79 LAMPIRAN 80 A. 1Rumus yang digunakan dalam Marshall 1. Berat Jenis bulk agregat gabungan Gsb= P1+P2+⋯+Pn P1 G1 + P2 G2 +⋯+ Pn Gn Dimana: Gsb = berat jenis agregat bulk P1,P2,Pn = presentase masing-masing fraksi agregat G1,G2,Gn = berat jenis masing-masing fraksi agregat 2. Berat jenis efektif agregat gabungan Gse= 100−Pb 100 Gmm − Pb Gb Dimana: Gse = berat jenis efektif agregat Gmm = berat jenis maksimum campuran (metode AASHTO T 209-1990) Pb = kadar aspal berdasarkam berat jenis maksimum campuran yang diuji Gb = berat jenis aspal 3. Berat jenis maksimum campuran dengan kadar aspal campuran yang berbeda Gmm= Pmm Ps Gse − Pb Gb Dimana: Gmm = berat jenis maksimum Pmm = persen berat terhadap total campuran (=100) Ps = persen agregat terhadap total campuran Gse = berat jenis efektif agregat Gb = berat jenis aspal Pb = kadar aspal total, persen terhadap berat total campuran 81 4. Rongga di dalam campuran (void in mixture) VIM=100 Gmm−Gmb Gmm Dimana: VIM = rongga di dalam campuran, persen terhadap volume total campuran Gmb = berat jenis curah campuran padat Gmm = berat jenis maksimum campuran 5. Rongga di antara mineral agregat (void in mineral agregat) VIM=100− Gmb×Ps Gsb Dimana: VMA = rongga di antara mineral agregat, persen terhadap volume total campuran Gsb = berat jenis curah agregat Gmb = berat jenis curah campuran padat Ps = persen agregat terhadap total campuran Pb = kadar aspal total, persen terhadap berat total campuran 6. Rongga terisi aspal (void filled with bitumen) VFB= 100(VMA−VIM) VMA Dimana: VFB = rongga terisi aspal, persen terhadap VMA VMA = rongga di antara mineral agregat, persen terhadap volume total campuran VIM = rongga di dalam campuran, persen terhadap volume total campuran 7. Kadar aspal efektif Pbe=Pb− Pba 100 Ps Dimana: 82 Pbe = kadar aspal efektif, persen terhadap berat total campuran Ps = persen agregat terhadap total campuran Pb = kadar aspal total, persen terhadap berat total campuran Pba = penyerapan aspal, persen terhadap berat agregat 83 B. 1Hasil Pengujian karakteristik Marshall B.1 Pengujian karakteristik Marshall Campuran Ohio Ukur 1Ukur 2Ukur 3 Rata-rata Berat Benda Uji Kering (gr) Berat Benda Uji Jenuh Air (gr) Berat Benda Uji Dalam Air (gr) Pembacaan Arloji Stabilitas (div) Stabilitas dengan kalibrasi alat (kg) Koreksi Benda Uji Stabilitas Dengan Koreksi Benda Uji (Kg) a b d e f g h i j k l m n o p q r s t 1 5.32 64.530 63.520 64.130 64.060 1176.500 1186.900 665.800 521.100 2.258 2.412 2.607 2.496 19.583 6.396 67.338 425.000 1022.635 0.986 1008.318 2.390 421.890 2 5.32 64.160 64.980 64.330 64.490 1171.200 1182.700 657.400 525.300 2.230 2.412 2.607 2.496 20.585 7.563 63.261 420.000 1010.604 0.975 985.339 2.490 395.718 3 5.32 64.890 63.750 64.440 64.360 1180.200 1191.500 667.100 524.400 2.251 2.412 2.607 2.496 19.838 6.693 66.263 460.000 1106.852 0.979 1083.055 2.450 442.063 Rata-rata 523.600 2.246 20.002 6.884 65.620 435.000 1046.697 1025.571 2.443 419.891 1 5.82 63.910 63.890 63.330 63.710 1180.800 1187.100 668.200 518.900 2.276 2.429 2.649 2.478 19.375 6.316 67.401 585.000 1407.627 0.994 1399.181 3.720 376.124 2 5.82 63.140 62.200 62.630 62.657 1177.600 1185.200 670.200 515.000 2.287 2.429 