficient, and k0 is the reference permeability coefficient; the control range of Kvc is ≤0.35.

[0025] Furthermore, the contraction energy coefficient Kse mentioned in step S5 is calculated according to equation (3):

[0026] Kse=(εd / 300)×(E28 / 1200) / (ft28 / 0.60) (3)

[0027] Wherein, εd is the drying shrinkage strain after curing from 7d to 28d, E28 is the elastic modulus or compressive resilient modulus at 28d, ft28 is the splitting tensile strength at 28d; Kse is controlled within the range of ≤1.00.

[0028] Furthermore, the crack resistance risk index Rcr mentioned in step S6 is calculated according to formula (4):

[0029] Rcr=0.30×Dsk+0.35×Kvc+0.35×Kse (4)

[0030] Where Dsk is the penalty term for the skeleton interlocking coefficient Ksk deviating from the target range. When Ksk is in the range of 0.42 to 0.58, Dsk=0; the control range of Rcr is ≤0.85.

[0031] Furthermore, the granularity adjustment described in step S7 is performed according to the following rules:

[0032] When Ksk < 0.42, increase the proportion of coarse aggregates larger than 9.5mm by 2% to 4%, while simultaneously reducing the proportion of fine aggregates by 0.075 to 2.36mm by the same amount;

[0033] When Ksk>0.58, reduce the proportion of coarse aggregates larger than 9.5mm by 2% to 4%, and supplement with transitional particle sizes of 4.75 to 9.5mm;

[0034] When Kvc > 0.35, increase the proportion of 4.75–9.5mm transition aggregate by 2%–3% and the proportion of 0.075–2.36mm fine aggregate by 1%–2%.

[0035] When Kse>1.00, reduce the requirement for powder or cement paste below 0.075mm by 1% to 2% and increase the continuous transition particle size of 2.36 to 9.5mm;

[0036] After each round of adjustments, Ksk, Kvc, Kse, and Rcr are recalculated, with a maximum of 5 iterations.

[0037] Furthermore, the adjustments described in step S8 are performed with the following priority:

[0038] The first priority is to meet the standard gradation envelope and 7d strength requirements;

[0039] The second priority is to make Ksk between 0.42 and 0.58;

[0040] The third priority is to make Kvc ≤ 0.35;

[0041] The fourth priority is to make Kse ≤ 1.00;

[0042] Each adjustment is made in increments of 1% to 4%, with a maximum of 5 iterations.

[0043] Compared with the prior art, the beneficial effects of the present invention are:

[0044] This invention transforms the risk of cracking in cement-stabilized crushed stone from empirical gradation control to a calculable three-mechanism synergistic constraint, enabling the identification of potential cracking risks before specimen molding.

[0045] This invention controls the coarse aggregate load-bearing skeleton through Ksk, which avoids both insufficient skeleton leading to unstable force chain and excessively strong coarse skeleton causing difficulties in bridging and compaction.

[0046] This invention uses Kvc to control interconnected pores, thereby reducing moisture migration, freeze-thaw damage, and crack propagation channels.

[0047] This invention controls the accumulation of shrinkage energy through Kse, avoiding the coexistence of high modulus, high shrinkage and low tensile reserve caused by unilaterally increasing strength or slurry content.

[0048] This invention improves trial mixing efficiency through Rcr and feedback adjustment rules, enabling rapid determination of the particle size direction to be adjusted when raw material fluctuations occur on site.

[0049] This invention does not rely on special admixtures or specific equipment, making it easy to promote in conventional laboratories, mixing plants, and construction quality control systems. Attached Figure Description

[0050] Figure 1 This is a closed-loop schematic diagram of the cement-stabilized crushed stone crack-resistant gradation design of the present invention.

[0051] Figure 2 This is a schematic diagram of the system composition of the present invention.

[0052] Figure 3 This is a flowchart of the cement-stabilized crushed stone crack-resistant gradation design method of the present invention.

[0053] Figure 4 This is a schematic diagram of the three-mechanism indicator feedback adjustment rules of the present invention. Detailed Implementation

[0054] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0055] A method for designing crack-resistant gradation of cement-stabilized crushed stone based on the synergistic constraint of skeleton interlocking, pore connectivity and shrinkage energy is proposed. The process includes obtaining basic data of raw materials, generating candidate gradations, calculating the three-mechanism index, evaluating crack resistance risk, verifying through indoor tests and correcting through construction process feedback.

