Characterization of Cementitiously Stabilized Layers for Use in Pavement Design and Analysis (2014)

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7 C H A P T E R 3 Materials and Mixture Design Four types of material were used for stabilization in this project: high- and low-plasticity fine-grained soils (clay and silt) and two granular materials (sand and gravel). These materials were characterized in terms of moisture–density relationships, Atterberg limits, and gradation. Figure 3-1 presents the gradations of the four materials and Table 3-1 lists their Atterberg limits and designations. The binders used were cement, lime, and Class F and Class C fly ash. Nine mixtures were designed following the procedures developed by the National Lime Association (NLA) for soil– lime (NLA 2006), the Portland Cement Association (PCA) for soil–cement (PCA 1992), and the Federal Highway Admin- istration (FHWA) for soil–fly ash (Veisi et al. 2010) to deter- mine the appropriate binder contents. Table 3-2 lists the type and content of the binder used with each material (details are provided in Appendix B). The clay–lime material was cured at 104°F, and the other eight mixtures were cured at 68°F. These mixtures were used for model development rec- ognizing that the binder content could vary depending on Laboratory Tests and Model Development Figure 3-1. Gradation of soils. 0 10 20 30 40 50 60 70 80 90 100 0.0001 0.001 0.01 0.1 1 10 100 Pa ss in g, % Particle size (mm) Clay-sieve Clay-hydrometer Silt-sieve Silt-hydrometer Sand Gravel Table 3-1. Characteristics of soils. Clay Silt Sand Gravel Atterberg Limit Liquid Limit (LL) 39 17 – – Plastic Limit (PL) 23 15 – – Plasticity Index (PI) 16 2 – – Designation Unified Soil Classification System (USCS) CL ML SP GM AASHTO A-6 A-4 A-1-b A-1-a

8Table 3-2. Mix design of stabilized mixtures. Clay Silt Sand Gravel Cement 12% 8% 6% 3% Lime 6% 4% + 12%* – – Fly Ash C – 13% 13% 13% *Class F Fly Ash Table 3-3. Material properties and performance tests. Environmental Model Pavement Response Model Distress Model Freezing and Thawing Wetting and Drying Modulus Bottom-UpTensile Fatigue Top-Down Compressive Fatigue- Erosion Shrinkage Cracking Material Properties Strength Flexural modulus for heavily stabilized materials Resilient modulus for lightly stabilized materials Modulus of rupture Unconfined compressive strength Indirect tensile modulus Indirect tensile strength Ultimate drying shrinkage strain Gradient drying shrinkage strain Coefficient of thermal expansion Coefficient of friction Tests for Model Development or Calibration Freeze–thaw cycling Wet–dry cycling – Beam fatigue Cyclic impact erosion Restrained shrinkage cracking test the location of the material within the pavement structure (e.g., base or subbase). Three replicates were used for each UCS test. A 7-day UCS of 200 psi was used as the criterion to distinguish between heavily and lightly stabilized materials (i.e., heavily stabilized materials have a 7-day UCS ≥ 200 psi and lightly stabilized materials have a 7-day UCS < 200 psi). Based on this crite- rion, clay–lime and silt–C fly ash mixtures were categorized as lightly stabilized and the other seven mixtures were categorized as heavily stabilized materials. Tests and Model Development The material properties that influence the pavement per- formance were identified through the literature review. Also, the test methods for measuring these properties were iden- tified and assessed in terms of performance predictability, precision, accuracy, practicality, and cost. Promising test methods were then evaluated in the laboratory to determine their applicability to CSM (details are