2.649 2.478 18.984 5.862 69.120 579.000 1393.190 1.021 1422.447 2.910 488.813 3 5.82 63.560 62.550 62.950 63.020 1172.700 1179.600 667.300 512.300 2.289 2.429 2.649 2.478 18.896 5.760 69.518 582.000 1400.408 1.012 1417.213 3.030 467.727 Rata-rata 515.400 2.284 19.085 5.980 68.679 582.000 1400.408 1412.947 3.220 444.221 1 6.32 61.620 60.940 61.620 61.393 1174.800 1180.200 669.300 510.900 2.299 2.408 2.644 2.460 18.961 4.507 76.230 635.000 1527.937 1.053 1608.918 4.210 382.166 2 6.32 62.530 63.230 62.180 62.647 1169.000 1177.000 663.900 513.100 2.278 2.408 2.644 2.460 19.707 5.386 72.670 505.000 1215.131 1.021 1240.649 4.410 281.326 3 6.32 62.900 63.690 63.430 63.340 1182.700 1191.200 676.100 515.100 2.296 2.408 2.644 2.460 19.081 4.649 75.637 485.000 1167.007 1.048 1222.440 4.550 268.668 Rata-rata 512.000 2.289 19.334 4.946 74.450 541.667 1303.358 1424.783 4.310 331.746 1 6.82 62.270 61.900 61.840 62.003 1176.400 1182.700 675.800 506.900 2.321 2.378 2.627 2.442 18.647 2.407 87.094 499.000 1200.694 1.037 1245.119 4.380 284.274 2 6.82 61.670 62.230 62.390 62.097 1174.200 1180.600 671.700 508.900 2.307 2.378 2.627 2.442 19.118 2.972 84.455 512.000 1231.974 1.035 1275.094 5.250 242.875 3 6.82 61.100 61.600 62.100 61.600 1173.400 1177.200 674.500 502.700 2.334 2.378 2.627 2.442 18.176 1.842 89.865 618.000 1487.032 1.048 1557.666 4.690 332.125 Rata-rata 504.800 2.327 18.412 2.124 88.480 543.000 1306.567 1401.393 4.535 308.199 1 7.32 61.370 62.340 61.790 61.833 1169.500 1173.400 674.400 499.000 2.344 2.393 2.669 2.424 18.284 2.061 88.730 539.000 1296.942 1.042 1351.413 6.030 224.115 2 7.32 59.430 60.540 59.660 59.877 1167.600 1171.400 674.900 496.500 2.352 2.393 2.669 2.424 18.006 1.727 90.406 497.000 1195.881 1.090 1303.511 4.840 269.320 3 7.32 62.220 61.540 61.770 61.843 1172.300 1175.500 678.900 496.600 2.361 2.393 2.669 2.424 17.693 1.352 92.360 680.000 1636.216 1.041 1703.301 5.710 298.301 Rata-rata 496.550 2.356 17.850 1.540 91.383 572.000 1376.346 1503.406 5.275 283.811 No. Sampel % Aspal Terhadap Campuran Tinggi Benda Uji (mm) Berat Benda uji (gr) Isi Benda Uji (ml) Stabilitas Kelelahan (Flow) (mm) Marshall Quotient (Kg/mm) c Bj. Maksimum Campuran (Gmm) Bj. Efektif Agregat (Gse) Bj. Maksimum Teoritis % Rongga Dalam Mineral Agregat (VMA) (%) % Rongga Dalam Campuran (VIM) (%) % Rongga Terisi Aspal (VFA) (%) Berat Isi Benda Uji (Gmb) (gr/mm) 84 B.2 Pengujian karakteristik Marshall Campuran SMA-Tipis Ukur 1Ukur 2Ukur 3 Rata-rata Berat Benda Uji Kering (gr) Berat Benda Uji Jenuh Air (gr) Berat Benda Uji Dalam Air (gr) Pembacaan Arloji Stabilitas (div) Stabilitas dengan kalibrasi alat (kg) Koreksi Benda Uji Stabilitas Dengan Koreksi Benda Uji (Kg) a b d e f g h i j k l m n o p q r s t 1 5.10 65.540 65.970 66.310 65.940 1183.000 1202.800 682.700 520.100 2.275 2.446 2.639 2.505 18.795 7.009 62.709 330.000 794.046 0.944 749.579 2.970 252.384 2 5.10 67.270 66.600 66.390 66.753 1180.100 1203.700 678.600 525.100 2.247 2.446 2.639 2.505 19.765 8.120 58.917 281.000 676.142 0.929 627.854 3.480 180.418 3 5.10 66.980 66.310 66.480 66.590 1179.200 1203.000 678.700 524.300 2.249 2.446 2.639 2.505 19.704 8.050 59.145 286.000 688.173 0.932 641.377 3.050 