[0056] S1: Acquisition of basic raw material data;

[0057] Sieve data of the aggregates to be used were collected, and apparent density, flaky and needle-like particle content, crushing value, water absorption, mud content, vibratory density, and coarse aggregate skeleton porosity were measured. Aggregates can be classified according to particle size into coarse aggregate skeleton phase, transitional filler phase, fine aggregate interstitial phase, and powder cementing phase. For example, in a cement-stabilized crushed stone base course with a nominal maximum particle size of 31.5 mm, particle sizes above 9.5 mm can be considered as the coarse aggregate skeleton phase, particle sizes from 4.75 mm to 9.5 mm and from 2.36 mm to 4.75 mm can be considered as the transitional filler phase, particle sizes from 0.075 mm to 2.36 mm can be considered as the fine aggregate interstitial phase, and the portion below 0.075 mm can be considered as the powder cementing phase.

[0058] Table 1 Physical property parameters of raw materials from different sources

[0059] Group Source of raw materials Apparent / Volume Density (g / cm³) Needle-like and flaky content / % Crushing value / % Water absorption rate / % Mud content / % Physical property evaluation Group A High-quality limestone crushed stone 2.70 6.2 14.3 0.32 0.4 High density, low crushing value, and low water absorption make it suitable for forming a stable skeleton. Group B Crushed pebble material with high needle-like and flaky content 2.64 18.5 21.8 1.15 0.7 Insufficient angularity and excessive needle-like structure necessitate increasing the proportion of coarse skeleton and supplementing the transitional grain size. Group C Soft sandstone crushed material 2.60 10.8 26.7 3.54 1.2 The crushing value and water absorption rate are relatively high, and the strength reserve is weak. It is necessary to reduce the risk of shrinkage in interconnected pores and slurry.

[0060] Table 2. Optimal gradation selected according to the method of this application (unit: sieve aperture passing rate %)

[0061] Sieve aperture / mm Group A: High-quality limestone Group B: Crushed needle-shaped and flaky pebbles Group C: Soft sandstone 31.5 100 100 100 26.5 96 94 97 19.0 78 72 80 9.5 52 42 50 4.75 35 31 37 2.36 24 21 25 0.6 11 10 13 0.075 3.5 3.0 3.8

[0062] Note: These three groups are all different from candidate gradation B in Example 1.

[0063] Group A limestone aggregate is of good quality, so there is no need to significantly increase the proportion of coarse aggregate; the key is to maintain continuous compactness and low permeability. Group B gravel crushed material has a high proportion of needle-like and flaky particles and insufficient angularity, so the proportion of coarse aggregate above 9.5 mm should be increased, while retaining a transitional particle size of 4.75–9.5 mm to avoid skeleton voids. Group C soft sandstone has a high crushing value and water absorption rate, so a gradation of "moderate coarse skeleton + strong transitional gap filling" should be adopted to avoid excessive coarseness leading to local crushing, and also to avoid excessive fineness leading to excessive slurry shrinkage energy.

[0064] Table 3 Calculation results of Ksk, Kvc, Kse, and Rcr

[0065] Group Mc / % Ac Dc Ksk Kvc Kse Dsk Rcr Does it meet the threshold? Group A: High-quality limestone 48 1.08 1.08 0.560 0.23 0.66 0 0.312 satisfy Group B: Crushed needle-shaped and flaky pebbles 58 0.93 0.94 0.507 0.31 0.82 0 0.396 satisfy Group C: Soft sandstone 50 0.97 0.96 0.466 0.30 0.91 0 0.424 satisfy

[0066] Calculation instructions:

[0067] Ksk = Mc / 100 × Ac × Dc

[0068] Rcr = 0.30 × Dsk + 0.35 × Kvc + 0.35 × Kse

[0069] Since all three Ksk values ​​are between 0.42 and 0.58, Dsk = 0.

[0070] The Rcr values ​​for all three groups were well below 0.85, indicating that the method can screen out low-risk gradations from materials of different sources.

[0071] Table 4 Indoor Validation Results

[0072] Group Cement dosage / % Maximum dry density (g / cm³) Optimal moisture content / % 7d UCS / MPa 28d UCS / MPa 28d splitting strength / MPa Drying strain / με Permeability coefficient m / s Group A: High-quality limestone 4.0 2.38 4.7 5.2 7.3 0.86 220 <![CDATA[7.0×10 -7 ]]> Group B: Crushed needle-shaped and flaky pebbles 4.3 2.33 5.0 4.8 6.6 0.78 255 <![CDATA[9.5×10 -7 ]]> Group C: Soft sandstone 4.8 2.25 5.6 4.5 5.9 0.68 285 <![CDATA[1.40×10 -6 ]]>

[0073] The indoor verification results of the three raw materials show that limestone cement-stabilized crushed stone has the highest unconfined compressive strength and splitting strength; sandstone has relatively weak strength and frost resistance due to its high crushing value and water absorption rate, and needs to be controlled in the mix design; crushed pebbles can effectively improve mechanical properties and crack resistance due to drying shrinkage and thermal shrinkage through dense gradation of the skeleton.

