# Study on Expansion Characteristics and Expansion Potential of Gypsum Rock

Authors: Junfu Fu; Huayun Li; Kaicheng Zhu; Yelei Chen; Zhongcheng Lei
Journal: Geofluids
 (2022)

---

## Abstract

In this study, the relationship between four expansion indices and the expansion potential of gypsum rock was studied; on this basis, a criterion for judging expansion potential is established for gypsum rock. The results show that the free expansion rate is unsuitable for grading gypsum rocks’ expansion potential. Setting the gypsum rock in the Wuzhishan tunnel as the research subject, the ultimate expansion rate is 24.28% on the 7th day and 34.08% on the 30th day; the ultimate expansion rate on the 7th day of the indoor rock sample can be estimated by the fitting formula on the 30th day, the ultimate expansion force is 304.51 kPa, and the BET-specific surface area is 6.31 m2/g. The ultimate expansion ratio and BET-specific surface area have an excellent linear relationship with the ultimate expansion force. Setting the ultimate expansion force, ultimate expansion ratio and BET-specific surface area as the standard, the criterion for judging the expansion potential of gypsum rock is determined, which is more convenient and accurate than existing standards. The standard in this paper can predict the potential disasters that may occur in underground engineering.


---

## Body

## 1. Introduction

Different rock layers have different effects on engineering structures [1–3], and some indicators can be used to predict the possible effects [4], such as landslide prediction and tunnel lining failure prediction [5–8]. In the construction of expansive rock strata, after contact with water, the expansive compressive effect of expansive rock will influence the safety of the engineering structure, and the expansion potential is one of the important indicators for designers to judge the expansive compressive effect, making it crucial to the normal construction and safe operation of engineering structures [9–12].At present, expansive rocks are divided into two categories [13–18]: the first one is caused by chemical expansion reaction, the mechanism is complex, and the time is long (such as anhydrite and glauberite); the second one is caused by hydrophilic minerals, and the expansion of this type of rock is cyclically reciprocated under the action of water absorption and loss (such as mudstone and tuff) [19]. The main indicators for judging the expansion potential of expansive rocks include water content [20–22], viscous material content [9, 15, 23–25], free expansion rate [25], ultimate expansion rate [26], dry saturated water absorption rate [27], and ultimate expansion force [9, 25].Most of the criteria for the above indicators are determined based on the test results of the second type of expansive rock, which are not suitable for the first type of rock. Gypsum rock is the first type of expansive rock, and it contains anhydrite (CaSO4), plaster of paris (CaSO4∙H2 O), and hemihydrate gypsum (CaSO4∙0.5H2O); these three minerals will be converted into Gypsum (CaSO4∙2H2O). The increase of crystal water leads to the expansion of crystal structure and then increases the volume of rock samples [28–34].Abu [30] studied the expansion characteristics of gypsum rocks and clay minerals in Egypt and found that the water absorption of montmorillonite mainly causes the expansion of clay minerals, and the key factor for the expansion of gypsum rocks is the anhydrite. The expansiveness of rock is proportional to the anhydrite content. Ma et al. [29] analyzed the effect of CaSO4∙H2O composition on four different gypsum rocks; it was found that the higher the content of CaSO4∙H2O composition, the lower the strength and energy change of gypsum rocks, but the larger the microscopic size of rock samples. Xu et al. [16] studied the expansion characteristics of rerigid gypsum rock and found that its maximum expansion rate in a short time was 2.6%. Wu [18] conducted a short-term laboratory test to analyze the expansion characteristics of the remolded gypsum rock. The free expansion rate was 3.5%, the expansion rate was 6.01%, and the expansion force was 2.20 kPa. However, the predicted ultimate expansion force can reach up to 824 kPa based on its linear expansion coefficient. Azam et al. [28] analyzed the porosity and CaSO4 content of gypsum rock by XRD and SEM to evaluate the expansion characteristics of gypsum rock microscopically, and it was concluded that its expansion force could reach up to 1660 kPa. Rauh et al. [35] used a remolded sample of anhydrite to analyze the expansion characteristics and found that the expansion of the rock mainly depends on the crystallinity.According to literatures [10, 18, 28, 36], the expansion stress of gypsum rock can be increased by more than ten times after a few years, so the short-term expansion rate and expansion force are not accurate in evaluating its expansion potential. If the expansion potential is incorrectly estimated, the initially designed strength of the project structure will not be enough, which may lead to a potential safety hazard for the safe operation of the project later [36]. Chang et al. [37] used software to analyze the causes of landslides. Huang et al. [38] use environmental factors to guide machine self-learning to predict landslides. Therefore, in this paper, the free expansion rate test, the ultimate expansion rate test, the ultimate expansion force test, and the BET-specific surface area test were carried out on the gypsum rock from the Wuzhishan Tunnel; at the same time, based on the existing methods [13, 14, 18, 30], the expansion potential of gypsum rocks can be quickly and accurately predict by combining the ultimate expansion rate and specific surface area indexes.