provided in Appen- dix B). Table 3-3 lists the proposed material properties and test procedures; brief descriptions are provided in the follow- ing sections. Modulus/Strength Growth When cement is used as the binder, high modulus/ strength can form fairly quickly. However, early-age modulus/ strength development for lime and/or fly ash–stabilized CSM is relatively slow in comparison to that of cement- stabilized CSM but can continue for years due to pozzolanic reactions. The modulus/strength development of CSM was examined; a brief description is provided (details are pro- vided in Appendix C). Strength The strength of CSM is characterized by the UCS, indirect tensile (IDT) strength, and modulus of rupture (MOR). The strength gain after 3, 7, 28, 90, 180, and 360 days of curing at 68°F and 100% relative humidity (RH) was measured, with one replicate of each mixture. The relationships between MOR and UCS and between IDT strength and UCS are illustrated in Figures 3-2 and 3-3 and presented by Equations 3-1 and 3-2, respectively. The relationship between IDT strength and MOR, presented in Equation 3-3, was derived from these two equations. These relationships provide estimates of the strength values that can be used as Level 2 inputs in the MEPDG (ARA 2004). MOR 0.14 UCS (3-1)= × 0.12 UCS (3-2)IDTS = × 0.86 MOR (3-3)IDTS = ×

9 Figure 3-2. Modulus of rupture versus unconfined compressive strength. y = 0.14x R2 = 0.72 0 50 100 150 200 250 0 500 1000 1500 2000 M O R (p si) UCS (psi) Figure 3-3. Indirect tensile versus unconfined compressive strength. y = 0.12x R2 = 0.92 0 50 100 150 200 250 0 500 1000 1500 2000 ID T St re ng th (p si) UCS (psi) Figure 3-4. Predicted versus measured strength. y = 1.03x R2 = 0.91 0 500 1000 1500 2000 0 500 1000 1500 2000 Pr ed ic te d St re ng th (U CS , M OR , a nd ID T St re ng th ) ( ps i) Measured Strength (UCS, MOR, and IDT Strength) (psi) UCS MOR IDT Strength Regression Line Line of Equality Figure 3-5. Modulus of rupture versus flexural modulus. R2 = 0.95 0 50000 100000 150000 200000 250000 0 20 40 60 80 100 120 140 160 Fl ex ur al M od ul us (p si) MOR (psi) where MOR = modulus of rupture, psi SIDT = indirect tensile strength, psi UCS = unconfined compressive strength, psi Because the 28-day strength is commonly used for qual- ity control and performance prediction, a model based on the 28-day strength was developed to predict the UCS, IDT, or MOR at any age for the 68°F and 100% RH cur- ing condition. The model is presented by Equation 3-4; the measured versus predicted strength is illustrated in Figure 3-4. (3-4)28 1 1 1 1 0 2S t S pt t t p( ) ( )=     ( )− + −    where St(t) = strength (UCS, IDT, or MOR) at age t months, psi S28 = strength (UCS, IDT, or MOR) after 28 days of cur- ing at 68°F and 100% RH t0 = time corresponding to S28 in months (e.g., 28/30.5 assuming 30.5 days/month) p1, p2 = regression parameters (1.59 and 1.61, respectively) Modulus The relationships between the different types of strength and modulus are illustrated in Figures 3-5 and 3-6 and presented by Equations 3-5 through 3-7. Equation 3-7 was derived from Equations 3-1 and 3-5. These relationships provide estimated values that can be used as Level 2 inputs in the MEPDG. 936.28 MOR 62382 (3-5)E f = × + 7980.1 (3-6)IDTE St = × 131.08 UCS 62382 (3-7)E f = × + where Ef = flexural modulus, psi Et = indirect tensile modulus, psi SIDT = indirect tensile strength, psi MOR = modulus of rupture, psi