[0074] Table 5 Comparison of the effects of the standard value gradation with the traditional standard.

[0075] Group Comparison Methods 28d UCS / MPa Drying strain / με Permeability coefficient m / s This application reduces the shrinkage ratio. The permeability coefficient of this application is reduced by a certain percentage. Group A: Limestone Traditional standard median gradation 7.2 295 <![CDATA[1.10×10 -6 ]]> 25.4% 36.4% Group A: Limestone This application's gradation 7.3 220 <![CDATA[7.0×10 -7 ]]> — — Group B: Crushed gravel Traditional standard median gradation 6.5 342 <![CDATA[1.65×10 -6 ]]> 25.4% 42.4% Group B: Crushed gravel This application's gradation 6.6 255 <![CDATA[9.5×10 -7 ]]> — — Group C: Soft sandstone Traditional standard median gradation 5.8 390 <![CDATA[2.35×10 -6 ]]> 26.9% 40.4% Group C: Soft sandstone This application's gradation 5.9 285 <![CDATA[1.40×10 -6 ]]> — —

[0076] Under conditions where the unconfined compressive strength at 28 days is essentially similar, the target gradation determined by the method in this application, compared with the median gradation in traditional specifications, reduces the drying shrinkage strain of three types of raw materials from different sources by approximately 25.4%–26.9%, and the permeability coefficient by approximately 36.4%–42.4%. This result indicates that the method in this application does not depend on a specific stone source, but rather, through the synergistic constraint of skeleton interlocking, pore connectivity, and shrinkage energy, it is applicable to high-quality limestone, crushed pebble material with high needle-like and flaky content, and soft sandstone.

[0077] S2: Candidate gradation generation;

[0078] Multiple candidate gradations are generated within the specified gradation range. These candidate gradations should cover continuous dense gradations, as well as coarse-skeleton reinforced gradations and fine-particle gap-filling reinforced gradations. Each candidate gradation is not selected based on a single maximum dry density, but rather on meeting the specified envelope requirement before proceeding to the calculation of the three-mechanism index.

[0079] Multiple candidate gradations are generated within the specified gradation range. The specific generation method is as follows: using the recommended gradation window in Table 9 or the corresponding specified gradation range as the boundary, the passing rate of a 31.5mm sieve is fixed at 100%; the passing rates for 26.5mm sieves are 92%, 96%, and 100%; for 19.0mm sieves, they are 70%, 78%, and 86%; for 9.5mm sieves, they are 40%, 48%, and 56%; for 4.75mm sieves, they are 26%, 32%, and 38%; for 2.36mm sieves, they are 18%, 23%, and 28%; for 0.6mm sieves, they are 8%, 12%, and 16%; and for 0.075mm sieves, they are 2.5%, 4.0%, and 5.5%. During generation, the passing rate of the next higher sieve should not be less than that of the next lower sieve, and combinations that do not meet the specified envelope, exceed powder limits, or exhibit abrupt gradation changes are discarded. When manually testing the mix design, there should be no fewer than 3 sets of each template, forming 9 to 15 candidate gradations. When using a mixing plant or a programmed screening process, it is recommended to generate 21 to 45 candidate gradations, and then sort and screen them according to Ksk, Kvc, Kse, and Rcr.

[0080] S3: Calculation of skeleton interlocking coefficient Ksk;

[0081] The skeleton interlocking coefficient Ksk is used to characterize the ability of coarse aggregate to form a stable load-bearing skeleton, and is calculated as Ksk = (Mc / 100) × Ac × Dc. Ac is the coarse aggregate morphology correction coefficient, which can be graded from 0.90 to 1.10 according to the content of needle-like and flaky particles, angularity, or crushing value; Dc is the coarse aggregate contact density correction coefficient, which can be graded from 0.85 to 1.15 according to the coarse aggregate skeleton porosity, vibration density, or discrete element contact number. It is recommended that Ksk be controlled between 0.42 and 0.58. When Ksk is lower than 0.42, the proportion of coarse aggregate with a diameter of 9.5 mm or more should be increased or the angularity of the coarse aggregate should be improved; when Ksk is higher than 0.58, the transition particle size should be checked to avoid skeleton suspension, compaction difficulties, or local void concentration.