## 2. Materials and Methods

### 2.1. Rock Sample Pretreatment

The rock samples were obtained from the gypsum surrounding rock section of Wuzhishan Tunnel. In order to obtain gypsum rocks with different expansion potentials, remolded samples are used in the tests of expansion characteristic index [15–18, 39, 40]. Although the sample used in this paper is the remolded sample, the expansion of gypsum rock is due to the volume expansion caused by the increase of crystal water. The cellular structure of gypsum rock is not damaged in the process of remolding, so the expansion potential of the rock sample is not affected. Besides, the expansion time of gypsum rock is extremely long, and the remolded sample can be used to shorten the expansion time so as to get the ultimate expansion force and ultimate expansion rate. Therefore, it is meaningful to use remolded gypsum rock samples for research in this paper.The gypsum rock collected on site was ground into powder, passed through a 0.5 mm sieve, and then was divided into 5 groups (every group weights 2 kg), which were numbered A, B, C, D, and E, respectively. Five groups of samples were pretreated, as shown in Table1.Table 1
Sample processing.
Serial numberProcess modeAPut sample A into distilled water to fully absorb water; then remove excess water and leave the sample indoor to dry, and grind the sample to powder with a disintegrator and pass through a 0.5 mm sieve; finally, place the powder in an oven to dry at 75°C for 48 hours and storeBAdd 400 g of distilled water to sample B, and then seal the chamber until the water absorption is completed. After grinding to powder with a disintegrator and passing through a 0.5 mm sieve, it was then placed in an oven to dry at 75°C for 48 hoursCAdd 200 g of distilled water to sample C, and then seal the chamber until the water absorption is completed. After grinding to powder with a disintegrator and passing through a 0.5 mm sieve, it was then placed in an oven to dry at 75°C for 48 hours and storeDKeep sealing the sampleEPlace sample D in an oven to dry at 220°C for 48 hours and storeFinally, each group was evenly divided into two parts.


### 2.2. X-Ray Photoelectron Spectroscopy and X-Ray Fluorescence Spectroscopy

In the X-ray Photoelectron Spectroscopy (XPS) test, ESCALAB Xi+ XPS developed by Thermoscientific Company (as shown in Figure1) was used for qualitative and quantitative analysis of gypsum rock [41–43]. The X-ray gun uses an Al target with relatively high intensity. The data obtained from the test was firstly analyzed by the software and then compared with the existing element database. The X-Ray Fluorescence (XRF) analysis was performed using the Zetium (XRF) instrument from PANalytical, the Netherlands, as shown in Figure 2. Refer to the literature for XRF test process [44–47].Figure 1
XPS test system.Figure 2
XRF test system.


### 2.3. Expansion Characteristics Test

#### 2.3.1. Free Expansion Rate

The free expansion rate is defined as the percentage of the volume change after the expansion to the initial volume when weathered expansive rock particles with a certain amount are placed in water without any constraints [48]. The free expansion rate is related to the content of hydrophilic minerals and the thickness of particles, which can reflect the expansion performance of expansive rocks to a certain extent. Therefore, it is often used as one of the indicators to judge the expansion potential. The free expansion rate test was carried out according to the specification [49, 50]. The test process and data processing refer to the standard [51]. Free expansion rate test steps are as follows:
(Step 1)
Clean the measuring cylinder, agitator, and measuring cup; then dry and set aside.(Step 2)
The vector earth cup is loaded with sufficient gypsum rock powder.(Step 3)
Put the following components into the 50 mL measuring cylinder in turn: 30 mL distilled water and 5 mL 5% NaCl solution, and the sample in the measuring cup. Then, stir 10 times along the vertical direction of the cylinder.(Step 4)
The stirrer is rinsed with distilled water in the cylinder and then infused with distilled water to 50 mL along the cylinder wall.(Step 5)
Stay for a while, and then, the readings are recorded.


#### 2.3.2. Ultimate Expansion Rate

Under lateral confinement, the remolded sample had an expansion reaction through the slow contact between the permeable stone and the water from top to bottom [50, 52, 53]. The ratio of the axial increased amount after expansion to the initial amount is defined as the ultimate expansion ratio. The limit expansion rate and the free expansion rate are both judging indicators of the expansion potential, and their difference is that in the limit expansion rate test, the sample is chemically reacted with the water in the permeable stone, and the contact area between the sample and the water is larger, slowing the expansion and the surface hardening, which will affect the expansion of the internal gypsum rock powder. The expansion ratio test apparatus is shown in Figure 3. The test process and data processing refer to the standard [51, 54]. The expansion rate test steps are as follows:
(Step 1)
The ring cutter and pervious stone were cleaned and dried; then, the pervious stone was buried in gypsum rock powder for 60 minutes.(Step 2)
After adding gypsum rock powder of 1/3 of its height into the ring cutter each time, compaction is carried out until the sample height is flush with the ring cutter.(Step 3)
Assemble expander, adjust dial gauge, and record initial reading.(Step 4)
Add distilled water to the water box, and the water level is 5 mm higher than the sample. Record the dial gauge reading after a period of time. Disassemble the dilatometer, and sort out the test instruments.Figure 3
The dilatometer.


#### 2.3.3. Ultimate Expansion Force

Under the limitation of the surrounding rock and soil, the increase of the water absorption volume of expansive rock or expansive soil will produce a limiting reaction force, which is called the expansion force [48, 50, 55–57]. In this test, the expansion force measured by the gypsum rock remolded sample is under the limit condition. The test adopts a WG single-lever consolidation instrument, as shown in Figure 4. The test process and data processing refer to the standard [51]. The steps of expansion force test are as follows:
(Step 1)
The ring cutter and pervious stone were cleaned and dried; then, the pervious stone was buried in gypsum rock powder for 60 minutes.(Step 2)
After adding gypsum rock powder of 1/3 of its height into the ring cutter each time, compaction is carried out until the sample height is flush with the ring cutter.(Step 3)
Add distilled water to the water box, and the water level is 5 mm higher than the sample.(Step 4)
When the sample begins to expand and the expansion is not higher than 0.01 mm, add the load to make the gauge recover the initial reading. Excessive disturbance to the sample should be avoided when adding the charge.(Step 5)
With the 24-hour deformation as the boundary, the charge returns the scale to the previous 24-hour deformation position. After a period of time, the test was terminated and the load value was recorded.Figure 4
Expansion force testing instrument.