10 Figure 3-6. IDT strength versus IDT modulus. R2 = 0.65 0 500000 1000000 1500000 2000000 0 50 100 150 200 250 ID T M od ul us (p si) IDT Strength (psi) Table 3-4. Parameters for IDT strength/ modulus model. Model Parameter 1 2 3 4 5 IDT strength p 1.59 1.61 −1.50 23.41 0.11 IDT modulus q 1.59 1.61 −0.23 0 1223 The flexural modulus after t months can be derived from Equations 3-4 and 3-7 as follows: ( )= ×     + ( )− + −   131.08 UCS 62382 (3-8)28 1 1 1 1 0 2E pf t t p The resilient modulus (Mr) for lightly stabilized materi- als can be estimated from the UCS (ARA 2004) using Equa- tion 3-9. 0.12 UCS 9.98 (3-9)Mr = × + where Mr = resilient modulus, ksi Similarly, the resilient modulus after t months of curing at 68°F and 100% RH can be estimated from Equation 3-10. = ×     + ( )− + −   0.12 (UCS ) 9.98 (3-10)28 1 1 1 1 0 2M pr t t p where UCS28 = UCS after 28 days of curing at 68°F and 100% RH t = time in months corresponding to Mr (assuming each month has 30.5 days) t0 = time in months corresponding to UCS28 (i.e., 28/30.5) p1, p2 = regression parameters (1.59 and 1.61, respectively). IDT Strength and Modulus Models Considering Temperature and RH Effects Shrinkage cracking is influenced by the early-age tensile strength/modulus and the environmental conditions, par- ticularly the temperature and RH. Therefore, models were developed for estimating the IDT strength and modulus val- ues at various temperatures and RH. These models are pre- sented as Equation 3-11a and 3-11b. p p t p Tp p S UCS (3-11a) IDT 5 28 1 1 1 1 28 30.5 1 RH 100 2 32 1.8 273.15 293.15 2 3 4 ( )=       − + −  +     − +    E q qt t q Tq q UCS (3-11b) 5 28 1 1 1 1 28 30.5 1 RH 100 2 32 1.8 273.15 293.15 2 3 4 ( )=       − + −  +     − +    where SIDT = IDT strength at age t months, psi Et = IDT modulus at age t months, psi UCS28 = unconfined compressive strength after 28 days of curing at 68°F and 100% RH, psi t = curing time, months (assuming each month has 30.5 days) RH = curing relative humidity, % T = temperature, °F p1, p2, p3, p4, p5 = strength regression parameters (listed in Table 3-4) q1, q2, q3, q4, q5 = modulus regression parameters (listed in Table 3-4) Figure 3-7 presents a comparison of the measured and pre- dicted IDT strength and modulus values after 3, 7, 14, 28, and 56 days of curing. Durability Tests were conducted to determine the effect of wet–dry and freeze–thaw cycles on the UCS; Equation 3-12 presents this effect. Model parameters obtained from the laboratory test results are listed in Table 3-5; a comparison of the mea- sured and predicted UCS values is shown in Figure 3-8. N m e m n N UCS UCS ln UCS 1 1 ln UCS 2 (3-12) current 1 28 1 28 1 ( ) ( )( ) = + + −  ( )

11 where UCS(N) = UCS after N cycles of freeze–thaw or wet–dry, psi UCScurrent = UCS before freeze–thaw or wet–dry cycles, psi UCS28 = 28-day UCS, psi N = number of freeze–thaw or wet–dry cycles m1, n1 = model parameters for wet–dry or freeze–thaw durability models Fatigue Fatigue of CSL occurs as a result of repeated traffic loads and is categorized as bottom-up tensile fatigue or top-down Figure 3-7. Measured versus predicted IDT strength and modulus values. (a) IDT Strength (b) IDT Modulus R2 = 0.89 0 50 100 150 200 250 0 50 100 150 200 250 Pr ed ic te d ID T St re ng th (p si) Measured IDT Strength (psi) Regression Line Line of Equality R2 = 0.77 0.0E+00 5.0E+05 1.0E+06 1.5E+06 2.0E+06 0.0E+00 5.0E+05 1.0E+06 1.5E+06 2.0E+06 Pr ed ic te d ID T M od ul us (p si) Measured IDT Modulus (psi) Regression Line Line of Equality Table 3-5. Regression parameters of durability models. Model Parameter Value Wet–dry m1 2.58 n1 0.62 Freeze–thaw m1 6.68 n1 0.93 compressive fatigue. The fatigue life of CSL typically is related to the ratio of applied stress to strength or the ratio of applied strain to breaking strain (Austroads 2008, ARA 2004, Otte 1978, Sobhan and Das 2007, Yeo 2008). The