Table 4 Fitting equation for the strain energy density of rock under true triaxial compression.

From: Calculation method and evolution rule of the strain energy density of sandstone under true triaxial compression

Stress direction

Type

Fitting equation

Adj. R-square

σ1

ue

\(u_{1}^{e}\) = 0.53734u1-0.006010

0.99970

ud

\(u_{1}^{d}\) = 0.46266u1 + 0.00601

0.99959

σ2

ue

\(u_{2}^{e}\) = 1.97983u2-0.151430

0.99909

ud

\(u_{2}^{d}\) = -0.97983u2 + 0.15143

0.99630

σ3

ue

\(u_{3}^{e}\) = 2.17328u3-0.11290

0.99960

ud

\(u_{3}^{d}\) = -1.16561u3 + 0.11236

0.99719

Entirety

ue

ue = 0.515200u + 0.00279

0.99952

ud

ud = 0.48476u-0.0028

0.99946