### 2.4. BET-Specific Surface Area

Specific surface area (As) refers to the total surface area of solid particles per unit mass, and it is one of the important indicators for analyzing the coupling effect of liquid-solid and liquid-gas interfaces. In recent years, with the further study of expansive rock and soil from macro to micro, the specific surface area has been more focused [49, 58–66], which can reflect the expansion characteristics and expansion potential of expansive rock and soil. At present, there are many studies on the specific surface area of expansive soil [49, 58, 59, 63, 67, 68], while there are few studies on expansive rocks [60], especially the specific surface area of the first type of expansive rocks.This paper studies the specific surface area of gypsum rock based on the indoor nitrogen adsorption test. In the nitrogen adsorption method [69], when nitrogen is liquid at low temperature, it can be adsorbed on the surface of powder particles. After room temperature is recovered, the liquid nitrogen returns to a gaseous state and is detached from the surface of the powder particles. By measuring the gaseous nitrogen, the specific surface area of the powder particles completely wrapped by a layer of liquid nitrogen can be obtained.In fact, nitrogen is adsorbed on the surface of powder particles in multiple layers. According to the saturated adsorption amount of nitrogen in a single layer, combined with thermodynamics and kinetics, the actual adsorption amount of nitrogen can be accurately obtained, that is, the multilayer adsorption theory (BET) equation, as shown in Equation (1). The BET equation is a calculation method of nitrogen adsorption method, which can accurately calculate the actual adsorption amount of nitrogen, so it is widely used in the determination of specific surface area.
(1)P/VP0−P=1/Vm∙C+C−1P/Vm∙C∙P0where V is the actual adsorption amount of nitrogen, P0 is the saturated vapour pressure, P is the partial pressure of nitrogen, Vm is the monolayer saturated adsorption amount of nitrogen, and C is a material constant.The five groups of samples A, B, C, D, and E were ground with a natural agate grinder, then passed through a 500-mesh sieve, and 2 g of each group of samples were collected and sealed. In the specific surface area test, the JW-BK132F-specific surface area and pore size analyzer produced by Jingwei Gaobo Company are used, as shown in Figure5.Figure 5
JW-BK132F instruments.


## 2.1. Rock Sample Pretreatment

The rock samples were obtained from the gypsum surrounding rock section of Wuzhishan Tunnel. In order to obtain gypsum rocks with different expansion potentials, remolded samples are used in the tests of expansion characteristic index [15–18, 39, 40]. Although the sample used in this paper is the remolded sample, the expansion of gypsum rock is due to the volume expansion caused by the increase of crystal water. The cellular structure of gypsum rock is not damaged in the process of remolding, so the expansion potential of the rock sample is not affected. Besides, the expansion time of gypsum rock is extremely long, and the remolded sample can be used to shorten the expansion time so as to get the ultimate expansion force and ultimate expansion rate. Therefore, it is meaningful to use remolded gypsum rock samples for research in this paper.The gypsum rock collected on site was ground into powder, passed through a 0.5 mm sieve, and then was divided into 5 groups (every group weights 2 kg), which were numbered A, B, C, D, and E, respectively. Five groups of samples were pretreated, as shown in Table1.Table 1
Sample processing.
Serial numberProcess modeAPut sample A into distilled water to fully absorb water; then remove excess water and leave the sample indoor to dry, and grind the sample to powder with a disintegrator and pass through a 0.5 mm sieve; finally, place the powder in an oven to dry at 75°C for 48 hours and storeBAdd 400 g of distilled water to sample B, and then seal the chamber until the water absorption is completed. After grinding to powder with a disintegrator and passing through a 0.5 mm sieve, it was then placed in an oven to dry at 75°C for 48 hoursCAdd 200 g of distilled water to sample C, and then seal the chamber until the water absorption is completed. After grinding to powder with a disintegrator and passing through a 0.5 mm sieve, it was then placed in an oven to dry at 75°C for 48 hours and storeDKeep sealing the sampleEPlace sample D in an oven to dry at 220°C for 48 hours and storeFinally, each group was evenly divided into two parts.


## 2.2. X-Ray Photoelectron Spectroscopy and X-Ray Fluorescence Spectroscopy

In the X-ray Photoelectron Spectroscopy (XPS) test, ESCALAB Xi+ XPS developed by Thermoscientific Company (as shown in Figure1) was used for qualitative and quantitative analysis of gypsum rock [41–43]. The X-ray gun uses an Al target with relatively high intensity. The data obtained from the test was firstly analyzed by the software and then compared with the existing element database. The X-Ray Fluorescence (XRF) analysis was performed using the Zetium (XRF) instrument from PANalytical, the Netherlands, as shown in Figure 2. Refer to the literature for XRF test process [44–47].Figure 1
XPS test system.Figure 2
XRF test system.


