## 3 Results and Discussion
### DVC Analysis  
#### 3.2.1 Three-Dimensional Strain Field  
Six volumetric strain components (three principal strain components, \(\varepsilon_{\text{xx}}\), \(\varepsilon_{\text{yy}}\), and \(\varepsilon_{\text{zz}}\), and three shear strain components, \(\varepsilon_{\text{xy}}\), \(\varepsilon_{\text{xz}}\), and \(\varepsilon_{\text{yz}}\)) were calculated based on displacement fields. Strain fields under 30 MPa are exhibited in Figure 9. The strain values of \(\varepsilon_{\text{xx}}\) and \(\varepsilon_{\text{yy}}\) along the X- and Y-directions are positive (Figure 9a,b), indicating that the mortar expanded and produced a tensile strain in these directions. It should be noted that the values of \(\varepsilon_{\text{xx}}\) and \(\varepsilon_{\text{yy}}\) greatly differ from each other, and the strain along the X-direction is about 3-4 times that in the Y-direction. An eccentric compression occurred during in situ loading, and the heterogeneous internal structure of the mortar caused different responses to stress. The values of \(\varepsilon_{\text{zz}}\) along the loading direction (Z-direction) are all negative (Figure 9c), indicating that the mortar produced compressive strain in this direction. Moreover, the color gradient changes greatly, implying that the eccentric compression occurred during loading.  
Figure 10 presents the strain fields under 50 MPa; the values of the three principal strain components are all higher than 30 MPa. The values of \(\varepsilon_{\text{xx}}\) and \(\varepsilon_{\text{yy}}\) greatly increase, and the strain distribution is more uneven (Figure 10a,b). The difference between strain values along the X- and Y-directions decreases, and the strain in the X-direction is about twice that in the Y-direction. It might happen because, with the increased load, pores in the cement matrix were compacted, improving the stability of the internal structure. The red area of component \(\varepsilon_{\text{zz}}\) in the strain map expands observabl  
Figure 8: Analysis diagram of average crack widths under different loads: (**a**) 2D crack distribution under 3600 N; (**b**) 2D fracture distribution under 5000 N; (**c**) average crack widths under different loads.  
accounts for about two-thirds of the mortar volume and became darker, indicating the increase in the strain.  
The sections along the \(z\)-axis were selected, and the strain distributions at different sections were analyzed according to the three principal strain components \(\varepsilon_{\mathrm{xx}}\), \(\varepsilon_{\mathrm{yy}}\), and \(\varepsilon_{\mathrm{zz}}\), as shown in Figure 11. The strain components \(\varepsilon_{\mathrm{xx}}\) and \(\varepsilon_{\mathrm{yy}}\) under different stresses are mainly positive, indicating that the specimen expands and produces tensile strain in both X- and Y-directions. The strain distribution curves of \(\varepsilon_{\mathrm{xx}}\) and \(\varepsilon_{\mathrm{yy}}\) do not coincide, and with the increase in stress, the distance between the two curves became further and further. The curves of \(\varepsilon_{\mathrm{xx}}\) and \(\varepsilon_{\mathrm{yy}}\) are close to the horizontal line under 30 MPa, indicating that the strain develops evenly along two directions. When the stress increases to 50 MPa, the curve along the X-direction shows an obvious fluctuation, and the strain develops unevenly. The values of \(\varepsilon_{\mathrm{zz}}\) along the loading direction are all negative, indicating that the specimen produces compressive strain in this direction. It can be seen from the figure that the \(\varepsilon_{\mathrm{zz}}\) curves under different stresses are not tending to a horizontal line, and the deformation of each section is not consistent. With the increase in stress, the strain heterogeneity becomes more obvious, which further indicates that the stress distribution is not uniform and that eccentric compression occurred in the loading process.  
Figure 11: Strain distribution of different section position.