*3.2. Curve Normalization*

Due to the contingency and error in the unconfined compressive test, based on the research results of Long Hongbo et al. [34], the deviation between the peak points of different stress–strain curves was taken as the research object, and an improved weighted average method was proposed to optimize the curves of five repeated tests by using the weight of each peak point. The detailed calculation steps are as follows:

(1) Determining the standard value. First, the peak point is mean processed to obtain a set of standard values, as shown in Formula (1). *N* represents the number of tests, in this test, *N* = 5; *i* ∈ [1, *N*] is the peak stress of each curve; *q*<sup>−</sup> is the mean stress.

$$q^{-} = \frac{1}{N} \sum\_{i=1}^{N} q\_i \tag{1}$$

(2) Determining the deviation. The peak stress of each peak point is subtracted from the standard stress, and its absolute value is deviation *pi*, as shown in Formula (2).

$$p\_i = |q\_i - q^-| \tag{2}$$

(3) Determining the degree of deviation. The variance *M* is introduced to describe the degree of deviation between each peak stress and the standard stress, as shown in Formula (3).

$$M = \frac{1}{N} \sum\_{i=1}^{N} \left( q\_i - q^{-} \right)^2 \tag{3}$$

(4) Selecting the weighted weight. In order to determine the weight of each peak stress, each deviation value is divided by the variance *M*, respectively, to obtain the weighted weight *W* of each peak stress, as shown in Formula (4).

$$\mathcal{W} = \frac{p\_i}{\mathcal{M}}\tag{4}$$

(5) Determining the weight function. The weighted weight *W* of each peak stress and standard stress can be obtained from Formula (4). However, this weight does not conform to the traditional weighting law, which needs to be transformed to a certain extent. Combined with the above analysis, the use of a weight function to transform the initial weight is proposed, as shown in Formula (5).

$$C(\mathbf{x}) = \frac{1}{2}\cos^N(\pi\mathbf{x} + 1)\tag{5}$$

where *x* is the independent variable and *C*(*x*) is the dependent variable; *N* can be valued according to the actual situation, and its function is to improve the accuracy of the calculation results; in this test, *N* = 5.

**Figure 7.** Stress–strain curves of TCS with different iron tailing contents. (**a**) STCS-0-0; (**b**) STCS-0-10; (**c**) STCS-0-20; (**d**) STCS-0-30; (**e**) STCS-0-40.

1. Determining the weight. In order to determine whether Formula (5) is feasible, Formula (4) is substituted into the weight function *G*(*x*) to obtain the final weight *R*, as shown in Formula (6).

$$R = \mathbb{C}(W) = \frac{1}{2}\cos^N(\pi W + 1) \tag{6}$$

2. Determining the weighting factor. In order to obtain the weighting factor of each peak stress, the weights obtained from Formula (6) are divided by the weight sums, as shown in Formula (7).

$$Y\_i = \frac{R}{\sum\_{i=1}^{N} R} \tag{7}$$

3. Determining the weighted stress. Each weighting factor obtained in Formula (7) is multiplied by the corresponding peak stress, and the value of each peak stress in the weighted stress can be obtained. The final weighted peak stress *qm* can be obtained by adding them together, as shown in Formula (8).

$$q\_{\rm int} = \sum\_{i=1}^{N} q\_i \mathcal{Y}\_i \tag{8}$$

It can be seen from above that there were five stress–strain curves for each group of samples, the peak points of the five curves of STCS-0-0 were taken as reference to perform a weighted average, and the obtained specific gravity was multiplied by the standard curve to obtain the q-ε representative curve of the test. In order to verify the applicability of this method, the calculation results were compared with the original curve, and the comparison results are shown in Figure 8. The results show that the representative q-ε curve obtained by the new method has a good correlation with the original q-ε curve.

**Figure 8.** q-ε curve of STCS-0-0.

#### *3.3. Peak Strength and Peak Strain Analysis*

The peak strength is the maximum stress value on the stress–strain curve of the unconfined compressive test of the soil. The peak strain is the strain corresponding to the peak strength. According to the method in Section 3.2, the peak strength and peak strain of various types of cemented soil are summarized in Table 6. Table 6 shows that the peak strengths of STCS-0-0, STCS-0-10, and STCS-0-20 were 955kPa, 986kPa, and 1080kPa, respectively. When the iron tailing content was 10% and 20%, the peak strength of TCS was 3% and 13% higher than that of CS, respectively. When the iron tailing content continued to increase, the unconfined compressive strength of TCS began to decrease, and the iron tailings began to show a deterioration effect, which gradually increased with the increase in the iron tailing content. It can be found from Hou Rui's research that when the iron

tailing content was less than 25%, iron tailings had a certain improvement effect on the compressive strength of CS, which was consistent with the results in this paper [35].