## 2.3. Expansion Characteristics Test

### 2.3.1. Free Expansion Rate

The free expansion rate is defined as the percentage of the volume change after the expansion to the initial volume when weathered expansive rock particles with a certain amount are placed in water without any constraints [48]. The free expansion rate is related to the content of hydrophilic minerals and the thickness of particles, which can reflect the expansion performance of expansive rocks to a certain extent. Therefore, it is often used as one of the indicators to judge the expansion potential. The free expansion rate test was carried out according to the specification [49, 50]. The test process and data processing refer to the standard [51]. Free expansion rate test steps are as follows:
(Step 1)
Clean the measuring cylinder, agitator, and measuring cup; then dry and set aside.(Step 2)
The vector earth cup is loaded with sufficient gypsum rock powder.(Step 3)
Put the following components into the 50 mL measuring cylinder in turn: 30 mL distilled water and 5 mL 5% NaCl solution, and the sample in the measuring cup. Then, stir 10 times along the vertical direction of the cylinder.(Step 4)
The stirrer is rinsed with distilled water in the cylinder and then infused with distilled water to 50 mL along the cylinder wall.(Step 5)
Stay for a while, and then, the readings are recorded.


### 2.3.2. Ultimate Expansion Rate

Under lateral confinement, the remolded sample had an expansion reaction through the slow contact between the permeable stone and the water from top to bottom [50, 52, 53]. The ratio of the axial increased amount after expansion to the initial amount is defined as the ultimate expansion ratio. The limit expansion rate and the free expansion rate are both judging indicators of the expansion potential, and their difference is that in the limit expansion rate test, the sample is chemically reacted with the water in the permeable stone, and the contact area between the sample and the water is larger, slowing the expansion and the surface hardening, which will affect the expansion of the internal gypsum rock powder. The expansion ratio test apparatus is shown in Figure 3. The test process and data processing refer to the standard [51, 54]. The expansion rate test steps are as follows:
(Step 1)
The ring cutter and pervious stone were cleaned and dried; then, the pervious stone was buried in gypsum rock powder for 60 minutes.(Step 2)
After adding gypsum rock powder of 1/3 of its height into the ring cutter each time, compaction is carried out until the sample height is flush with the ring cutter.(Step 3)
Assemble expander, adjust dial gauge, and record initial reading.(Step 4)
Add distilled water to the water box, and the water level is 5 mm higher than the sample. Record the dial gauge reading after a period of time. Disassemble the dilatometer, and sort out the test instruments.Figure 3
The dilatometer.


### 2.3.3. Ultimate Expansion Force

Under the limitation of the surrounding rock and soil, the increase of the water absorption volume of expansive rock or expansive soil will produce a limiting reaction force, which is called the expansion force [48, 50, 55–57]. In this test, the expansion force measured by the gypsum rock remolded sample is under the limit condition. The test adopts a WG single-lever consolidation instrument, as shown in Figure 4. The test process and data processing refer to the standard [51]. The steps of expansion force test are as follows:
(Step 1)
The ring cutter and pervious stone were cleaned and dried; then, the pervious stone was buried in gypsum rock powder for 60 minutes.(Step 2)
After adding gypsum rock powder of 1/3 of its height into the ring cutter each time, compaction is carried out until the sample height is flush with the ring cutter.(Step 3)
Add distilled water to the water box, and the water level is 5 mm higher than the sample.(Step 4)
When the sample begins to expand and the expansion is not higher than 0.01 mm, add the load to make the gauge recover the initial reading. Excessive disturbance to the sample should be avoided when adding the charge.(Step 5)
With the 24-hour deformation as the boundary, the charge returns the scale to the previous 24-hour deformation position. After a period of time, the test was terminated and the load value was recorded.Figure 4
Expansion force testing instrument.


## 2.3.1. Free Expansion Rate

The free expansion rate is defined as the percentage of the volume change after the expansion to the initial volume when weathered expansive rock particles with a certain amount are placed in water without any constraints [48]. The free expansion rate is related to the content of hydrophilic minerals and the thickness of particles, which can reflect the expansion performance of expansive rocks to a certain extent. Therefore, it is often used as one of the indicators to judge the expansion potential. The free expansion rate test was carried out according to the specification [49, 50]. The test process and data processing refer to the standard [51]. Free expansion rate test steps are as follows:
(Step 1)
Clean the measuring cylinder, agitator, and measuring cup; then dry and set aside.(Step 2)
The vector earth cup is loaded with sufficient gypsum rock powder.(Step 3)
Put the following components into the 50 mL measuring cylinder in turn: 30 mL distilled water and 5 mL 5% NaCl solution, and the sample in the measuring cup. Then, stir 10 times along the vertical direction of the cylinder.(Step 4)
The stirrer is rinsed with distilled water in the cylinder and then infused with distilled water to 50 mL along the cylinder wall.(Step 5)
Stay for a while, and then, the readings are recorded.


