Shakedown analysis on the integrity of cement sheath under deep and large-scale multi-section hydraulic fracturing

In the process of deep shale gas exploitation through horizontal drilling and large-scale multi-section hydraulic fracturing, the cement sheath can easily fail due to the high peak pressure and the frequent and violent fluctuations. In this paper, firstly, the deformation characteristics of the cement was studied based on the uniaxial and triaxial compression experiments at different temperature conditions. Then, mechanical model of cement sheath was set up. Based on Melan's shakedown theorem, shakedown load of the cement sheath under the periodic alternating loads is obtained and then converted to the internal pressure of the casing. Results shows that: (1) Compared with that at 25 degrees C, the compression resistance and elastic modulus of cement reduced significantly under 130 degrees C. The cement exhibits obvious plastic flow characteristics and can be regarded as a rational elasticplastic material. (2) During the cyclic loading and unloading process, new plastic strains are continuously generated, the width of hysteresis loops is continuously reduced, and the hysteresis loop becomes denser, which indicates that the accumulation rate of plastic deformation is continuously decreasing. (3) The shakedown load is the smaller of the loading and unloading yield pressures, and reverse yielding tend to occur in the depths. (4) The shakedown load of the cement sheath has a positive linear and non-linear relationship with the cohesive force and the friction angle, respectively. (5) the shakedown load has a positive linear relationship with the external pressure. The external pressure, as the most influence of the calculation result of the shakedown load, accounts for close to 80%. The research could provide valuable theoretical and engineering guidance for the design and construction of shale gas well cement.