**Table 6.** Peak strength and peak strain of each group of TCS.

The peak strain of TCS with different iron tailing contents fluctuated between 1.303 and 1.379. When the iron tailing content was 20%, the peak strain increased the most, but only by 2%. The addition of iron tailings had little effect on the peak strain of CS.

Iron tailings can be categorized as a high-silicon type ultra-fine tailing sand. Their particle size is larger than that of clay particles, and thus, they act as a coarse aggregate in soil. The addition of iron tailings in small quantities can improve the gradation of soil particles and reduce the internal pores of the soil. Under the action of cementitious substances formed by cement hydration and consolidation, iron tailings and soil particles clump together to form a whole structure, so as to improve the soil's compressive strength. With the increase in the iron tailing content, the proportion of iron tailings in the composite cemented soil increases, the properties of the composite material begin to approach the sand soil, the internal structure of the soil begins to loosen, the cohesion between particles decreases, and the compressive strength of the soil decreases.

#### *3.4. Residual Strength Analysis*

According to "GBT 50123-2019", the sample is defined as damaged when the strain reaches the peak strain in the unconfined compressive stage, and the stress measured at 5% strain, after the selection of the peak strain, is selected as the residual strength. The residual strength of TCS is summarized in Table 7.


**Table 7.** Residual strength of each group of TCS.

It can be seen from Table 7 that iron tailings have a greater impact on the residual strength of TCS. When the iron tailing content is 20%, the residual strength of TCS reaches its peak, which is increased by 60% compared with that of CS. When the iron tailing content continues to increase, the residual strength of TCS begins to decrease, and its mechanism of action is similar to the peak strength.

#### *3.5. Elastic Modulus Analysis*

The elastic moduli of TCS are summarized in Figure 9.

**Figure 9.** Elastic moduli of TCS.

It can be seen from Figure 9 that after adding 10%, 20%, 30%, and 40% iron tailings, the elastic modulus of TCS increased by 14%, 35%, 24%, and 6%, respectively. When the iron tailing content was 20%, the elastic modulus increased the most.

#### **4. Unconfined Compressive Test Analysis of STCS**

#### *4.1. Stress–Strain Curve Analysis*

Under the condition that the optimal iron tailing content was 20%, 0.5%, 1.5%, and 2.5% quantities nano silica content were added to modify TCS. The stress–strain curves of STCS with different nano silica contents are summarized in Figure 10, which are all softening curves.

**Figure 10.** Stress–strain curve of STCS. (**a**) STCS-0.5-20; (**b**) STCS-1.5-20; (**c**) STCS-2.5-20.

#### *4.2. Peak Strength and Peak Strain Analysis*

The peak strength and peak strain of STCS are summarized in Figures 11 and 12.

**Figure 11.** Peak strength of STCS.

**Figure 12.** Peak strain of STCS.

It can be seen from Figure 11 that after adding 0.5%, 1.5%, and 2.5% nano silica, the compressive strength of TCS increased by 24%, 137%, and 323%, respectively, which significantly enhanced the compressive strength of TCS.

The peak strain represents the strain variable when the sample reaches the peak stress. The larger the peak strain is, the later the sample reaches failure, which is of great significance in engineering applications. It can be seen from Figure 12 that nano silica increased the peak strain of TCS, but with the increase in the nano silica content, the increment gradually decreased. When the nano silica content was 0.5%, the peak strain of TCS increased by 15%, which indicates that nano silica can help to delay the time of sample failure, but the effect is limited. Because with the increase in nano silica content, the brittleness of the material was also increasing, the increment of peak strain of TCS began to decrease.

#### *4.3. Residual Strength Analysis*

The residual strength of STCS is summarized in Table 8.

**Table 8.** Residual strength of each group of STCS.


Table 8 shows that the addition of nano silica effectively improves the residual strength of TCS. When the nano silica content was 0.5%, the residual strength increased by 20kPa; when the nano silica content was 1.5%, the residual strength increased by 142kPa; but when the nano silica content reached 2.5%, the residual strength increased by only 42kPa. The increment of the residual strength of TCS by adding nano silica shows a trend of first increasing and then decreasing, and of reaching the maximum when the nano silica content is 1.5%, which is consistent with the increasing of the peak strength of STCS.

#### *4.4. Elastic Modulus Analysis*

The elastic modulus of STCS are summarized in Figure 13.

**Figure 13.** Elastic modulus of STCS.

It can be seen from Figure 13 that after adding 0.5%, 1.5%, and 2.5% nano silica, the elastic modulus of STCS increased by 1%, 106% and 183%, respectively. which significantly enhanced the elastic modulus of TCS.

#### **5. Microscopic Mechanism Analysis**

#### *5.1. SEM Test Analysis*

In order to better analyze the strength growth mechanism of STCS, the microscopic morphology of various cement soils was observed by SEM. Four groups of unconfined samples of STCS-0-0, STCS-0-20, STCS-0-40, and STCS-2.5-20 were selected for microscopic testing. Via SEM scanning with an electron microscope, four groups of microstructure photos of STCS were obtained at 5000 times magnification, as shown in Figure 14.

