*2.1. Materials*

The materials used throughout the experimental tests include subgrade soil, water, cement and nano-MgO. The subgrade soil was collected from a coastal area in Shaoxing city of Zhejiang province, China. The main physical and mechanical indexes are shown in Table 1. Guyue brand P.C 42.5 composite Portland cement produced by Shaoxing Keqiao Third Cement Co., Ltd. (Shaoxing City, China) was used as shown in Figure 1a, and the main physical and mechanical parameters are shown in Table 2. The nano-MgO was a 50 nm spherical MgO produced by Shanghai Macklin Biochemical Technology Co., Ltd (Shanghai City, China). The appearance was white to light yellow powder, as shown in Figure 1b, and its physical and mechanical properties are shown in Table 3.

**Table 1.** The physical indexes of subgrade soil in coastal area of Shaoxing.


**Figure 1.** Physical picture of cement and nano MgO. (**a**) Composite Portland cement; (**b**) nano-MgO.



**Table 3.** The physical and mechanical parameters of nano MgO.

#### *2.2. Test Program*

The samples were divided into 25 groups according to different nano-MgO contents and carbonization times, and the mix proportion of each group of materials is shown in Table 4. MCS represents nano-MgO-modified cement soil. Unconfined compressive strength tests were carried out on 25 groups of MCS. In order to reduce the random error and the discreteness of the test data in the test process, five repeated tests were performed on each group of samples.



*2.3. Sample Preparation*


the mixture was poured, it was vibrated. The sample was left to stand for 2 h after completion, and the upper and lower surfaces of the samples were flattened with a scraper, wrapped with filter paper and placed into water for curing.

(5) Sample curing. The moisture content of the sample was high, so it was difficult to form; therefore, it needed to soak in water for 3 days before demolding. Then, it was placed into a standard curing box or carbonization curing box to continue curing. The curing methods and conditions are shown in Figure 2 and Table 5, and the soaking and carbonization curing are shown in Figure 3a,b, respectively.

**Figure 2.** The relationship between carbonation time and curing age.

**Table 5.** The maintenance conditions.


**Figure 3.** Maintenance method. (**a**) Immersion curing; (**b**) carbonization curing.

#### *2.4. Mechanical Test*

TKA-WXY-1F automatic unconfined pressure gauge produced by Nanjing TKA Technology Co., Ltd. was used in the unconfined compressive strength test. The loading rate was set to 1 mm/min during the test. According to the GB/T 50123-2019 Geotechnical Test Standard, when the axial force reaches its peak value, the test can be stopped by performing another 3–5% axial strain value. In this paper, the test was stopped when the axial strain of uncarburized MCS reached 10%. The test was stopped when the axial strain of carburized MCS reached 12%.

#### **3. Unconfined Data Analysis**

#### *3.1. Stress–strain Curve Analysis*

The stress–strain curves of MCS with different nano-MgO contents and carbonization times are shown in Figures 4–8. It can be seen from the figures that the stress–strain curves of MCS are all softening curves. At the initial stage of loading, the stress of MCS increases linearly with the increase in strain. As the strain continued to increase, the upward trend of stress gradually slowed down, and finally, the stress reaches the peak value. At this point, the strain corresponding to the peak stress is the peak strain of the sample. When the peak strain occurs, the sample will be destroyed and inclined cracks will appear, and the force on the sensor will drop sharply, so the stress attenuation rate will increase. With the increase in strain, the sample will be compressed, and the friction force will be generated at the inclined cracks, so the stress attenuation rate will decrease. With the continuous increase in strain, the sample will be further compressed, and the force on the sensor will not change.

**Figure 4.** The stress–strain curve of MCS with 0% nano-MgO content. (**a**) Carbonization 0 d; (**b**) carbonization 6 h; (**c**) carbonization 1 d; (**d**) carbonization 2 d; (**e**) carbonization 4 d.

**Figure 5.** The stress–strain curve of MCS with 0.5% nano-MgO content. (**a**) Carbonization 0 d; (**b**) carbonization 6 h; (**c**) carbonization 1 d; (**d**) carbonization 2 d; (**e**) carbonization 4 d.

