Guía de Evaluación del Módulo Dibujo asistido por computadora en 3D

clear all;

%Define signal variables.

data = xlsread('RCC5-1.xls'); time = data(:,1);

voltage = data(:,2);

%Perform Fast Fourier Transform.

L = length(time); %number of data points.

T = time(2)-time(1); %sampling period.

t = (0:L-1)*T; n = 2^nextpow2(L);

FFT = fft(voltage,n); %imaginary and real components.

FFT_abs = abs(FFT/n);

f = Fs*(0:(n/2))/n; %frequency spectrum up to Nyquist frequency.

f1 = Fs*(1:n)/n; %full frequency spectrum. %Plot results of Fast Fourier Transform.

plotlim = [0 10000]; %not interested in frequencies above 10 kHz for this specimen geometry.

plot(f,FFT_abs(1:n/2+1),'linewidth',2); hold on%only plot up to Nyquist frequency.

xlim(plotlim);

legend('237.2', '281.7', '326.2'); %cementitious contents.

ylabel('Amplitude (-)'); %non-dimensional parameter.

xlabel('Frequency, f (Hz)');

%Determine transverse resonance frequency.

[x,freq] = findpeaks(FFT_abs,f1); %determine peak amplitudes and corresponding indices.

[max_amp,I] = max(x); %define maximum of all peak amplitudes.

res_freq = freq(I) %resonance frequency.

APPENDIX C: GYRATORY AND MODIFIED PROCTOR

COMPACTION CURVES

This appendix contains gyratory and modified Proctor compaction curves for the 17 mix designs presented in Appendix L.

Figure C1. Gyratory and Modified Proctor Compaction Curves for Mix 1. (1 kg/m3 _{= 1.686 lb/yd}3₎

Figure C2. Gyratory and Modified Proctor Compaction Curves for Mix 2. (1 kg/m3 _{= 0.063 lb/ft}3₎

Figure C4. Gyratory and Modified Proctor Compaction Curves for Mix 4. (1 kg/m3 _{= 0.063 lb/ft}3₎

Figure C5. Gyratory and Modified Proctor Compaction Curves for Mix 5. (1 kg/m3 _{= 0.063}

Figure C6. Gyratory and Modified Proctor Compaction Curves for Mix 6. (1 kg/m3 _{= 0.063 lb/ft}3₎

Figure C7. Gyratory and Modified Proctor Compaction Curves for Mix 7. (1 kg/m3 _{= 0.063 lb/ft}3₎

Figure C8. Gyratory and Modified Proctor Compaction Curves for Mix 8. (1 kg/m3 _{= 0.063 lb/ft}3₎

Figure C9. Gyratory and Modified Proctor Compaction Curves for Mix 9. (1 kg/m3 _{= 0.063 lb/ft}3₎

Figure C10. Gyratory and Modified Proctor Compaction Curves for Mix O. (1 kg/m3 _{= 0.063 lb/ft}3₎

Figure C12. Gyratory and Modified Proctor Compaction Curves for Mix B. (1 kg/m3 _{= 0.063 lb/ft}3₎

Figure C13. Gyratory Compaction Curves for Site B. (1 kg/m3 _{= 0.063 lb/ft}3₎

Figure C14. Gyratory Compaction Curves for Site C. (1 kg/m3 _{= 0.063 lb/ft}3₎

Figure C16. Gyratory and Modified Proctor Compaction Curves for Mix Trap Rock. (1 kg/m3 _{= 0.063 lb/ft}3₎

Figure C17. Gyratory and Modified Proctor Compaction Curves for Mix River Gravel. (1 kg/m3 _{= 0.063 lb/ft}3₎

APPENDIX D: EXPERIMENTAL DESIGN DATA

This appendix contains the data used to develop the response data and contour plots in Chapter 4. Table D1. Modified Proctor and Vebe Properties (1 kg/m3 _{= 0.063 lb/ft}3₎

Design Point

Label Maximum Dry Density (kg/m3₎ Optimum Moisture _{Content (%)} Vebe Time _(sec) Vebe Density _(kg/m3₎