[0082] The skeleton interlocking coefficient Ksk is used to characterize the ability of coarse aggregates to form a stable load-bearing skeleton, and is calculated as Ksk = (Mc / 100) × Ac × Dc. Ac is the coarse aggregate morphology correction coefficient, which is determined according to the following deterministic rules: Ac = 1.10 when the needle-like and flaky content is ≤8%, Ac = 1.05 when >8% and ≤12%, Ac = 1.00 when >12% and ≤16%, Ac = 0.95 when >16% and ≤20%, and Ac = 0.90 when >20%. When both angularity and crushing value are used for evaluation, the lower Ac value is taken as the final value. Dc is the contact density correction factor for coarse aggregate, determined by the void ratio Vca of the coarse aggregate skeleton under vibration: Dc=1.15 when Vca≤38%, Dc=1.10 when >38% and ≤40%, Dc=1.05 when >40% and ≤42%, Dc=1.00 when >42% and ≤44%, Dc=0.95 when >44% and ≤46%, Dc=0.90 when >46% and ≤48%, and Dc=0.85 when >48%. The testing methods and grading rules for Ac and Dc remain unchanged within the same project batch. It is recommended that Ksk be controlled between 0.42 and 0.58; when Ksk is below 0.42, the proportion of coarse aggregate larger than 9.5mm should be increased or the angularity of the coarse aggregate should be improved; when Ksk is above 0.58, the transition particle size should be checked for insufficiency to avoid skeleton suspension, compaction difficulties, or localized void concentration.

[0083] S4: Calculation of pore connectivity coefficient Kvc;

[0084] The pore connectivity coefficient Kvc is used to characterize the tendency of pores to evolve from a closed state to a connected channel, according to Kvc=(Vcon / Vt)×(k / k0). 0.25 Calculation. k0 is the reference permeability coefficient, which can be taken as the permeability coefficient of similar cement-stabilized crushed stone target gradation specimens, or 1×10. -5m / s should be used as a normalized reference value and kept consistent within the same batch of projects. It is recommended that Kvc not exceed 0.35. If Kvc is too high, the proportion of 4.75 mm to 9.5 mm transition aggregate should be increased first, and the gap-filling capacity of 0.075 mm to 2.36 mm fine aggregate should be appropriately increased; simply increasing cement paste or powder is not advisable, as it may reduce interconnected pores but increase shrinkage energy.

[0085] The pore connectivity coefficient Kvc is used to characterize the trend of pores developing from a closed state to a connected channel, and is calculated as Kvc = (Vcon / Vt) × (k / k0)^0.25. k0 is determined in the following order: priority is given to the permeability coefficient measured by specimens of the same engineering specification's median gradation under the same cement dosage, compaction degree, curing age, and testing method; if no reference specimen is available, it is fixed at 1 × 10⁻⁵ m / s; once k0 is determined within the same engineering batch, it cannot be adjusted with candidate gradations. Vcon / Vt is preferably based on the measured value of the connected pore volume; if actual measurement is not possible, it is estimated using the alternative input formula in Example 3. It is recommended that Kvc not exceed 0.35. If Kvc is too high, priority should be given to increasing the proportion of 4.75mm to 9.5mm transition aggregates, and appropriately increasing the pore-filling capacity of 0.075mm to 2.36mm fine aggregates; simply increasing cement paste or powder is not advisable, as it may reduce connected pores but increase shrinkage energy.

[0086] S5: Calculation of contractile energy coefficient Kse;

[0087] The shrinkage energy coefficient Kse characterizes the degree to which shrinkage deformation is converted into cracking driving force under material stiffness constraints, and is calculated as Kse = (εd / 300) × (E28 / 1200) / (ft28 / 0.60). εd is preferably obtained from drying shrinkage tests or thermal shrinkage tests after 7 to 28 days of curing. E28 is the 28-day elastic modulus or compressive resilient modulus, and ft28 is the 28-day splitting tensile strength or equivalent tensile strength. It is recommended that Kse not exceed 1.00. If Kse is too high, further increases in powder or cement content should be avoided. Shrinkage energy should be reduced by improving the continuity of transitional particle sizes, reducing the specific surface area requirement of fine powder, optimizing the optimum moisture content, and increasing tensile reserve.