**Figure 6.** The stress–strain curve of MCS with 1.0% nano-MgO content. (**a**) Carbonization 0 d; (**b**) carbonization 6 h; (**c**) carbonization 1 d; (**d**) carbonization 2 d; (**e**) carbonization 4 d.

**Figure 7.** The stress–strain curve of MCS with 1.5% nano-MgO content. (**a**) Carbonization 0 d; (**b**) carbonization 6 h; (**c**) carbonization 1 d; (**d**) carbonization 2 d; (**e**) carbonization 4 d.

**Figure 8.** The stress–strain curve of MCS with 2.0% nano-MgO content. (**a**) Carbonization 0 d; (**b**) carbonization 6 h; (**c**) carbonization 1 d; (**d**) carbonization 2 d; (**e**) carbonization 4 d.

#### *3.2. Curve Normalization*

During the test, five repeated tests were conducted for all the tests designed in Table 4 to reduce the test error. The results of five repeated samples are different, so obtaining a reasonable standard value from these five results is particularly critical. In this paper, the deviation of five peak stresses were taken as the research object, and the weight of each peak stress was calculated. Then, the weight of each peak stress was taken as the weight of this curve, and the five curves were further normalized to one curve. The normalization method is as follows:

1. Determination of the average value of peak stress? σ*i*.

$$\overline{\sigma} = \frac{1}{N} \sum\_{i \in \{1, N\}} \sigma\_i \tag{1}$$

where *σi* is the peak stress of each stress–strain curve of the sample, and *N* is the number of repeated tests in this group of samples. In this study, there were five repeated tests in each group, so *N* = 5, and *i* is the serial number of the data in the sample.

2. Determination of the deviation Δ*σi* of each peak stress.

$$
\Delta \sigma\_{\bar{l}} = |\sigma\_{\bar{l}} - \overline{\sigma}| \tag{2}
$$

3. Determination of the variance *S* of the peak stress.

$$s = \frac{1}{N} \sum\_{i \in \{1, N\}} \Delta \sigma\_i^2 \tag{3}$$

4. Determination of the initial weight *pi* of each peak stress. In order to ensure that the initial weight is between [0,1], the maximum value Δ*σimax* of peak stress deviation is introduced to calculate the initial weight of each peak stress.

$$p\_i = \frac{\Delta \sigma\_i}{\Delta \sigma\_i \text{max} + S} \tag{4}$$

5. Determination of the weight mapping function *f*(*x*). In the above equations, the greater the deviation of the peak value is, the greater the weight of the peak stress is. Therefore, it is necessary to assign the weight of peak stress, so that the larger the deviation of the peak stress is, the smaller the weight after assignment is. The mapping function is shown in Equation (5). As the function decreases monotonously, the greater the Δ*σi* is, the smaller the weight after conversion is.

$$f(x) = \frac{2}{\pi} \times \arccos(x) \tag{5}$$

6. Determination of the converted weight *mi* of each peak stress.

$$m\_i = f(p\_i) \tag{6}$$

7. Determination of the weighting factor *ni* of each peak stress.

$$m\_i = \frac{m\_i}{\sum\_{i \in \left[1, N\right]}}\tag{7}$$

8. Determination of the standard value *σ* of peak stress.

$$\sigma = \sum\_{i \in \{1, N\}} \sigma\_i \times n\_i \tag{8}$$

Five curves of MCS with 1.0% nano-MgO after 6 h carbonization were taken as examples and weighted by the above methods. Five test curves and the weighted curves are shown in Figure 9. It can be seen from the figure that the normalized curve has a good correlation with the original five test curves.

Five stress–strain curves of MCS with different nano MgO contents and carbonization times were normalized by the above method. The normalized curve is shown in Figure 10.

**Figure 9.** Weighted curve of MCS with 1.0% nano-MgO content after 6 h carbonization.

 **Figure 10.** The Normalized stress–strain curves of MCS. (**a**) Carbonization 0 d; (**b**) carbonization 6 h; (**c**) carbonization 1 d; (**d**) carbonization 2 d; (**e**) carbonization 4 d.

