Figure 23: Example shear wave velocity- strength curves

models agree better with the lab-measured flexural strength than the maturity-based model. However, the modified model is more appropriate for estimation of early hour strength as the conventional model would predict unreliable negative strength for concrete with 2000 m/s shear wave velocity.

900

700

i ) s ( p t h g r e n t S l a u r x F l e

500

300

100

7 days

3 days

5 days 14 days

1 day

2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 -100

-300

Beam Shear Wave Velocity (m/s) Modified Model Beam Conventional Model

Figure 23: Example shear wave velocity- strength curves.

Substituting Equation (8) into Equation (14) leads to the following relationship between the field-measured shear wave velocity and concrete flexural strength for the long-life concrete mix tested:

(15)

To combine the benefits of maturity and ultrasonic tomography, a procedure was created using maturity predictive abilities to relate shear wave velocity to strength gain. This proposed procedure is outlined below.

Step 1: Conduct laboratory testing of concrete compressive and flexural strengths at various ages.

Concrete cylinders and beams should be prepared with the same concrete mix design as expected to be used for the pavement project. Compressive strength and flexural strength should be tested using cylinders and beams, respectively, at various ages, say 6 hours, 12 hours, 18 hours, 1 day, 3 days, 7 days, and 14 days. Concrete maturity should be measured for cylinders

and beams. The shear wave velocity should be measured on the beams prior to each flexural strength testing.

Step 2: Establish maturity-strength and shear wave velocity-flexural strength relationships.

Using the data collected at Step 1, obtain

a. coefficients am and bm of the flexural strength – maturity relationship Equation (11), b. coefficients cm and dm of the compressive strength – maturity relationship Equation (12), and c. coefficients as and bs of the flexural strength – shear wave velocity relationship

Equation (14)

Step 3: Obtain the relationship between the compressive strength and shear wave velocity using the relationships obtain in Step 2:

) (1 6)

Step 4: Select PCC compressive or flexural strength, or , respectively to be considered for traffic opening.

Step 5: Determine the minimum shear laboratory (beam) shear wave velocity corresponding to the concrete flexural or compressive strength considered for traffic opening. This shear wave velocity is obtained by solving Equations (17) and (18).

(17)

(18)

Step 6: Determine the field shear wave velocity corresponding to the concrete strength specified for traffic opening using Equation (15).

Step 7: Determine the maturity level corresponding to the specified opening to traffic concrete strength by inverting Equations (11) and (12).

(19)

(20)

Step 8: Predict concrete strength development after traffic opening based on the anticipated change in maturity:

(21)

(22)

where:

is the time from traffic opening in hours;

is the mid-depth mean PCC slab temperature depending on the pavement location, concrete slab thickness, and construction month.

5 Mechanistic-Based Early Opening Damage Analysis

The National Road Research Alliance (NRRA) recently performed a study to determine the long-term effects of early loading (Khazanovich, 2021). This project began in 2017 as part of MnROAD, a pavement test track used for different research projects in Minnesota. The purpose of that study was to explore the short- and long-term effects of early loading at different times and axle weights. Six testing cells were loaded at varying times: one early enough to leave rutting, one control was not loaded at all, and the final four had stepwise loading at different maturity levels. The cells were split into two lanes of which one was loaded using a 31,000-lb MnDOT snowplow and the other using a ¾-ton pickup truck. Each load application included one forward and one backward pass. The first loading began in Cell 124 at maturity 100°C-hr. There was no visible damage after early loading.

All sections were loaded with about 10,000 ESALs per year and were monitored regularly until 2021. Several aspects of the pavement were monitored including maturity, dynamic and static strains, curling, strength, durability, and international roughness index (IRI). The effect on joints was analyzed using an ultrasonic tomography device to locate damage near dowels and using falling weight deflectometer (FWD) testing to determine load transfer efficiency (LTE). Petrographic data was also collected to consider possible surface damage effecting friction. Despite the extensive analysis using pavement performance measures, nondestructive testing, and embedded sensors, no significant, identifiable damage could be associated to early loading.

Using the knowledge gained from field testing, a mechanistic-based early opening damage analysis model was developed. The effect of strength gain rate, traffic volume, climate, load characteristics, and pavement structure properties were included in the predictive performance reliability model. A probabilistic approach was applied to evaluate critical stresses for each early applied vehicle pass. The maturity-strength relationship was then used to calculate strength at a random time chosen to open to traffic. If the critical strength is greater than the strength calculated at the same time, then the simulation is counted as a failure. This is done for each vehicle and the total number of failures are used to calculate the probability of failure for the chosen opening time and then the corresponding reliability. This procedure was used for two types of damage: cracking and dowel bar failure.

In this study, the NRRA model was generalized to allow for the strength estimation using the shear wave velocity measurements. In addition, it was adapted for Pennsylvania climate conditions. The details of this procedure are provided below.

5.1 Concrete Property Estimation

Accurate estimation of concrete flexural strength, compressive strength, and elastic modulus is needed to perform a reliable damage analysis. The user is expected to provide the strength-maturity models so that the concrete maturity at any time after loading can be used in the analysis. The model developed in this study adapts the NRRA approach but adds an option to estimate in-place concrete strength using the shear wave velocity method. Each of these options is described below.