## 2.3.2. Ultimate Expansion Rate

Under lateral confinement, the remolded sample had an expansion reaction through the slow contact between the permeable stone and the water from top to bottom [50, 52, 53]. The ratio of the axial increased amount after expansion to the initial amount is defined as the ultimate expansion ratio. The limit expansion rate and the free expansion rate are both judging indicators of the expansion potential, and their difference is that in the limit expansion rate test, the sample is chemically reacted with the water in the permeable stone, and the contact area between the sample and the water is larger, slowing the expansion and the surface hardening, which will affect the expansion of the internal gypsum rock powder. The expansion ratio test apparatus is shown in Figure 3. The test process and data processing refer to the standard [51, 54]. The expansion rate test steps are as follows:
(Step 1)
The ring cutter and pervious stone were cleaned and dried; then, the pervious stone was buried in gypsum rock powder for 60 minutes.(Step 2)
After adding gypsum rock powder of 1/3 of its height into the ring cutter each time, compaction is carried out until the sample height is flush with the ring cutter.(Step 3)
Assemble expander, adjust dial gauge, and record initial reading.(Step 4)
Add distilled water to the water box, and the water level is 5 mm higher than the sample. Record the dial gauge reading after a period of time. Disassemble the dilatometer, and sort out the test instruments.Figure 3
The dilatometer.


## 2.3.3. Ultimate Expansion Force

Under the limitation of the surrounding rock and soil, the increase of the water absorption volume of expansive rock or expansive soil will produce a limiting reaction force, which is called the expansion force [48, 50, 55–57]. In this test, the expansion force measured by the gypsum rock remolded sample is under the limit condition. The test adopts a WG single-lever consolidation instrument, as shown in Figure 4. The test process and data processing refer to the standard [51]. The steps of expansion force test are as follows:
(Step 1)
The ring cutter and pervious stone were cleaned and dried; then, the pervious stone was buried in gypsum rock powder for 60 minutes.(Step 2)
After adding gypsum rock powder of 1/3 of its height into the ring cutter each time, compaction is carried out until the sample height is flush with the ring cutter.(Step 3)
Add distilled water to the water box, and the water level is 5 mm higher than the sample.(Step 4)
When the sample begins to expand and the expansion is not higher than 0.01 mm, add the load to make the gauge recover the initial reading. Excessive disturbance to the sample should be avoided when adding the charge.(Step 5)
With the 24-hour deformation as the boundary, the charge returns the scale to the previous 24-hour deformation position. After a period of time, the test was terminated and the load value was recorded.Figure 4
Expansion force testing instrument.


## 2.4. BET-Specific Surface Area

Specific surface area (As) refers to the total surface area of solid particles per unit mass, and it is one of the important indicators for analyzing the coupling effect of liquid-solid and liquid-gas interfaces. In recent years, with the further study of expansive rock and soil from macro to micro, the specific surface area has been more focused [49, 58–66], which can reflect the expansion characteristics and expansion potential of expansive rock and soil. At present, there are many studies on the specific surface area of expansive soil [49, 58, 59, 63, 67, 68], while there are few studies on expansive rocks [60], especially the specific surface area of the first type of expansive rocks.This paper studies the specific surface area of gypsum rock based on the indoor nitrogen adsorption test. In the nitrogen adsorption method [69], when nitrogen is liquid at low temperature, it can be adsorbed on the surface of powder particles. After room temperature is recovered, the liquid nitrogen returns to a gaseous state and is detached from the surface of the powder particles. By measuring the gaseous nitrogen, the specific surface area of the powder particles completely wrapped by a layer of liquid nitrogen can be obtained.In fact, nitrogen is adsorbed on the surface of powder particles in multiple layers. According to the saturated adsorption amount of nitrogen in a single layer, combined with thermodynamics and kinetics, the actual adsorption amount of nitrogen can be accurately obtained, that is, the multilayer adsorption theory (BET) equation, as shown in Equation (1). The BET equation is a calculation method of nitrogen adsorption method, which can accurately calculate the actual adsorption amount of nitrogen, so it is widely used in the determination of specific surface area.
(1)P/VP0−P=1/Vm∙C+C−1P/Vm∙C∙P0where V is the actual adsorption amount of nitrogen, P0 is the saturated vapour pressure, P is the partial pressure of nitrogen, Vm is the monolayer saturated adsorption amount of nitrogen, and C is a material constant.The five groups of samples A, B, C, D, and E were ground with a natural agate grinder, then passed through a 500-mesh sieve, and 2 g of each group of samples were collected and sealed. In the specific surface area test, the JW-BK132F-specific surface area and pore size analyzer produced by Jingwei Gaobo Company are used, as shown in Figure5.Figure 5
JW-BK132F instruments.


## 3. Results

### 3.1. Mineral Composition

The XPS spectrum of gypsum rock can be obtained, as shown in Figure6. It can be seen from Figure 6, each element’s peak area and sensitivity factor were quantitatively analyzed, and the percentage of gypsum rock element content was obtained after normalization. The highest atomic percentage of O element is 61.61%, and the lowest atomic percentage of Ca element is 12.20%. Therefore, the content of CaSO4 was higher than that of CaSO4·2H2O. In order to analyze the content of CaSO4 and CaSO4·2H2 O accurately, the samples were then subjected to XRF.Figure 6
XPS map of gypsum rocks.The percentage of oxide content of gypsum rock is shown in Table2. According to the existing data [18, 29, 30, 35, 39], the theoretical percentages of CaO and SO3 in gypsum (CaSO4·2H2O) are 32.6% and 46.5%, respectively, while their percentages in anhydrite (CaSO4) are 41.2% and 58.8%, respectively.Table 2
Percentage of oxide content in gypsum rock.
OxideContent percentageOxideContent percentageOxideContent percentageSO356.438%MgO1.219%Fe2O30.058%CaO39.703%SrO0.395%Na2O0.047%SiO21.964%Al2O30.143%K2O0.023%As shown in Table2, the percentage of CaO in the gypsum rock of the Wuzhishan Tunnel is 39.703%, and the percentage of SO3 is 56.438%; their contents are between the theoretical percentages of gypsum and anhydrite, but close to the theoretical percentages of anhydrite, which further verifies the conclusion obtained by XPS analysis, so the rock sample is not a single gypsum rock or anhydrite but a gypsum rock composed of a mixture of the two, and the content of anhydrite (CaSO4) is more than that of gypsum (CaSO4·2H2O).