number of load repetitions that reduces the modulus value to 50% of its initial value is considered the fatigue life (Midgley and Yeo 2008). Bottom-Up Tensile-Fatigue Test Beam fatigue tests were conducted on 12 types of materials to determine the bottom-up tensile-fatigue life of CSM. Test results are shown in Figure 3-9 and the stress-based fatigue model is presented by Equation 3-13. ( ) = − σ   ln MOR (3-13)1 2 3 N k k k ft t where Nft = bottom-up tensile-fatigue life st = tensile stress at the bottom of beam, psi MOR = modulus of rupture, psi Figure 3-8. Measured versus predicted UCS values after wet–dry/freeze–thaw cycles. (a) Wet–Dry (b) Freeze–Thaw R² = 0.99 0 500 1000 1500 2000 0 500 1000 1500 2000 Pr ed ic te d U C S (p si) Measured UCS (psi) Line of Equality Regression Line R2 = 0.90 0 100 200 300 400 500 0 100 200 300 400 500 Pr ed ic te d U C S (p si) Measured UCS (psi) Regression Line Line of Equality

12 Figure 3-9. Bottom-up tensile-fatigue life versus stress ratio. 0 0.2 0.4 0.6 0.8 1 1.2 1 10 100 1000 10000 100000 St re ss R at io Number of Cycles to Failure (N) Clay-Cement (12%) Gravel-Cement (3%) Gravel-Cement (3%) [90% MDD] Gravel-Cement (5%) Sand-Cement (6%) Sand-Cement (8%) Silt-Cement (8%) Silt-Cement (8%) [90% MDD] Sand-Fly Ash (13%) Silt-Fly Ash (18%) Silt-Lime-Fly Ash (4/12%) Clay-Lime (6%) Table 3-6. Parameters of bottom-up tensile-fatigue life model. Material (Binder Content) Regression Parameters R2 k2 k3 Clay–Cement (12%) 0.03 1.03 0.82 Gravel–Cement (3%) 0.04 0.90 0.95 Sand–Cement (6%) 0.04 1.20 0.88 Silt–Cement (8%) 0.06 1.43 0.87 Sand–Fly Ash (13%) 0.02 0.80 0.95 Silt–Lime–Fly Ash (4%/12%) 0.06 1.28 0.94 Clay–Lime (6%) 0.03 0.99 0.72 Gravel–Cement (3%) [90% MDD] 0.07 1.02 0.93 Silt–Cement (8%) [90% MDD] 0.02 1.02 0.74 Gravel–Cement (5%) 0.03 0.85 0.89 Sand–Cement (8%) 0.03 1.06 0.89 Silt–Fly Ash (18%) 0.04 0.70 0.70 Average 0.04 1.02 – E D E m e m n D ( ) = ( ) + + −( )[ ]current UCS2 28 2 1 1 2 ln sinh ln ( )UCS -28 2 3 15 ( )    where D = accumulated damage j = total number of load groups ni = number of repetitions of load group i Ni = number of repetitions to fatigue of load group i E(D) = modulus after accumulated damage D UCS28 = 28-day unconfined compressive strength, psi Ecurrent = modulus before fatigue damage at age t in months, psi m2 and n2 = regression parameters for bottom-up tensile fatigue or top-down compressive-fatigue and erosion models. Top-Down Compressive-Fatigue and Erosion Test The combined effect of moisture and top compressive strain significantly accelerates top-down compressive-fatigue failure (De Beer 1990). A model that combines top-down compressive fatigue and erosion was developed. The pressure from traffic saturates and weakens the CSM, making it prone to top-down compressive fatigue. The compressive stress from traffic detaches the particles, and then shear stress caused by water movement under traffic transports the particles and leads to erosion. The cyclic impact erosion (CIE) test developed by Sha and Hu (2002), shown schematically in Figure 3-10, sim- ulates CSL erosion and top-down compressive fatigue in the field. Controlled-displacement tests were conducted on speci- mens submerged in water. When the vertical load impacts the k1 = parameter used for field calibration (1.0 for labo- ratory tests) k2, k3 = regression parameters The k2 and k3 values for the different materials are listed in Table 3-6. The accumulated damage and the modulus of the material after experiencing damage can be obtained from Equations 3-14 and 3-15, respectively. (3-14) 1 D n N i i i j∑= =

