## 3 Model Test Results
### Model Test Results under the Unrestraint Conditions  
The model test here was similar to the model test in Section 3.1, except that the top of the specimens was set to be free. The upward displacement at the centre of the specimen top was measured while applying water pressure. The test was run in a step loading creep manner, and the water pressure was increased every 2 days. The model test was actually a short-term extension creep test. The specimens with and without cracks were tested. The extensional strain was calculated on the basis of the measured top displacement of the specimen, and the height of specimen for the calculation was taken to be 120 mm. The test results are shown in Figure 6.  
Figure 6 shows that the asphalt specimens with different crack depths could be fractured in extension by applying a water pressure of 80-200 kPa over a few days at 20 \({}^{\circ}\)C. The water pressure in the crack could cause the local tensile strain in the crack plane of the asphalt specimen to exceed the allowable strain of the asphalt concrete and fracture the asphalt specimen. The extensional strain at failure is defined as the inflection point from the steady creep strain increase to the sharp increase. The extensional strains at failure for the specimens with different crack depths are compared and shown in Figure 7.  
Figure 5: Induced average stress versus water pressure for the asphalt specimen with air porosity of 8.0% in the middle part under the vertical displacement restraint conditions at 5 \({}^{\circ}\)C and 20 \({}^{\circ}\)C, respectively. Figure 6: _Cont._  
Figure 6: Extensional strain vs. time for the specimen with different crack depths at 20 \({}^{\circ}\)C by applying various step creep loadings, step loading every 2 days. (**a**) Water pressure: 100–150–200 kPa; (**b**) Water pressure: 100–120–140 kPa; (**c**) Water pressure: 100–120–140 kPa; (**d**) Water pressure: 60–80–100 kPa; (**e**) Water pressure: 60–80–100 kPa. Figure 7 shows that the area of the crack in the specimen significantly reduced the extensional strain at failure. When the percentage of the crack area was 19%, 36%, and 64%, respectively, the extensional strains at failure were reduced by about 20%, 50%, and 60%, respectively, compared with that of the specimens without cracks. The extensional strain at failure (dark spots in Figure 7) was reduced by about 30%, though the semicircle cracked area was 50%. That was smaller than the estimated extensional strain at failure of about 55% for the specimen with ring cracks. The specimen with a semicircle crack underwent bending because the bending strain at failure was larger than the tensile strain at failure for the asphalt concrete [12]. The model test results for the specimens with different air porosities are shown in Figure 8.  
Figure 8: _Cont._  
Figure 7: Extensional strain at fracture vs. percentage of area of crack in the specimen by applying water pressure at 20 \({}^{\circ}\)C.  
Figure 8 shows that the asphalt specimens with different air porosities could be fractured in extension by applying various water pressures over a few days at 5 \({}^{\circ}\)C and 20 \({}^{\circ}\)C. The extensional strains at failure for the specimens with different air porosities in the middle part of the specimens are compared and shown in Figure 9.  
Figure 8: Extensional strain vs. time for the specimens with different air porosities in the middle part of the specimens at 5 \({}^{\circ}\)C and at 20 \({}^{\circ}\)C by applying various step creep loading, step loading every 2 days. (a) 5 \({}^{\circ}\)C, water pressure: 160–180–200–220–240 kPa; (b) 20 \({}^{\circ}\)C, water pressure: 60–80–100–120–140–160 kPa; (c) 20 \({}^{\circ}\)C, water pressure: 60–80–100–120–140–160 kPa. Figure 9 shows that the large air porosity in the middle layer of the specimen significantly reduced the extensional strain at failure. When the air porosity was 5.0%, the extensional strain at failure was reduced by about 30% at 5 \({}^{\circ}\)C when compared with that of the specimens with an air porosity of 1.0%.