A 2391.6 6.59 12.5 2250.4 B 2364.1 6.26 17.8 2260.4 C 2394.2 5.95 17.0 2324.5 D 2382.7 6.44 15.8 2303.6 E 2387.2 6.23 12.9 2266.0 F 2324.4 6.64 20.1 2229.2 G 2301.5 6.84 13.0 2237.1 H 2411.5 6.31 11.0 2311.5 I 2319.9 6.52 11.6 2285.3 K 2358.7 6.57 13.9 2230.0 L 2358.8 6.24 18.5 2259.1 M 2390.5 6.55 13.2 2278.4 N 2383.2 6.38 14.6 2222.8 O 2390.5 6.39 13.7 2288.3 P 2407.0 6.00 15.0 2284.7 Q 2411.3 6.05 18.2 2342.5 R 2371.9 6.11 16.4 2246.3 S 2380.1 6.22 19.2 2274.1 T 2414.2 6.16 16.2 2271.7 U 2392.6 6.11 16.0 2210.8

Table D2. Compressive Strength (average of 3 replicates) (1 ksi = 6.89 MPa)

Design Point Label 1-Day Compressive _{Strength (MPa)} 7-Day Compressive _{Strength (MPa)} 28-Day Compressive _{Strength (MPa)}

A 18.47 38.01 51.03 B 27.95 51.10 63.47 C 16.69 40.39 55.94 D 28.11 46.03 57.37 E 17.52 42.54 55.61 F 18.51 34.40 50.29 G 17.19 33.98 48.38 H 32.42 62.55 64.49 I 28.85 52.34 60.39 K 18.23 35.26 47.22 L 27.45 51.21 65.09 M 26.92 49.36 60.90 N 24.69 48.28 59.24 O 16.28 35.58 48.68 P 25.14 60.99 64.39 Q 24.13 43.67 62.36 R 17.03 39.35 60.71 S 25.25 48.35 63.35 T 25.29 47.60 58.37 U 21.91 45.02 60.76

Table D3. Split Tensile Strength (average of 3 replicates) (1 ksi = 6.89 MPa)

Design Point Label 1-Day Split Tensile _{Strength (MPa)} 7-Day Split Tensile _{Strength (MPa)} 28-Day Split Tensile _{Strength (MPa)}

A 2.23 3.70 4.46 B 2.83 3.73 3.99 C 2.23 3.31 3.85 D 3.51 3.95 5.65 E 2.22 3.54 3.71 F 2.15 3.11 4.25 G 2.01 3.14 3.77 H 4.13 4.46 4.96 I 3.29 4.26 4.73 K 2.31 3.58 4.83 L 3.62 3.73 4.28 M 3.09 3.51 3.86 N 3.09 4.60 5.52 O 2.66 3.46 5.25 P 2.96 4.60 5.11 Q 3.16 3.92 4.47 R 2.23 3.73 4.18 S 2.97 3.69 4.57 T 2.92 4.00 4.83 U 2.71 3.66 4.27

Table D4. 28-Day Flexural Strength, Elastic Modulus, and Drying Shrinkage Strains (all measurements are averages of 3 replicates); (1 ksi = 6.89 MPa; 1 GPa = 145.03 ksi) Design

Point Label 28-Day Flexural Strength (MPa) 28-Day Elastic Modulus (GPa) 7-Day Drying Shrinkage Strain (με) 28-Day Drying Shrinkage Strain (με)

A 7.40 34.27 260.00 426.67 B 6.24 36.81 226.67 393.33 C 7.02 35.38 183.33 340.00 D 6.22 33.35 210.00 356.67 E 7.19 31.18 183.33 286.67 F 6.13 30.76 150.00 270.00 G 5.29 30.59 150.00 280.00 H 6.08 33.88 246.67 356.67 I 5.76 33.35 253.33 380.00 K 5.31 33.67 203.33 303.33 L 5.93 31.62 203.33 256.67 M 6.55 31.56 206.67 263.33 N 6.23 30.50 260.00 336.67 O 6.03 33.89 233.33 363.33 P 7.02 34.46 180.00 280.00 Q 6.79 33.84 170.00 283.33 R 6.88 34.68 163.33 263.33 S 6.98 31.11 166.67 253.33 T 6.74 31.68 163.33 246.67 U 6.65 32.11 233.33 306.67

APPENDIX E: GYRATORY RCC MIX DESIGN FRAMEWORK

The application of the Superpave Gyratory Compactor to RCC specimen preparation can lead to more consistent mixture design process. The gyratory compactor applies a kneading action for compaction of the RCC sample, which is more representative of the method that RCC is compacted for pavement applications in the same manner as for asphalt materials. Additionally, the gyratory applies a more consistent compactive effort. For example, in the compaction delay study, Appendix M, the gyratory compactor was found to be a better tool for assessing the effect of compaction delay on RCC because of the more precise results that arise from the consistent compactive effort. Appendix E summarizes work performed with the gyratory compactor for use in the mix design of RCC. This appendix is separated into a literature review, a summary of the work that has been performed throughout this report related to gyratory-based mix design of RCC, and finally a proposed framework for an RCC mix design method.