[0088] This formula is a normalized evaluation formula proposed in this application and is not a commonly used formula in this field. 300με is the reference shrinkage strain selected in this application based on the 28-day drying shrinkage strain control level of ordinary cement-stabilized crushed stone; 1200MPa is the normalized reference value for the 28-day compressive resilient modulus or elastic modulus; and 0.60MPa is the normalized reference value for the 28-day splitting tensile strength. εd uses the drying shrinkage strain test results from 7 days after standard curing to the end of 28 days. If it is necessary to evaluate thermal shrinkage, the converted value from the thermal shrinkage test under the same specification can be used and kept consistent within the same engineering batch. E28 uses the 28-day elastic modulus or compressive resilient modulus, and ft28 uses the 28-day splitting tensile strength or equivalent tensile strength. The above-mentioned tests for drying shrinkage, thermal shrinkage, unconfined compressive strength, splitting tensile strength, compressive resilient modulus, and compaction all adopt the "Test Procedure for Inorganic Binder Stabilized Materials in Highway Engineering" JTG3441—2024; if subsequent specifications are updated, equivalent test methods will be used. It is recommended that Kse not exceed 1.00. If Kse is too high, further increases in powder or cement content should be avoided. Shrinkage energy should be reduced by improving the continuity of transitional particle sizes, reducing the specific surface area requirement of fine powder, optimizing the optimum moisture content, and increasing tensile reserve.

[0089] S6: Calculation and ranking of crack resistance risk index Rcr;

[0090] Under the premise of meeting the standard gradation and strength requirements, the crack resistance risk index is calculated according to Rcr = 0.30 × Dsk + 0.35 × Kvc + 0.35 × Kse. Candidate gradations are sorted from low to high according to Rcr, and candidate gradations that meet the control range of Ksk, Kvc, and Kse are selected as the initial gradations. The Rcr should not be higher than 0.85, and the Rcr should not be higher than 0.75 in arid, large temperature difference, heavy load, or strong base constraint environments.

[0091] S7: Indoor test verification;

[0092] The initially selected gradation is subjected to compaction, unconfined compressive strength, splitting, drying shrinkage, thermal shrinkage, water permeability, or interconnected pore tests. If the test results show that the strength, compaction, and crack resistance all meet the design requirements, it is determined as the target gradation; if any indicator does not meet the requirements, the particle size is adjusted according to the deviation direction of Ksk, Kvc, or Kse, and the calculation and verification are repeated.

[0093] The initially selected gradation is subjected to compaction, unconfined compressive strength, splitting crack, drying shrinkage, thermal shrinkage, water permeability, or interconnected pore tests. If the test results show that the strength, compaction, and crack resistance all meet the design requirements, it is determined as the target gradation; if any index does not meet the requirements, the particle size is adjusted and recalculated according to the following step sizes: when Ksk < 0.42, the proportion of coarse aggregates larger than 9.5mm is increased by 2% to 4%, while the proportion of fine aggregates smaller than 4.75mm is reduced by an equal amount, with a single adjustment step size preferably of 3%; when Ksk > 0.58, the proportion of coarse aggregates larger than 9.5mm is increased by 2% to 4%. For example, reduce the proportion of 4.75–9.5 mm transition aggregate by 2%–4% and supplement the 4.75–9.5 mm transition aggregate; when Kvc > 0.35, increase the proportion of 4.75–9.5 mm transition aggregate by 2%–3% and increase the proportion of 0.075–2.36 mm fine aggregate by 1%–2%, while reducing the amount of coarse aggregate or powder of equal quality; when Kse > 1.00, prioritize reducing the demand for powder or cement paste below 0.075 mm by 1%–2% and increase the continuous transition aggregate of 2.36–9.5 mm. After each round of adjustment, recalculate Ksk, Kvc, Kse, and Rcr, with a maximum of 5 iterations; if the requirements are still not met, the raw materials should be replaced or the gradation window should be reset.

[0094] S8: Feedback and correction during construction process;

[0095] During construction, if the daily aggregate screening or moisture content fluctuates, Ksk, Kvc, Kse, and Rcr are recalculated, and the proportions of coarse aggregate, transition aggregate, fine aggregate, or powder are adjusted according to the deviation of the indicators to bring the actual production gradation back to the crack resistance control range.

