| Summary: | To study the mechanical and energy evolution characteristics of sandstone under true triaxial cyclic loading, a sandstone mechanical test with different intermediate principal stress under true triaxial loading was conducted using the rock true triaxial disturbance unloading test system. The influence of axial load on the deformation, energy evolution, and macroscopic failure characteristics of sandstone under different intermediate principal stress in a true triaxial test was systematically analyzed, and the damage evolution law of sandstone under true triaxial cyclic load was revealed. Results showed that the failure mode of sandstone under true triaxial compression changed from tension–shear composite failure to tension failure. Grading cyclic load <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula> greatly influenced maximum principal strain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula> and minimum principal strain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula> but had little influence on intermediate principal strain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>. Under the same <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> condition, the input energy and elastic energy in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula> directions increased nonlinearly. Under different <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> conditions, the dissipated energy in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula> directions decreased with the increase in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>. With the increase in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, graded cycles <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula> decreased considerably, and the failure mode changed from tensile failure to shear failure. When the cyclic loading rate increased, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula>, and volume strain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi>v</mi></mrow></msub></mrow></semantics></math></inline-formula> of sandstone failure decreased, but the expansion point increased. Under true triaxial grading cyclic loading and unloading, the total dissipated energy of sandstone increased exponentially. The larger <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> was, the smaller the damage variable was.
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