5.1.1 Concrete Strength Prediction with Maturity Method

The NRRA model required the user to specify the concrete maturity, , at the time of opening to traffic, i.e., it is expected that maturity of the concrete pavement would be monitored after concrete placement and the pavement would be opened to traffic after concrete maturity would reach the specified value. The PCC compressive and flexural strength between the time of traffic opening and the time concrete reaches the design strength is determined using the predicted maturity and relationships between strength and maturity.

In this study, the NRRA approach was adapted with the following modifications:

1. The functional forms of the maturity-strength relationships were modified as described in Section 0. 2. Instead of asking the user to specify the required maturity, the model asks the user to specify the concrete strength for opening to traffic. The required concrete maturity level is determined using Equation (13). 3. The climate database required to predict the concrete maturity increase after opening to traffic is updated using the PittRigid climate stations.

5.1.2 Concrete Strength Prediction with Combined Shear Wave Velocity and Maturity

In this method, the time of opening to traffic is determined when a certain level of shear wave velocity has been reached, but the strength development predictions are made using the maturity method. It is expected the shear wave velocity would be monitored after concrete placement and the pavement would be opened to traffic after the concrete shear wave velocity reaches the specified value, .

The user is asked to specify the compressive strength at the time of traffic opening and the required shear wave velocity is determined using Equations (17) and (18). The effective maturity corresponding to this shear wave velocity level is determined using Equations (19) and (20) and the flexural strength and compressive strength are determined using Equations (21) and (22).

5.1.3 Concrete Modulus of Elasticity estimation

The concrete modulus of elasticity can be estimated using the ACI equation:

(23)

5.1.4 Concrete Properties Variability Predictions

The methods described above will only predict the mean concrete properties at any given time. The spatial variability of the concrete strength at an early age is much higher than for mature concrete and therefore must be accounted for in this analysis (Freeseman et al, 2016). A young concrete will have a high variability (typically about 25%), however as concrete matures, the variability becomes smaller (around 6%). The following model was adapted to evaluate the strength coefficient of variation,

(24)

where:

C, D, E are calibration coefficients with default values of 0.25, 0.001, and 0.075, respectively.

To account for the strength spatial variability, the following expression for the damage analysis strength is adopted:

(25)

where:

is the maturity estimated flexural or compressive strength, psi,

is the damage analysis flexural or compressive strength, psi,c is a coefficient with a default of 1.

5.2 Transverse Cracking Performance

Transverse cracking is a major distress in concrete pavements that can lead to failure. Cracking initiates when the combined stresses from axle load and temperature curling are greater than the concrete strength.

Only the bottom-up fatigue damage is considered in this study. The flexural strength and elastic modulus were determined using the procedure above. The longitudinal stresses at the bottom of the slab were computed using an adapted neural network developed under the NCHRP 1-37A project (Khazanovich et al., 2001). The temperature curling stresses were computed using Westergaard’s Solutions (Westergaard, 1926).

It is assumed that an early age pavement does not significantly separate from the subgrade and therefore the axle load stress can be computed independently from temperature curling stresses. This also permitted using the dynamic coefficient of subgrade reaction for the moving axle load stress calculation and the static coefficient of subgrade reaction in the curling analysis. The static coefficient of subgrade reaction was assumed to be half the dynamic coefficient of subgrade reaction. The total stress is obtained by summation of the axle-induced and temperature curling stresses.

5.2.1 Thermal Load Characterization

Thermal gradients throughout the rigid pavement greatly affect critical stresses in the concrete slab contributing to cracking. Distributions of thermal gradients are required over each month throughout the year (both day and night). The Enhanced Integrated Climatic Model

(EICM) module of AASHTO M-E Design software generates the thermal profiles throughout concrete slab thickness for every hour of pavement life.

To improve computation efficiency, the AASHTO M-E procedure converts these hourly predictions into monthly distributions of probability of combinations of traffic and temperature (known as the thermal linearization process). The AASHTO M-E linearization process eliminates the need to compute the number of loads as a function of both linear and nonlinear temperature differences by equating stresses due to nonlinear temperature distribution with those due to linear gradients (NCHRP, 2004; Yu et al., 1998).

The equivalent temperature distribution concept was introduced by Thomlinson in 1940 and further developed by others (Thomlinson, 1940; Choubane and Tia, 1992). The concept, later generalized for non-uniform slabs (Khazanovich, 1994; Ioannides and Khazanovich, 1998), states that if two slabs have the same plane-view geometry, flexural stiffness, self-weight, boundary conditions, and applied pressure, and rest on the same foundation, then these slabs have the same deflections and bending moment distribution if the throughout-the-thickness temperature distributions satisfy the following condition:

∫ ( ) ∫ ( ) (26)

where:

a, b are the subscripts denoting two slabs;

z is the distance from the neutral axis;

T0, is the temperatures at which theses slabs are assumed to be flat;

is the coefficient of thermal expansion;

E is the modulus of elasticity;

h is the slab thickness.

The temperature distribution throughout the slab thickness can be split into three components, namely: the part that causes constant strain throughout-the-slab-thickness, the part that causes linear throughout-the-slab-thickness strains, and finally the part that causes nonlinear strains.

The first step in the AASHTO M-E linearization process is to compute the monthly PCC stress frequency distribution in the pavement at critical locations for linear temperature