[0096] During construction, if there are fluctuations in the daily aggregate screening or moisture content, Ksk, Kvc, Kse, and Rcr are recalculated and adjusted according to conflict priority: the first priority is to meet the specification gradation envelope and 7-day strength requirements; the second priority is to bring Ksk back to 0.42–0.58; the third priority is to ensure Kvc is no higher than 0.35; and the fourth priority is to ensure Kse is no higher than 1.00. When both Ksk and Kvc are too low, the continuity of the 4.75–19.0 ​​mm medium-coarse aggregate is increased first, and then the fine aggregate of 0.075–2.36 mm is finely adjusted. When Ksk is qualified but Kse is too high, the proportion of coarse aggregate is not increased, and the requirements for powder and cement paste are reduced first. The above adjustments are made in increments of 1%–4%, with a maximum of 5 iterations, to bring the actual production gradation back to the crack resistance control range.

[0097] Example 1: Indoor gradation design.

[0098] Using cement-stabilized crushed stone with a nominal maximum particle size of 31.5 mm as the research object, three candidate gradations, A1, B1, and C1, were selected. Candidate gradation A1 emphasizes the coarse aggregate skeleton, candidate gradation B1 emphasizes continuous compaction, and candidate gradation C1 emphasizes fine aggregate filling. Maximum dry density, optimum moisture content, 7-day unconfined compressive strength, 28-day splitting tensile strength, drying shrinkage strain, and permeability or interconnected porosity indices were tested, and Ksk, Kvc, Kse, and Rcr were calculated. The candidate gradations and the calculation and verification results are shown in Tables 6 to 8.

[0099] Table 6 Examples of Candidate Grading Sieve Passing Rate

[0100] Sieve aperture / mm A1 robust skeleton reinforced type / % B1 Continuous Dense Type / % C1 Fine Filler Type / % Recommended range / % 31.5 100 100 100 100 26.5 96 95 94 90～100 19.0 82 76 70 68～86 9.5 50 48 42 38～58 4.75 30 34 39 25～40 2.36 20 23 28 16～30 0.6 10 12 16 7～17 0.075 3.0 4.0 5.5 2～6

[0101] Table 7. Examples of Calculation Results for the Three Mechanisms Indicators

[0102] plan Ksk Kvc Kse Dsk Rcr Preliminary assessment A 0.58 0.38 0.88 0 0.441 The coarse-grained structure is too strong and the KVC is too high, so we need to supplement the transitional granularity. B 0.51 0.27 0.72 0 0.347 A balance among the three indicators is used as a candidate for the target gradation. C 0.43 0.22 1.08 0 0.455 A high Kse level reduces the requirement for fine powders or slurries.

[0103] Table 8 Examples of Indoor Test Verification Results

[0104] plan <![CDATA[Maximum dry density / (g / cm 3 )]]> Optimal moisture content / % 7-day unconfined compressive strength / MPa 28-day splitting strength / MPa Drying strain / με Permeability / Connected Pore Index in conclusion A 2.32 4.9 5.2 0.78 275 0.34 A review is required after supplementing the transition granularity. B 2.35 5.0 5.0 0.82 235 0.25 Determined as the target gradation C 2.33 5.4 5.4 0.76 330 0.20 Strength is sufficient, but the risk of shrinkage is relatively high.

[0105] As shown in Tables 6 to 8, candidate gradation B meets the strength and compaction requirements, while having Ksk in the target range, low Kvc, low Kse, and the lowest Rcr. Therefore, it can be used as the target gradation. Although candidate gradations A and C have strong skeleton or good gap-filling ability, they have the risk of connected pores or high shrinkage energy. They need to be adjusted according to the feedback rules and then verified.

[0106] Example 2: Gradation correction during construction.

[0107] During construction, when the daily aggregate sieving showed that the 9.5 mm–19.0 ​​mm particle size was too low and the 0.075 mm–2.36 mm particle size was too high, the system calculated that Ksk decreased while Kse increased. According to the feedback rules of this invention, priority should be given to supplementing the medium and coarse particle sizes and controlling the introduction of fine powder, rather than compensating for strength by increasing the cement dosage. After adjustment, Ksk returned to the target range, Kse decreased, and the drying shrinkage strain and early crack risk of the specimen decreased simultaneously.

[0108] Example 3: Alternative detection path.

[0109] When the site lacks the conditions for testing the volume of interconnected pores, porosity, permeability, or water absorption can be used as substitute inputs for Kvc. When the conditions for testing the elastic modulus are unavailable, splitting tensile strength, compressive resilient modulus, or fracture energy can be used for equivalent correction. The above substitutions do not change the core idea of ​​this invention, which is to constrain the gradation through three types of indicators: skeleton, porosity, and shrinkage energy.