**Figure 14.** SEM images of different types of STCS. (**a**) STCS-0-0; (**b**) STCS-0-20; (**c**) STCS-0-40; (**d**) STCS-2.5-20.

Figure 14 shows that a large amount of hydration products were produced in each group of samples, including a relatively large amount of flocculated colloid C-S-H, which has strong adsorption capacity. The internal particles of CS are of different sizes and there are many pores. When 20% iron tailings was added, it can be seen from the microscopic image that there were particles of different sizes in the composite cemented soil, forming a good gradation. Some iron tailings particles filled the large particles in the soil, and a large amount of flocculated colloid C-S-H was adsorbed on the soil particles, forming a stable whole structure with iron tailings. The composite cemented soil mixed with 40% iron tailing content was mostly composed of medium and small units, and the gaps between the particles were large and not well filled.

The characteristics of nanomaterials effectively played their role in the improvement of TCS with 2.5% nano silica content. It can be seen from the microscopic pictures of STCS-2.5-20 that the structure was very compact, and the nano silica adequately filled the pores of the composite cemented soil.

#### *5.2. SEM Image Processing*

The basic properties of CS depend largely on its particle bonding characteristics at the microscopic level, and the macro-mechanical performance of CS largely depends on the pore size at the microscopic level. In order to quantitatively evaluate the relationship between the compressive strength of CS and the size of microscopic pores, the SEM image obtained at 5000 times magnification was binarized to obtain the quantitative pore size of relevant samples, as shown in Table 9.

**Table 9.** Porosities of different STCS.


Table 9 shows that the porosity of the four types of STCS samples, from high to low, was STCS-0-40 > STCS-0-0 > STCS-0-20 > STCS-2.5-20. This is consistent with the order of the unconfined compressive strength of each group of STCS samples.

Compared with STCS-0-0, the porosity of STCS-0-20 was reduced by 32%, which shows that the compressive strength of STCS with 20% iron tailing content was improved compared with that of CS. The porosity of STCS-0-40 was higher than that of STCS-0-0, which was because the particle size of iron tailings was larger than that of clay particles; the proportion of fine particles in the mixture decreased due to the increasing of the iron tailing content, which was not enough to fill the pores between the cement and the soil. As a result, the fine aggregate particle gradation became worse after the iron tailing content exceeded 20%. Compared with STCS-0-20, the porosity of STCS-2.5-20 was reduced by 56%. It can be seen that the internal pores of STCS were very small and the structure was compact. Therefore, the unconfined compressive strength of STCS with 2.5% nano silica content reached more than three times that of TCS.

#### **6. Conclusions**

The mechanical properties and micro mechanism of TCS and STCs at 7d curing age were studied by unconfined compressive strength test and SEM test. The following conclusions can be drawn.

(1) With the increase in the content of iron tailings, the unconfined compressive strength, peak strain, residual strength, and elastic modulus of TCS first increased and then decreased. The optimal content of iron tailings was 20%.

(2) Nano silica could significantly modify the unconfined compressive strength and elastic modulus of TCS. The unconfined compressive strength of STCS increased with the increasing of the nano silica content. Compared with STCS-0-20, the unconfined compressive strength of STCS-0.5-20, STCS-1.5-20, and STCS-2.5-20 was increased by 24%, 137%, and 323% respectively. At the same time, the addition of nano silica effectively improved the peak strain and residual strength of the TCS. With the increasing of the nano silica content, the peak strain, residual strength and elastic modulus first increased and then decreased.

(3) Analysis of SEM pictures showed that the flocculation colloid C-S-H generated by cement hydration and the porosity of the samples were the main factors affecting the strength of TCS and STCS. An appropriate amount of iron tailings can fill the pores in TCS. With the increase of iron tailings, the porosity of TCS increased, resulting in the decreasing of the strength. In addition, on the one hand, nano silica can promote the hydration reaction of cement and improve the cementation of particles in STCS. On the other hand, nano silica can fill the pores between particles and improve the compactness of STCS.

The above conclusions are based on the test data of 7d curing age. The strength of TCS and STCs will gradually increase with the curing age, and final strength of the composite may be achieved after 2–3 months.

**Author Contributions:** Conceptualization, X.S. and H.X.; investigation, D.Z. and K.Y.; formal analysis, F.T. and P.J.; writing—review and editing, W.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant number 41772311, and the Shandong Provincial Natural Science Foundation, grant number ZR202102240826.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** This authors thank Linxia Wang from the Micro Testing Center of Shaoxing University for her help in the process of micro testing.

**Conflicts of Interest:** The authors declare no conflict of interest.