## **4. Discussion**

#### *4.1. The Influence of Nano-MgO Content*

The maximum value of the normalization curve of each group of samples is taken as the peak stress of each group of samples. The compressive strength of MCS with different nano-MgO contents is shown in Figure 11. It can be seen from the figure that under the same carbonization time, the compressive strength of MCS increases first and then decreases with the increase in nano-MgO content. When the nano-MgO content is 1.0%, the compressive strength of MCS reaches the maximum. When the carbonization time is 0 h, 6 h, 1 d, 2 d and 4 d, the compressive strength is 440.69 Pa, 547.33 kPa, 818.25 kPa, 724.10 kPa and 489.18 kPa, respectively, which is 23.3%, 13.3%, 50.2%, 41.5% and 15.1% higher than that of cement soil without nano-MgO.

**Figure 11.** The influence of different nano-MgO contents on the compressive strength of MCS.

This is mainly because when the nano-MgO content is between 0% and 1.0%, cement and nano-MgO generate carbonate precipitation after hydration and carbonization, and the volume increases and gradually fills the pores inside MCS. As a result, the internal structure of the soil is denser. However, with the increase in nano-MgO content, the reaction generates excessive carbonate precipitation, and the volume expansion exceeds the volume of the pores inside MCS [25,36], which gradually compresses the surrounding soil, resulting in the failure of cementation between soil particles. Microcracks appear inside MCS, and the compressive strength decreases.

#### *4.2. The Influence of Carbonization Time*

The influence of different carbonization times on the compressive strength of MCS is shown in Figure 12. It can be seen from the figure that the compressive strength of MCS with the same nano-MgO content increases first and then decreases with the increase in carbonization time, so there is an optimal carbonization time. Under the five nano-MgO contents, the optimal carbonization time is 1 d. At this time, the compressive strength of MCS is 544.92 kPa, 579.36 kPa, 818.25 kPa, 497.55 kPa and 470.92 kPa, respectively, which is 52.5%, 40.5%, 85.7%, 29.5% and 38.8% higher than that of non-carbonized MCS. When the carbonization time is 4 d, the compressive strength of MCS under five nano-MgO contents is 425.01 kPa, 465.68 kPa, 489.18 kPa, 461.74 kPa and 397.26 kPa, respectively, which is still 18.9%, 12.9%, 11.0%, 20.2% and 17.08% higher than that of non-carbonized MCS.

**Figure 12.** The influence of carbonization time on the compressive strength of MCS.

The mechanism of action is similar to the influence of nano-MgO content. When the carbonization time is short, the carbonate precipitation formed by carbonization can fill the internal pores. However, as the carbonization time increases, excessive carbonate precipitation causes cracks inside MCS, leading to a decrease in the compressive strength.

#### **5. Ductility and Energy Dissipation Analysis**

#### *5.1. Curve Simplification*

According to the change trend of the normalized stress–strain curve, the stress–strain curve of MCS can be divided into four stages, as shown in Figure 13:


**Figure 13.** The change trend of stress–strain curve.

**Figure 14.** Failure mode. (**a**) OA section; (**b**) AB section; (**c**) BC section; (**d**) CD section.

#### *5.2. Ductility Analysis*

The strain at point B of the normalized curve of each group of samples was taken as the peak strain of the group. The influence of different carbonization times on the peak strain of MCS is shown in Figure 15. It can be seen from the figure that when the nano-MgO content is 0 and 0.5%, the peak strain of MCS increases with the increase in carbonization time. However, when the carbonization time increases from 0 to 2 d, the peak strain of MCS increases significantly, and the difference between the peak strain of MCS and the non-carbonized MCS is 3.8% and 3.0%, respectively; when the carbonization time increases from 2 d to 4 d, the peak strain increases by 0.1% and 0.6%, respectively. Therefore, the effect of 2 d carbonization on the peak strain of MCS is more obvious, which can significantly increase the ductility of MCS.