[0110] When the engineering site does not have the conditions for testing the volume of connected pores, porosity, water absorption rate or permeability coefficient can be used as alternative inputs for Vcon / Vt. Only one alternative path should be selected and kept unchanged within the same engineering batch. Porosity method: Vcon / Vt≈clamp[(Va-2.0) / (8.0-2.0),0,1], where Va is the porosity of the compacted specimen, in units of %; Water absorption method: Vcon / Vt≈clamp[(W24-0.5) / (3.0-0.5),0,1], where W24 is the 24h water absorption rate, in units of %; Permeability coefficient method: Vcon / Vt≈clamp[(log10k-log10(1×10-7)) / (log10(1×10-4)-log10(1×10-7)),0,1], where k is the measured permeability coefficient, in units of m / s, and when k is less than 1×10-7 m / s, it is calculated as 1×10-7 m / s, and when k is greater than 1×10-4 m / s, it is calculated as 1×10-4 m / s. The above clamp[a,0,1] represents 0 when a<0 and 1 when a>1. When the conditions for testing the elastic modulus are not available, the 28d compressive resilient modulus or the equivalent elastic modulus of the specimen under the same conditions can be used; the above substitution does not change the core idea of ​​this invention to constrain the gradation through the three types of indicators of skeleton, porosity and shrinkage energy.

[0111] Example 4: Recommended gradation window.

[0112] In cement-stabilized crushed stone base courses with a nominal maximum particle size of 31.5 mm, the following recommended window can be used as the initial candidate gradation range. Actual engineering projects should adjust this range based on specifications, maximum particle size, road grade, and local material properties:

[0113] Table 9 Recommended gradation window for cement-stabilized crushed stone base course with a nominal maximum particle size of 31.5 mm

[0114] sieve aperture size Recommended pass rate range 31.5 mm 100% 26.5 mm 90%～100% 19.0 mm 68%～86% 9.5 mm 38%～58% 4.75 mm 25%～40% 2.36 mm 16%～30% 0.6 mm 7%～17% 0.075 mm 2%～6%

[0115] The recommended gradation window is used to limit the initial generation range of candidate gradations. When using different maximum particle sizes, different base layer grades, or different local materials, the range of each sieve aperture can be reset under the same calculation logic, and screening and feedback correction can be performed through Ksk, Kvc, Kse, and Rcr.

[0116] Example 5: Verification of Technical Effect. To verify the technical effect of the method of the present invention, the target gradation determined by the present invention can be compared with the median gradation, the maximum dry density preferred gradation, and the simple strength preferred gradation in traditional specifications. The comparison indicators include Ksk, Kvc, Kse, Rcr, 7-day unconfined compressive strength, 28-day splitting strength, drying shrinkage strain, water seepage or interconnected porosity, crack rate of the trial section, and core integrity.

[0117] Table 10 Examples of Technical Effect Comparison

[0118] Comparison Object Rcr 7-day strength / MPa 28-day splitting strength / MPa Drying strain / με Water seepage / pore connectivity Crack rate / evaluation Traditional standard median gradation 0.52 4.7 0.73 300 0.32 Medium risk of cracks Maximum dry density preferred gradation 0.47 5.1 0.76 280 0.30 Good compaction but average crack resistance reserves Pure strength preferred gradation 0.58 5.6 0.72 340 0.34 High strength but high risk of shrinkage The target gradation of the present invention 0.35 5.0 0.82 235 0.25 Low risk of cracking

[0119] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification.

Claims

1. A method for designing the crack-resistant gradation of cement-stabilized crushed stone with synergistic constraints of three mechanisms, characterized in that, Includes the following steps: S1. Obtain the screening data and physical parameters of the aggregate, including apparent density, needle-like and flaky content, crushing value, water absorption rate, mud content, vibratory density, and coarse aggregate skeleton porosity. S2. Generate several candidate gradations within the standard gradation range; S3. Calculate the skeleton interlocking coefficient Ksk of the candidate gradation, whereby Ksk is used to characterize the ability of coarse aggregate to form a stable load-bearing skeleton; S4. Calculate the pore connectivity coefficient Kvc of the candidate gradation, whereby Kvc is used to characterize the trend of pores developing from a closed state to a connected channel. S5. Calculate the shrinkage energy coefficient Kse of the candidate gradation, where Kse is used to characterize the degree to which shrinkage deformation is converted into cracking driving force under material stiffness constraints. S6. Calculate the crack resistance risk index Rcr based on Ksk, Kvc, and Kse, and sort and screen the candidate gradations from low to high according to Rcr to obtain the preliminary gradation. S7. Conduct indoor tests to verify the initial gradation. If it meets the design requirements, it is determined as the target gradation. If it does not meet the requirements, the particle size is adjusted and recalculated. S8. During construction, Ksk, Kvc, Kse and Rcr are recalculated based on the fluctuation of aggregate screening, and the proportions of each particle size are adjusted.

