## 3 Experimental Results and Analysis  
### Mercury Pressure Test and Analysis of Results  
The basic principle of the mercury pressure test involves assuming a cylindrical pore of radius r. Mercury is pressed into the pore by pressure, and when equilibrium is reached, the pressure \(P\cdot\uppi^{2}\) acting in the direction normal to the mercury contact ring cross-section is equivalently reversed with the component \(2\uppi^{2}\cdot\cos\alpha\) of the tension on the same cross-section normal to that surface, i.e., we have:  
\[P\cdot\uppi^{2}=-2\uppi R^{2}-\upalpha\cos\alpha \tag{1}\]  
The above equation yields:  
\[p=-\frac{2\upsigma\cos\alpha}{r} \tag{2}\]  
where \(p\) is the required pressure; \(r\) is the pore radius; \(\sigma\) is the surface tension coefficient of mercury; \(\alpha\) is the infiltration angle of mercury on the material. The mercury pressure test is one of the most commonly used methods for conducting tests, such as for studying soil microstructure. The mercury intake versus pore distribution curve and cumulative mercury intake curve can be obtained, and microstructure pore distribution can be visualized through images. Because of metallic mercury's inability to enter closed pores, part of the fine pores can be easily overlooked. The results of the mercury pressure test on red clay contaminated with different concentrations of Pb\({}^{2+}\) in soil samples contaminated for five days are plotted in Figures 1 and 2. As can be seen in Figure 1a, the pore distribution of the red clay soil that was not contaminated with Pb\({}^{2+}\) consisted of two peaks: the first peak area occurred at 0.01 \(\upmu\)m\(-\)0.1 \(\upmu\)m, and the second peak area occurred at 4 \(\upmu\)m\(-\)20 \(\upmu\)m. The pores in the 0.01 \(\upmu\)m\(-\)0.1 \(\upmu\)m region did not considerably change as the Pb\({}^{2+}\) concentration in the soil rose, whereas the pores in the 4 \(\upmu\)m\(-\)20 \(\upmu\)m region dramatically changed as the Pb concentration in the soil rose. The magnified image in the range of 0.1 \(\upmu\)m to 100 \(\upmu\)m is a cut-off of Figure 1b from Figure 1a. The number of pores within the range of 0.2 \(\upmu\)m\(-\)4 \(\upmu\)m decreased as the heavy metal (Pb\({}^{2+}\)) concentration inside the red clay grew, whereas the number of pores within the range of 4 \(\upmu\)m\(-\)20 \(\upmu\)m accordingly increased. This demonstrated that the heavy metal Pb\({}^{2+}\) had a significant impact on the microstructure of the red clay, and that the complex physical and chemical properties of red clay cause the cementation of the soil to be eroded between the particles, and increased agglomeration and particle clusters, resulting in a smaller and gradually disappearing cementation structure between the particles. Therefore, the original small pores gradually enlarged into larger pores, and there was a significant increase in pores in the region of 4-20 \(\upmu\)m, which also indicated that the microstructure was limited by the influence of heavy metal ions, and heavy metal ions were incapable of eroding the finer pore structure. Figure 2 depicts the relationship between the pore size of red clay and the accumulated mercury input volume for various concentrations of Pb\({}^{2+}\), which was mercury pressed into a long strip of the soil sample with external pressure. The accumulated mercury input volume corresponds to the unit horizontal coordinate in the figure, which is expressed as the incremental magnitude. With the increase of mercury injection pressure, the content of metal mercury in soil increases, which is consistent with this phenomenon. As shown in the figure, the initial stage occurred when the pore space (100-1000 \(\upmu\)m) was large, and the volume of mercury in the soil contaminated with different concentrations of heavy metals was the same; during the rising stage, the increase in pressure in the pore space distribution  
Figure 1: Pore distribution of Guilin red clay under the effect of different Pb\({}^{2}\)concentrations.