When the nano-MgO content is 1.0%, 1.5% and 2.0%, the peak strain of MCS first increases and then decreases with the increase in carbonization time. When the carbonization time is 2 d, the peak strain reaches the maximum, which is 6.5%, 6.2% and 6.7%, respectively, and the difference between the peak strain of MCS and non-carbonized MCS is 4.6%, 4.2% and 4.4%, respectively.

When the carbonization time is 0 h, 6 h, 1 d, 2 d and 4 d, the difference between the maximum and minimum peak strains of MCS with different nano-MgO contents is 1.2%, 1.3%, 0.7%, 0.6% and 1.1%, respectively. It can be found that the influence of different nano-MgO contents on the peak strain is far less significant than that of carbonization time.

**Figure 15.** The influence of carbonation time on the peak strain of MCS.

Therefore, under the same nano-MgO content, 2 d carbonization has the best effect on improving the peak strain of MCS, which can significantly increase the ductility of MCS. Under the same carbonization time, the nano-MgO content has little effect on the peak strain of MCS.

#### *5.3. Energy Dissipation Analysis*

During the loading process, energy dissipation leads to the process of the formation of internal cracks. In the elastic stage, there are almost no cracks inside MCS, so the energy storage and release are reversible. In the strengthening stage, damage and cracks occur inside MCS, leading to energy dissipation. The greater the energy dissipation is, the stronger the ability of MCS to resist damage is. Therefore, energy dissipation can be used to measure the ability of MCS to resist damage.

As shown in Figure 13, the area enclosed by ABCFE is the total energy dissipation density *S* of the sample; the area enclosed by ABC is the enhanced energy dissipation density S1 of the sample; the area enclosed by ACFE is the basic energy dissipation density *S*2 of the sample. The calculation formula is shown in Equation (9), and the unit is kJ/m3.

$$\begin{cases} S &= \int\_{\varepsilon\_1}^{\varepsilon\_2} f(\varepsilon) d\varepsilon \\ S\_2 &= \sigma\_1 \times (\varepsilon\_2 - \varepsilon\_1) \\ S\_1 &= S - S\_2 \end{cases} \tag{9}$$

*σ*1 is the stress at point A on the *f*(*x*) curve; *ε*1 and *ε*2 are the strains at point A and point C on the *f*(*x*) curve, respectively. As shown in Figure 10, the normalized curve of each group of samples can be obtained by using the above curve normalization method, so as to better determine the specific location of points A, B, C and D. In order to better measure the degree of energy dissipation of MCS, the ratio of S1 and S is taken as the energy dissipation rate K of MCS to reflect the ability to resist external damage. The larger the K

is, the stronger the ability of MCS to resist external damage is. The influence of different carbonization times on the energy dissipation rate of MCS is shown in Figure 16.

**Figure 16.** The influence of carbonization time on the energy dissipation rate of MCS.

It can be seen from Figure 16 that the K of MCS increases first and then decreases with the increase in carbonization time under the same content of nano-MgO. When the carbonization time is 1 d, the K of MCS with five nano-MgO content reaches the maximum, which is 0.17, 0.24, 0.16, 0.18 and 0.18, respectively. This is much higher than that of noncarbonized MCS. Therefore, under five nano-MgO contents, the MCS after 1 d carbonization can better resist external damage.

When the carbonization time is 0 h, 6 h and 1 d, the K of MCS with 0.5% nano-MgO content is the largest, which is 0.10, 0.17 and 0.24, respectively. When the carbonization time is 2 d, the K of MCS with 1.0% nano-MgO content reaches the maximum value, 0.10. When the carbonization time is 4 d, the K of MCS under five nano-MgO contents is 0.02, 0.02, 0.03, 0.05 and 0.04, respectively, and the range of change is small. Therefore, when the carbonization time is 4 d, different nano-MgO contents have no significant influence on the K of MCS.

In summary, MCS with 0.5% nano-MgO content has the largest energy dissipation rate after 1 d carbonization, which is much greater than the other MCS with other nano-MgO contents and after other carbonization times. This indicates that MCS with 0.5% nano-MgO content can better resist external damage after 1 d carbonization.

#### **6. Conclusions and Discussion**