2. The method according to claim 1, characterized in that, The skeleton interlocking coefficient Ksk mentioned in step S3 is calculated according to formula (1): Ksk=(Mc / 100)×Ac×Dc (1) Wherein, Mc is the cumulative sieve residue percentage of the coarse aggregate skeleton phase, in %; Ac is the coarse aggregate morphology correction coefficient, which is graded according to the needle-like and flaky content or crushing value; Dc is the coarse aggregate contact density correction coefficient, which is graded according to the coarse aggregate skeleton porosity under vibration condition; Ksk is controlled within the range of 0.42 to 0.

58.

3. The method according to claim 2, characterized in that, The Ac value is determined according to the following rules: Ac = 1.10 when needle-like and flaky content is ≤8%, Ac = 1.05 when >8% and ≤12%, Ac = 1.00 when >12% and ≤16%, Ac = 0.95 when >16% and ≤20%, and Ac = 0.90 when >20%. The Dc value is determined according to the following rules: Dc = 1.15 when the coarse aggregate skeleton porosity is ≤38%, Dc = 1.10 when it is >38% and ≤40%, Dc = 1.05 when it is >40% and ≤42%, Dc = 1.00 when it is >42% and ≤44%, Dc = 0.95 when it is >44% and ≤46%, Dc = 0.90 when it is >46% and ≤48%, and Dc = 0.85 when it is >48%.

4. The method according to claim 1, characterized in that, The pore connectivity coefficient Kvc mentioned in step S4 is calculated according to equation (2): Kvc=(Vcon / Vt)×(k / k0) 0.25 (2) Where Vcon / Vt is the ratio of the volume of the connected pores to the total volume, k is the measured permeability coefficient, and k0 is the reference permeability coefficient; the control range of Kvc is ≤0.

35.

5. The method according to claim 1, characterized in that, The contraction energy coefficient Kse mentioned in step S5 is calculated according to equation (3): Kse=(εd / 300)×(E28 / 1200) / (ft28 / 0.60) (3) Wherein, εd is the drying shrinkage strain after curing from 7d to 28d, E28 is the elastic modulus or compressive resilient modulus at 28d, ft28 is the splitting tensile strength at 28d; Kse is controlled within the range of ≤1.

00.

6. The method according to claim 1, characterized in that, The crack resistance risk index Rcr mentioned in step S6 is calculated according to formula (4): Rcr=0.30×Dsk+0.35×Kvc+0.35×Kse (4) Where Dsk is the penalty term for the skeleton interlocking coefficient Ksk deviating from the target range. When Ksk is in the range of 0.42 to 0.58, Dsk=0; the control range of Rcr is ≤0.

85.

7. The method according to claim 1, characterized in that, The particle size adjustment in step S7 is performed according to the following rules: When Ksk < 0.42, increase the proportion of coarse aggregates larger than 9.5mm by 2% to 4%, while simultaneously reducing the proportion of fine aggregates by 0.075 to 2.36mm by the same amount; When Ksk>0.58, reduce the proportion of coarse aggregates larger than 9.5mm by 2% to 4%, and supplement with transitional particle sizes of 4.75 to 9.5mm; When Kvc > 0.35, increase the proportion of 4.75–9.5mm transition aggregate by 2%–3% and the proportion of 0.075–2.36mm fine aggregate by 1%–2%. When Kse>1.00, reduce the requirement for powder or cement paste below 0.075mm by 1% to 2% and increase the continuous transition particle size of 2.36 to 9.5mm; After each round of adjustments, Ksk, Kvc, Kse, and Rcr are recalculated, with a maximum of 5 iterations.

8. The method according to claim 1, characterized in that, The adjustments described in step S8 are performed with the following priority: The first priority is to meet the standard gradation envelope and 7d strength requirements; The second priority is to make Ksk between 0.42 and 0.58; The third priority is to make Kvc ≤ 0.35; The fourth priority is to make Kse ≤ 1.00; Each adjustment is made in increments of 1% to 4%, with a maximum of 5 iterations.

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