13 sample surface, the particles detach from the specimen causing the load to decrease; the modulus is also decreased. The top-down compressive-fatigue–erosion life is calcu- lated from Equation 3-16. ( )= ρω − σ log log 1 UCS (3-16)4 5N k kfc c where Nfc = top-down compressive-fatigue–erosion life (defined as the number of cycles that reduce the modulus to 50% of its initial value) r = maximum dry density, lb/ft3 w = optimum moisture content, % sc = compressive stress applied on the top of specimen, psi UCS = current unconfined compressive strength, psi k4, k5 = regression parameters After the top-down compressive-fatigue–erosion life is estimated, the damage and the reduced modulus can be cal- culated using Equations 3-14 and 3-15, respectively. Table 3-7 lists the model parameters and Figures 3-11 and 3-12 present comparisons of the measured and predicted fatigue life and modulus values, respectively. Figure 3-10. Schematic view of CIE test setup. (a) Load Case (b) Unload Case Table 3-7. Parameters for top-down compressive-fatigue–erosion model. Model Parameter Top-Down Compressive- Fatigue–Erosion Fatigue Life k4 2.79 k5 3.39 Top-Down Compressive- Fatigue–Erosion Modulus Reduction m2 6.77 n2 1.99 Figure 3-11. Measured versus predicted fatigue life values for top-down compressive-fatigue–erosion model. R2 = 0.15 0 1 2 3 4 5 0 1 2 3 4 5 Pr ed ic te d lo g (N fc) Measured log (Nfc) Regression Line Line of Equality Figure 3-12. Measured versus predicted modulus values for top-down compressive-fatigue–erosion model. R2 = 0.89 0.E+00 1.E+05 2.E+05 0.E+00 1.E+05 2.E+05 Pr ed ic te d M od ul us (p si) Measured Modulus (psi) Regression Line Line of Equality

14 Figure 3-13. COTE test setup (left: gravel–cement; right: clay–lime). 65% or 98%. Figure 3-14 shows the typical change in strain versus time (temperature cycles), and Table 3-8 lists the COTE values for the clay–cement, silt–cement, clay–lime, and gravel–cement at different temperatures and RHs. Ultimate Drying Shrinkage Strain Ultimate drying shrinkage strain is the shrinkage strain that develops after extended exposure of CSL to drying conditions. The ultimate drying shrinkage strain was deter- mined from tests on 11.25 × 4 × 4 in. beam specimens stored Shrinkage Shrinkage cracking test sets were conducted on clay– cement, silt–cement, and clay–lime at various combinations of RH and temperatures (68°F and 65% RH, 68°F and 40% RH, and 104°F and 40% RH). Each set included tests for determining the coefficient of thermal expansion (COTE), ultimate drying shrinkage strain, drying shrinkage strain gradient, large-scale restrained shrinkage cracking (using epoxy as the bonding agent), coefficient of friction, and IDT strength and modulus values. For the restrained shrinkage cracking tests, the sides of the beams were sealed and only the top surface was exposed to air to simulate field drying. The shrinkage strain was measured by a linear variable differential transformer (LVDT). IDT strength/modulus tests were con- ducted after 3, 7, 14, 28, and 56 days of curing. Coefficient of Thermal Expansion The COTE is required for determining the thermal strain, which is a key input in the shrinkage cracking model. Fig- ure 3-13 shows the COTE test setup. In this test, a specific temperature cycle was applied, displacements were mea- sured by LVDTs, and temperatures inside the specimens and in the environmental chamber were monitored by thermal couples. The COTE was determined from the cyclic strain, which does not include strain due to autogenous and/or dry- ing shrinkage. Tests were conducted at different temperature ranges with amplitude set to 9°F and RH maintained constant at either Figure 3-14. Strain versus time for COTE test of clay–lime (77F to 86F).