### 3.2. Expansion Characteristic Index

#### 3.2.1. Free Expansion Rate

The gypsum rock powder before and after free expansion is shown in Figures7 and 8. The free expansion rate test results are shown in Table 3. It can be seen from Table 3 that the free expansion rate of the samples in group A is the lowest, with an average value of 1.51%; the free expansion rate of the samples in group E is the highest, with an average value of 10.55%. With the deepening of the hydration degree, the free expansion rate of gypsum rock also decreases, and the shrinkage reaches a maximum of 9.04%.Figure 7
Before expansion.Figure 8
After Expansion.Table 3
Test results of free expansion rate.
Sample numberTime (h)Initial volume (mL)Expanded volume (mL)Free expansion rate (%)Experimental valueAverage valueA-1722.09.910.01.011.51A-2722.010.010.22.00B-1721.010.110.31.982.45B-2721.010.310.62.91C-1715.09.710.25.155.13C-2715.09.810.35.10D-1723.09.910.67.077.11D-2723.09.810.57.14E-1721.09.910.910.1010.55E-2721.010.011.011.00In this test, the highest free expansion rate is 10.55%; it is found that gypsum rock does not belong to the expansive rock compared with most expansion classification standards, which is obviously contrary to the existing research [16, 17, 28, 39]. At the same time, in the free expansion rate test, it was found that the gypsum rock powder occurred to harden, as shown in Figure 9; the upper anhydrite in the graduated cylinder hydrated into gypsum and hardened, resulting in a weakened reaction between the lower anhydrite and water, which in turn decreased the free expansion rate of gypsum rock. Therefore, it is not accurate to judge the expansion potential of gypsum rock by the free expansion rate.Figure 9
The hardening of Gypsum rock powder.


#### 3.2.2. Ultimate Expansion Rate

The test results of the ultimate expansion rate are shown in Table4. The gypsum rock sample before and the confining expansion is shown in Figures 10 and 11.According to the comparison of the top and side views of the sample before and after the expansion, it is found that the upper and lower parts of the ring knife have a prominent expansion of the sample, and the upper part has the most significant expansion and the surface is rich in water, suggesting that the ultimate expansion rate test does not appear phenomenon similar to the free expansion rate test.Table 4
Test results of ultimate expansion rate.
Sample numberThe reading of the dial gauge (mm)Expansion rate (%)Average expansion rate (%)0 days7 days30 days7 days30 days7 days30 daysA-19.009.419.652.053.251.833.05A-29.009.329.571.602.85B-14.005.536.037.6510.156.939.68B-24.005.245.846.209.20C-15.008.269.8516.3024.2515.3524.08C-25.007.889.7814.4023.90D-15.009.3611.5021.8032.5024.2834.08D-25.0010.3512.1326.7535.65E-15.0010.5313.7327.6543.6527.9542.13E-25.0010.6513.1228.2540.60Figure 10
Before the confined expansion.Figure 11
After the confined expansion.According to the ultimate expansion ratio in Table4, it can be seen that on the 7th and 30th days, the expansion ratio of the samples of group A is the smallest, with an average value of 1.83% and 3.05%, respectively; on the 7th and 30th days, the expansion ratio of the samples of group E is the largest, with an average value of 27.95% and 42.13%. The maximum expansion rate and the minimum expansion rate differ by about 14 times; with the deepening of the hydration degree, the expansion rate of the sample decreases. Compared with the free expansion rate, the results of the ultimate expansion rate test are more valuable.During the test of the ultimate expansion rate of gypsum rock, the change of the expansion rate showed a trend of first increasing and then decreasing, with an obvious inflexion point. According to the statistics of 10 groups of data, the inflexion point was basically shown in the range from the 5th day to the 7th day. Therefore, considering the worst case, the 7th day is considered the moment when the inflexion point appears, and its expansion rate is recorded. By analyzing the ultimate expansion rate of the sample on the 7th day and the 30th day, a certain linear relationship is found. The fitting curve is shown in Figure12, and the linear relationship is shown in
(2)δ30t=1.45δ7t+0.41R2=0.964,where δ30t is the expansion rate on the 30th day (%) and δ7t is the expansion rate on the 7th day (%).Figure 12
Fitting curve of expansion rate on the 7th day and the 30th day.In the limit expansion rate test, there is a good fitting relationship between the expansion rate on the 7th day and the expansion rate on the 30th day, and the expansion rate on the 30th day can be predicted by the expansion rate on the 7th day, which greatly saves the test time.