210.288 Rata-rata 523.167 2.257 19.421 7.726 60.257 299.000 719.454 672.937 3.167 214.363 1 5.60 66.640 66.150 65.800 66.197 1183.100 1202.700 679.300 523.400 2.260 2.443 2.657 2.486 19.725 7.474 62.110 240.000 577.488 0.939 542.261 3.880 139.758 2 5.60 65.660 65.470 64.960 65.363 1187.200 1200.600 681.500 519.100 2.287 2.443 2.657 2.486 18.780 6.384 66.005 280.000 673.736 0.955 643.418 3.360 191.493 3 5.60 64.950 65.340 64.770 65.020 1185.500 1196.800 682.700 514.100 2.306 2.443 2.657 2.486 18.107 5.609 69.023 321.000 772.390 0.962 743.039 3.650 203.572 Rata-rata 518.867 2.284 18.871 6.489 65.713 280.333 674.538 642.906 3.630 178.275 1 6.10 64.880 64.750 64.360 64.663 1177.700 1183.700 673.600 510.100 2.309 2.447 2.685 2.468 18.442 5.649 69.368 342.000 822.920 0.971 799.056 4.580 174.466 2 6.10 65.410 64.710 65.160 65.093 1185.800 1192.100 680.400 511.700 2.317 2.447 2.685 2.468 18.138 5.297 70.795 356.000 856.607 0.960 822.343 4.200 195.796 3 6.10 65.390 64.950 64.770 65.037 1186.600 1192.500 679.500 513.000 2.313 2.447 2.685 2.468 18.291 5.474 70.074 332.000 798.858 0.962 768.502 3.370 228.042 Rata-rata 510.900 2.313 18.290 5.473 70.081 343.333 826.129 810.699 4.390 185.131 1 6.60 62.600 63.200 63.020 62.940 1179.300 1183.100 676.200 506.900 2.326 2.386 2.628 2.450 18.254 2.494 86.337 315.000 757.953 1.014 768.564 5.170 148.658 2 6.60 64.310 64.890 64.650 64.617 1182.300 1186.800 675.400 511.400 2.312 2.386 2.628 2.450 18.767 3.106 83.449 396.000 952.855 0.972 926.175 5.090 181.960 3 6.60 63.860 63.570 64.350 63.927 1177.500 1182.900 675.300 507.600 2.320 2.386 2.628 2.450 18.491 2.777 84.982 340.000 818.108 0.989 809.109 4.890 165.462 Rata-rata 507.250 2.323 18.372 2.635 85.660 350.333 842.972 788.837 5.030 157.060 1 7.10 62.470 62.800 63.070 62.780 1174.500 1177.600 676.600 501.000 2.344 2.351 2.604 2.432 18.069 0.285 98.425 300.000 721.860 1.018 734.853 6.720 109.353 2 7.10 63.560 63.770 63.920 63.750 1175.100 1178.300 674.200 504.100 2.331 2.351 2.604 2.432 18.531 0.847 95.429 304.000 731.485 0.994 727.096 5.960 121.996 3 7.10 63.960 63.720 64.280 63.987 1180.000 1182.800 677.500 505.300 2.335 2.351 2.604 2.432 18.385 0.670 96.355 320.000 769.984 0.988 760.744 6.970 109.146 Rata-rata 504.700 2.333 18.458 0.759 95.892 308.000 741.110 743.920 6.465 115.571 Stabilitas Kelelahan (Flow) (mm) Marshall Quotient (Kg/mm) c Bj. Maksimum Campuran (Gmm) Bj. Efektif Agregat (Gse) Bj. Maksimum Teoritis % Rongga Dalam Mineral Agregat (VMA) (%) % Rongga Dalam Campuran (VIM) (%) % Rongga Terisi Aspal (VFA) (%) Berat Isi Benda Uji (Gmb) (gr/mm) No. Sampel % Aspal Terhadap Campuran Tinggi Benda Uji (mm) Berat Benda uji (gr)Isi Benda Uji (ml) 85 C. 1Hasil Pengujian Modulus Resilien C.1 Hasil Pengujian Modulus Resilien Campuran Ohio suhu 25˚C 86 C.2 Hasil Pengujian Modulus Resilien Campuran Ohio suhu 35˚C 87 C.3 Hasil Pengujian Modulus Resilien Campuran Ohio suhu 45˚C 88 C.4 Hasil Pengujian Modulus Resilien Campuran SMA-Tipis 25˚C 89 C.5 Hasil Pengujian Modulus Resilien Campuran SMA-Tipis 35˚C 90 C.6 Hasil Pengujian Modulus Resilien Campuran SMA-Tipis 45˚C 91 D. 1Penentuan Nilai Modulus Kekakuan Aspal (Sbit) dengan Nomogram Van der Poel 92 E.