15 Table 3-8. COTE for different CSM. Material Temperature Cycles Relative Humidity (%) COTE (×10−6/°F) Clay–Cement 68–77°F 65 12.6 Silt–Cement 68–77°F 65 9.3 104–113°F 65 9.5 Clay–Lime 68–77°F 65 13.1 77–86°F 98 46.7 36–45°F 98 29.2 Gravel–Cement 77–86°F 98 14.4 36–45°F 98 2.6 Figure 3-15. Measured versus predicted ultimate drying shrinkage. y = 0.95x R2 = 0.98 0 2000 4000 6000 8000 10000 12000 14000 16000 0 5000 10000 15000 Pr ed ic te d U lti m at e S tr ai n (10 - 6 ) Measured Ultimate Strain (10-6) Line of equality Regression Line Figure 3-16. Free-drying shrinkage with moisture gradient test setup. at 68°F and about 40% RH. The shrinkage strain was measured with dial gauges placed on both sides and monitored until it became stable. The ultimate drying shrinkage is expressed by the follow- ing equation: C w mmi (3-17)su 1 21[ ]ε = + where esu = ultimate drying shrinkage strain, × 10-6 w = water content, lb/ft3 C1 = binder type factor: 0.993 for cement, 1.026 for lime, and 0.366 for C fly ash m1, m2 = regression parameters (m1 = 3.17, m2 = 313.76) Figure 3-15 shows the measured and predicted ultimate drying shrinkage results. Drying Shrinkage Strain Gradient Moisture loss due to evaporation from the top surface of the pavement results in a moisture gradient that leads to self- sustained drying shrinkage stress and early-age cracking in the CSL. The effect of moisture gradient on shrinkage was investigated in tests on 8 in. tall, 4 in. wide, and 11.25 in. long beams. The four beam sides were sealed with wax leaving only the top surface exposed to air. Figure 3-16 shows the test setup. The drying shrinkage strain at a specific depth from the surface can be determined from the following equation: tg c a 1 RH 100 (3-18)su 6( )( )ε = ε −  where eg(t) = drying shrinkage strain with moisture gradient at t days from placement, × 10-6 esu = ultimate drying shrinkage strain, × 10-6 (can be estimated from Equation 3-17) RHc = calculated relative humidity, %, esti- mated as follows: RHc = RH + (100 - RH)f(t) a5 RH = atmospheric relative humidity, % f(t) = 1/(1 + t/b)

16 Figure 3-17. Measured versus predicted gradient drying shrinkage strain values at various depths. (a) Silt–Cement at 68°F and 65% RH (b) Clay–Lime at 68°F and 40% RH -0.0005 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0 20 40 60 80 100 St ra in (+ Sh rin ka ge /-E xp an sio n) Time (Days) 0.01" measured 2.25" measured 4.50" measured 6.75" measured 0.01" predicted 2.25" predicted 4.50" predicted 6.75" predicted -0.002 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0 20 40 60 80 100 120 St ra in (+ Sh rin ka ge /-E xp an sio n) Time (Days) 0.01" measured 2.25" measured 4.50" measured 6.75" measured 0.01" predicted 2.25" predicted 4.50" predicted 6.75" predicted where t = time since placement in days b = a1(d + a2) a3(w/c)a4 d = depth from evaporation surface, ft w/c = water/calcium ratio in mass a1, a2, a3, a4, a5, a6 = regression parameters (listed in Table 3-9) Figure 3-17 shows a comparison between the measured and predicted drying shrinkage strain values at various depths for silt–cement and clay–lime maintained at certain temperature and relative humidity. Table 3-9. Parameters for drying shrinkage strain gradient model. a1 a2 a3 a4 a5 a6 1289202 0.085 0.94 1.24 10209 4.51 Restrained Shrinkage Cracking Shrinkage cracking occurs when CSL are restrained by the underlying layer and/or are self-restrained (e.g., by