#### 3.2.3. Ultimate Expansion Force

The test results of the ultimate expansion force of gypsum rock are shown in Table5; it can be seen that the expansive force of gypsum rock is up to 387.57 kPa, and the lowest is only 15.81 kPa; the difference between the expansive force of group A and group E is about 23 times. Anhydrite content leads to a big difference in swelling force between the two groups. Group A contains less anhydrite after treatment, while group E contains mostly anhydrite after treatment. The ultimate expansion force is negatively correlated with the degree of hydration of the sample.Table 5
Ultimate expansion force test results.
Sample numberTime (d)Expansion force (kPa)Experimental valueAverage valueA-13016.7316.27A-23015.81B-13083.2482.20B-23081.15C-130147.36145.98C-230144.59D-130296.54304.51D-230312.47E-130387.57374.93E-230362.28


### 3.3. BET-Specific Surface Area

The five groups of gypsum rock samples were tested twice for the BET-specific surface area, and five pairs ofP/P0 and P/VP0−P data were collected each time. The BET-specific surface area curve can be drawn through these 5 pairs of data, as shown in Figure 13.Figure 13
BET-specific surface area curve of gypsum rock samples.
(a)
BET-specific surface area curve of group A(b)
BET-specific surface area curve of group B(c)
BET-specific surface area curve of group C(d)
BET-specific surface area curve of group D(e)
BET-specific surface area curve of group EIt can be seen from Figure13 that the P/VP0−P of the sample A-2 is the largest, which is 1.01; the P/VP0−P of the sample D-2 is the smallest, which is 0.30. The P/P0 of each point in groups A, B, C, D, and E is in the range of 0.05~0.35 and has a good linear relationship with the P/VP0−P, which is in line with the requirements for multipoint determination of BET-specific surface area in the specification [70]. According to the linear relationship between the P/VP0−P and P/P0 of each group in Figure 13, combined with the specification, the specific surface area of gypsum rock can be obtained, as shown in Table 6.Table 6
BET-specific surface area test results of gypsum rock.
Sample numberα (inclination)β (intercept)Specific surface aream2/gExperimental valueAverage valueA-12.120.331.781.73A-22.170.421.68B-10.910.273.693.62B-20.920.313.55C-10.490.384.994.60C-20.520.524.20D-10.570.166.046.31D-20.510.166.57E-10.240.298.217.93E-20.330.247.65It can be seen from Table6 that the BET-specific surface area of sample A-2 is the smallest, which is 1.68 m2/g; the specific surface area of sample E-1 is the largest, which is 8.21 m2/g. According to the change of BET-specific surface area from group A to group E, it can be found that the BET-specific surface area is negatively correlated with the hydration degree; this is because the anhydrite (CaSO4) in gypsum rock converts into gypsum (CaSO4·H2O) after absorbing water, which manifests as an increase in unit cells in microscopic aspect and an increase in the volume of rock powder particles in macroscopic aspect.By analyzing the BET-specific surface area of the gypsum rock, it is concluded that the content of anhydrite affects the BET-specific surface area, indicating that the specific surface area of the gypsum rock is related to its expansion characteristics. Therefore, the expansion potential of gypsum rock samples can also be reflected by the BET-specific surface area.


## 3.1. Mineral Composition

The XPS spectrum of gypsum rock can be obtained, as shown in Figure6. It can be seen from Figure 6, each element’s peak area and sensitivity factor were quantitatively analyzed, and the percentage of gypsum rock element content was obtained after normalization. The highest atomic percentage of O element is 61.61%, and the lowest atomic percentage of Ca element is 12.20%. Therefore, the content of CaSO4 was higher than that of CaSO4·2H2O. In order to analyze the content of CaSO4 and CaSO4·2H2 O accurately, the samples were then subjected to XRF.Figure 6
XPS map of gypsum rocks.The percentage of oxide content of gypsum rock is shown in Table2. According to the existing data [18, 29, 30, 35, 39], the theoretical percentages of CaO and SO3 in gypsum (CaSO4·2H2O) are 32.6% and 46.5%, respectively, while their percentages in anhydrite (CaSO4) are 41.2% and 58.8%, respectively.Table 2
Percentage of oxide content in gypsum rock.
OxideContent percentageOxideContent percentageOxideContent percentageSO356.438%MgO1.219%Fe2O30.058%CaO39.703%SrO0.395%Na2O0.047%SiO21.964%Al2O30.143%K2O0.023%As shown in Table2, the percentage of CaO in the gypsum rock of the Wuzhishan Tunnel is 39.703%, and the percentage of SO3 is 56.438%; their contents are between the theoretical percentages of gypsum and anhydrite, but close to the theoretical percentages of anhydrite, which further verifies the conclusion obtained by XPS analysis, so the rock sample is not a single gypsum rock or anhydrite but a gypsum rock composed of a mixture of the two, and the content of anhydrite (CaSO4) is more than that of gypsum (CaSO4·2H2O).


