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• invariant measure
• Porous Materials
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Clear All  References  ABRAMOFF M.D., MAGALHAES P.J., RAM S.J., Image Processing with ImageJ, Biophotonics International, 2004, 11 (7), 36-42.  GLINICKI M.A., LITOROWICZ A., Diagnostyka rys w kompozytach o matrycy cementowej metodą komputerowej analizy obrazu, Drogi i Mosty, 2007, 3, 45-77.  HUANG H., YE G., QIAN C., SCHLANGEN E., Self-healing in cementitious materials: Materials, methods and service conditions, Materials and Design, 2016, 92, 499-511.  LOWE D.G., Distinctive image features from scale-invariant keypoints, International Journal of Computer Vision

, $${{\sigma }_{1}}=p+q,$$ (8) σ 2 = p − a q , $${{\sigma }_{2}}=p-aq,$$ (9) σ 3 = p − q , $${{\sigma }_{3}}=p-q,$$ (10) where: a = 2 b − 1 ∈ 〈 − 1 , 1 〉 $$a=2b-1\in \left\langle -1,1 \right\rangle$$ (11) is an equivalent measure of principal stress ratio. Introducing equations (8) - (10) into the definitions of invariants the following relations are obtained: I 1 = 3 p − a q , $${{I}_{1}}=3p-aq,$$ (12) J 2 = q 2 3 ( a 2 + 3 ) , $${{J}_{2}}=\frac{{{q}^{2}}}{3}\left( {{a}^{2}}+3 \right),$$ (13) J 3 = 2 a 27 q 3 ( − a 3 + 9 ) . $${{J}_{3}}=\frac{2a}{27}{{q}^{3}}\left tests are shown in Fig. 4 . On the left side, the displacement sensor is visible, which measures the vertical deformations, and on the right side, there is the extensometer that measures the horizontal deformations. It is mounted on steel plates glued to the opposite sides of samples. Figure 4 Compression with extensometer test. The Young modulus was calculated from the below equation: (3.1) E = h ⋅ κ A$$E=\frac{h\cdot \kappa }{A} where, h is the height of the sample, A is the area of horizontal cross-section of the sample and κ is the slope of the curve of

describing volumetric and deviatoric deformations of granular soil as a function of invariants: mean effective stress and deviator stress. The invariant form of the equations makes it possible to extend the model to 3D conditions, see [ 31 , 35 , 36 ]. A verification of this model based on plane strain tests is presented in [ 38 , 42 ]. Although the original model gives good predictions for many complex triaxial tests, its authors suggested the algorithmisation of the model and a clear definition of only one form of equations. In the latest version of the Sawicki and  