strain gra- dient). The shrinkage cracking potential of CSL materials can be determined by restrained shrinkage testing. The increase in friction between the CSL and underlying material reduces the shrinkage crack spacing. Shrinkage cracking can be gen- erated in a laboratory specimen by artificially creating a high level of bonding. To simulate the field pavement conditions, the beam sides were sealed, but the surface was exposed to air. The test setup is shown in Figure 3-18. Clay–cement, clay–lime, and silt–cement beams with dimensions of 48 in. × 6 in. × 4 in. were glued on a steel tube using epoxy. The restrained shrinkage was monitored by an LVDT, and crack spacing and width on the top surface were measured. Figure 3-19 shows typical cracking in the beam specimen and Table 3-10 lists the number of cracks and age when cracking occurred. Actual crack spacing could not be

17 Figure 3-18. Restrained shrinkage test setup with sides sealed. Figure 3-19. Transverse crack in clay–lime specimen (view from top). determined from these tests because of the short specimen length and the small number of observed cracks. Coefficient of Friction The interface friction/bond affects shrinkage cracking and it is therefore considered in the shrinkage cracking model. For the restrained shrinkage cracking test, the CSM specimen was glued to a steel substrate using epoxy and the coefficient of friction between the CSM and steel substrate was measured using the Iowa shear test (Iowa DOT 2000), which is similar to a direct shear test. In this test, setup shown in Figure 3-20, the load is applied at a constant deformation rate of 0.65 in./min until the CSL is separated from the base layer along the inter- Table 3-10. Laboratory restrained cracking summary. Materials Environment No. of Cracks Age when Crack Occurred (days) Clay–Cement 68°F and 65% RH 1 6 68°F and 40% RH 2 11 104°F and 40% RH 2 2 Clay–Lime 68°F and 65%RH 1 6 68°F and 40%RH 1 4 104°F and 40% RH 1 2 Silt–Cement 68°F and 65% RH 1 10 face, and the coefficient of friction is determined from the slope of the linear portion of the stress-displacement relationship. When epoxy was used as the bonding agent in the labora- tory, the coefficient of friction exhibited a linear relationship with the IDT strength of the CSM, as shown in Figure 3-21. In the field, the CSL bonds well with the underlying layer such that the failure interface usually occurs in the weaker material between the CSM and the underlying material (Romanoschi and Metcalf 2001). Therefore, the slope of the stress versus dis- placement curve in a direct shear test can be used to estimate the coefficient of friction. Figure 3-22 shows the relationship between the IDT strength of the CSM and the coefficient of friction determined in direct shear tests. A shrinkage cracking model for predicting crack width and spacing was developed using dimensional analysis, the restrained shrinkage cracking test results, and field data (see Chapter 4). Figure 3-20. Coefficient of friction test setup.

18 y = 79.12x R2 = 0.89 0 2000 4000 6000 8000 10000 12000 14000 0 50 100 150 C oe ffi ci en t o f F ri ct io n (p si/ in. ) IDT Strength (psi) Figure 3-21. IDT strength versus coefficient of friction. y = 156.48x R2 = 0.86 0 5000 10000 15000 20000 25000 0 50 100 150 C oe ffi ci en t o f F ri ct io n (p si/ in. ) IDT Strength (psi) Figure 3-22. IDT strength versus coefficient of friction in a direct shear test.