## 6 Summary and Conclusions  
Cylindrical test models were developed to investigate the possibility of hydraulic fracturing when the asphalt core in dams had cracks or a large air porosity. The model tests were conducted under restraint and unrestraint conditions at 5 \({}^{\circ}\)C and 20 \({}^{\circ}\)C. Water pressure was applied to the asphalt models in a step loading manner: 0.5 h per step or 2 days per step. The model test results for the asphalt specimens with ring cracks under the unrestraint conditions were back-analysed by applying finite element method. According to the model test results and the numerical back analysis results, the following conclusions are provided:  
* When asphalt concrete with cracks was under vertical restraint conditions, the cracks could experience an \"open-close\" progress with increasing water pressure. This suggested that if the asphalt concrete were long, low water pressure would trigger a fracturing through the cracks.
* When asphalt concrete with cracks was under vertical unrestraint conditions, low water pressure could cause the asphalt concrete to fail. The magnitude of the extensional strains at failure was significantly reduced by the cracked areas (crack depths).
* When the asphalt specimens with a large porosity were under vertical unrestraint conditions, low water pressure could cause the asphalt specimens to fail. The magnitude of the extensional strains at failure was significantly reduced by the large air porosity.
* When asphalt concrete with cracks was under vertical restraint conditions, high tensile stresses in the cracks were caused at 5 \({}^{\circ}\)C, while insignificant tensile stresses were caused at 20 \({}^{\circ}\)C by applying water pressure in the initial phase. When the asphalt specimens were under vertical unrestraint conditions, the extensional strains at failure at 5 \({}^{\circ}\)C were 20-50% smaller than those at 20 \({}^{\circ}\)C.  
On the basis of the discussions and the above conclusions, the following suggestions are provided for the design of an asphalt core in an embankment dam:  
* When an asphalt core embankment dam is located in a narrow valley or a deep narrow trench, the bottom of the asphalt core should be widened and the slopes of the trench should be gentle to avoid having the core be significantly arched by the rockfills.
* If large differential settlements between the upstream and downstream faces of the core are predicted, possibly due to deep compressive foundations, and/or the dam if is located in a very seismic region, the asphalt core should be widened and be more flexible to avoid or reduce cracks or dilations in the faces of the core.
* An asphalt core is a slender impervious wall in a dam, and its construction quality must be ensured. A specialty contractor is preferable for performing the asphalt core job, to rule out a possible weak bond between the layers and to ensure that there is an air porosity larger than 3.0% in the core.  
Conceptualization, W.W.; methodology, W.W.; software, Y.Z. ([PERSON]); validation, Y.Z. ([PERSON]) and S.F.; formal analysis, W.W.; investigation, Y.Z. ([PERSON]) and S.F.; resources, Y.Z. ([PERSON]); data curation, Y.Z. ([PERSON]); writing--original draft preparation, W.W.; writing-review and editing, W.W.; visualization, Y.Z. ([PERSON]); supervision, Y.Z. (YingboZhang); project administration, Y.Z. ([PERSON]); funding acquisition, Y.Z. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
The research work for the paper was supported by the National Natural Science Foundation of China (no. 52039008).  
Not applicable.  
The authors appreciate the assistance of [PERSON] during the experimental work.  
The authors declare no conflict of interest.