E.1 LITERATURE REVIEW

E.1.1 General Gyratory Compactor Information

The gyratory compactor can be adjusted to apply a varying amount of axial pressure at a range of selected angle of internal gyration. According to ASTM C1800, which summarizes a method to determine density of compacted samples of RCC using the gyratory compactor, the pressure should be 600 kPa and the internal angle of gyration should be 1.16 degrees. Additionally, the number of total gyrations is a parameter that must be determined. The gyratory compactor can either be used to compact to a certain number of gyrations or a certain density (fixed specimen height), given the initial mass of the material in the compactor. Previous research has reported that 50-75 gyrations best approximates field compaction (Amer et al., 2003).

E.1.2 Applying Gyratory Compactor in Mix Design for Moisture-Density Testing

The first general step of a mix design method using moisture-density testing is to determine the aggregate combination that will be used. Previous work has determined an optimal blend of aggregates using a gyratory compactor for packing density tests (Khayat and Libre, 2014). Other work, for example this report, has shown various aggregate gradations can result in acceptable mechanical properties. Williams (2013) concluded that aggregate gradations that are closer to the 0.45-power maximum density line yield RCC samples with a higher density. While other

considerations should be made when considering the appropriate particle size distribution of aggregates for RCC, e.g., resistance to segregation and finishability, an optimum aggregate

combination either from packing tests or from considering the maximum density gradation has been shown to be adequate (Williams, 2013; Khayat and Libre, 2014).

Cement content is the next parameter that must be selected in the mix design method. Khayat and Libre, 2014, indicate that a cement content as low as 250 kg/m3 _{(420 lb/yd}3_{) could be used to achieve}

Significant paste leakage in Williams’ study indicates that the cement content likely was high. Ideally, the paste fraction in RCC is just sufficient to fill the voids in between aggregates, allow compaction to the specified density, and provide a durable surface. Excessive cement content will produce a less stable mixture and defeats one main objective of RCC pavements.

Given a selected aggregate gradation and proportion and cement content, the gyratory compactor is able to determine the RCC moisture-density relationship, optimum moisture content, and maximum dry density. Some previous research has indicated that moisture-density testing with the gyratory will not yield a true optimum moisture content because at higher moisture contents the gyratory compactor will squeeze excess paste out of the sample (Williams 2013). This has been seen to be true in this study when excessive water or cement is added to the RCC mixture proportions. However, under normal RCC mixture proportions this should not generally occur. Using an adjusted procedure to determine the optimum moisture content from gyratory compaction, Williams (2013) reported that OMC using the gyratory was typically 0.75% lower than the OMC using the modified Proctor. Additionally, the MDD from the gyratory was typically 75 kg/m3 _{(4.7 lb/ft}3_{) higher than the MDD using}

the modified Proctor. Khayat and Libre (2014) did not observe the same behavior reported by Williams and a gyratory-based OMC existed like the modified Proctor test. Note, Khayat used an alternative gyratory compactor, called the Intensive Compaction Tester (ICT). Ultimately, it was recommended that a slightly higher optimum moisture content should be used for RCC mix design (relative to the Proctor) because the resulting mechanical properties are more sensitive to a decrease in water below optimum than an increase in water above optimum (Khayat and Libre, 2014).

E.1.3 Intensive Compaction Tester

As mentioned in the previous section, another gyratory compactor has been used by some researchers, called the Intensive Compaction Tester (ICT). While much work has focused on application of the Superpave Gyratory Compactor, this machine was not originally intended for application to RCC, and thus many have warned against damaging the Superpave Gyratory

Compactor when using it for RCC (ASTM C1800, 2017; Williams, 2013; Käppi and Nordenswan, 2007). Käppi and Nordenswan (2007) describe their experience using the ICT for applications to no-slump concrete. They have been using this machine since the late 1980s, and they suggest that the ICT would be a good alternative to the Superpave Gyratory Compactor for use in aggregate packing and mixture optimization tests (Käppi and Nordenswan, 2007). Khayat and Libre (2014) successfully used the ICT for both optimization of packing density and determining OMC from moisture-density testing of RCC.