## 3.2. Expansion Characteristic Index

### 3.2.1. Free Expansion Rate

The gypsum rock powder before and after free expansion is shown in Figures7 and 8. The free expansion rate test results are shown in Table 3. It can be seen from Table 3 that the free expansion rate of the samples in group A is the lowest, with an average value of 1.51%; the free expansion rate of the samples in group E is the highest, with an average value of 10.55%. With the deepening of the hydration degree, the free expansion rate of gypsum rock also decreases, and the shrinkage reaches a maximum of 9.04%.Figure 7
Before expansion.Figure 8
After Expansion.Table 3
Test results of free expansion rate.
Sample numberTime (h)Initial volume (mL)Expanded volume (mL)Free expansion rate (%)Experimental valueAverage valueA-1722.09.910.01.011.51A-2722.010.010.22.00B-1721.010.110.31.982.45B-2721.010.310.62.91C-1715.09.710.25.155.13C-2715.09.810.35.10D-1723.09.910.67.077.11D-2723.09.810.57.14E-1721.09.910.910.1010.55E-2721.010.011.011.00In this test, the highest free expansion rate is 10.55%; it is found that gypsum rock does not belong to the expansive rock compared with most expansion classification standards, which is obviously contrary to the existing research [16, 17, 28, 39]. At the same time, in the free expansion rate test, it was found that the gypsum rock powder occurred to harden, as shown in Figure 9; the upper anhydrite in the graduated cylinder hydrated into gypsum and hardened, resulting in a weakened reaction between the lower anhydrite and water, which in turn decreased the free expansion rate of gypsum rock. Therefore, it is not accurate to judge the expansion potential of gypsum rock by the free expansion rate.Figure 9
The hardening of Gypsum rock powder.


### 3.2.2. Ultimate Expansion Rate

The test results of the ultimate expansion rate are shown in Table4. The gypsum rock sample before and the confining expansion is shown in Figures 10 and 11.According to the comparison of the top and side views of the sample before and after the expansion, it is found that the upper and lower parts of the ring knife have a prominent expansion of the sample, and the upper part has the most significant expansion and the surface is rich in water, suggesting that the ultimate expansion rate test does not appear phenomenon similar to the free expansion rate test.Table 4
Test results of ultimate expansion rate.
Sample numberThe reading of the dial gauge (mm)Expansion rate (%)Average expansion rate (%)0 days7 days30 days7 days30 days7 days30 daysA-19.009.419.652.053.251.833.05A-29.009.329.571.602.85B-14.005.536.037.6510.156.939.68B-24.005.245.846.209.20C-15.008.269.8516.3024.2515.3524.08C-25.007.889.7814.4023.90D-15.009.3611.5021.8032.5024.2834.08D-25.0010.3512.1326.7535.65E-15.0010.5313.7327.6543.6527.9542.13E-25.0010.6513.1228.2540.60Figure 10
Before the confined expansion.Figure 11
After the confined expansion.According to the ultimate expansion ratio in Table4, it can be seen that on the 7th and 30th days, the expansion ratio of the samples of group A is the smallest, with an average value of 1.83% and 3.05%, respectively; on the 7th and 30th days, the expansion ratio of the samples of group E is the largest, with an average value of 27.95% and 42.13%. The maximum expansion rate and the minimum expansion rate differ by about 14 times; with the deepening of the hydration degree, the expansion rate of the sample decreases. Compared with the free expansion rate, the results of the ultimate expansion rate test are more valuable.During the test of the ultimate expansion rate of gypsum rock, the change of the expansion rate showed a trend of first increasing and then decreasing, with an obvious inflexion point. According to the statistics of 10 groups of data, the inflexion point was basically shown in the range from the 5th day to the 7th day. Therefore, considering the worst case, the 7th day is considered the moment when the inflexion point appears, and its expansion rate is recorded. By analyzing the ultimate expansion rate of the sample on the 7th day and the 30th day, a certain linear relationship is found. The fitting curve is shown in Figure12, and the linear relationship is shown in
(2)δ30t=1.45δ7t+0.41R2=0.964,where δ30t is the expansion rate on the 30th day (%) and δ7t is the expansion rate on the 7th day (%).Figure 12
Fitting curve of expansion rate on the 7th day and the 30th day.In the limit expansion rate test, there is a good fitting relationship between the expansion rate on the 7th day and the expansion rate on the 30th day, and the expansion rate on the 30th day can be predicted by the expansion rate on the 7th day, which greatly saves the test time.


### 3.2.3. Ultimate Expansion Force

The test results of the ultimate expansion force of gypsum rock are shown in Table5; it can be seen that the expansive force of gypsum rock is up to 387.57 kPa, and the lowest is only 15.81 kPa; the difference between the expansive force of group A and group E is about 23 times. Anhydrite content leads to a big difference in swelling force between the two groups. Group A contains less anhydrite after treatment, while group E contains mostly anhydrite after treatment. The ultimate expansion force is negatively correlated with the degree of hydration of the sample.Table 5
Ultimate expansion force test results.
Sample numberTime (d)Expansion force (kPa)Experimental valueAverage valueA-13016.7316.27A-23015.81B-13083.2482.20B-23081.15C-130147.36145.98C-230144.59D-130296.54304.51D-230312.47E-130387.57374.93E-230362.28


## 3.2.1. Free Expansion Rate

The gypsum rock powder before and after free expansion is shown in Figures7 and 8. The free expansion rate test results are shown in Table 3. It can be seen from Table 3 that the free expansion rate of the samples in group A is the lowest, with an average value of 1.51%; the free expansion rate of the samples in group E is the highest, with an average value of 10.55%. With the deepening of the hydration degree, the free expansion rate of gypsum rock also decreases, and the shrinkage reaches a maximum of 9.04%.Figure 7
Before expansion.Figure 8
After Expansion.Table 3
Test results of free expansion rate.
Sample numberTime (h)Initial volume (mL)Expanded volume (mL)Free expansion rate (%)Experimental valueAverage valueA-1722.09.910.01.011.51A-2722.010.010.22.00B-1721.010.110.31.982.45B-2721.010.310.62.91C-1715.09.710.25.155.13C-2715.09.810.35.10D-1723.09.910.67.077.11D-2723.09.810.57.14E-1721.09.910.910.1010.55E-2721.010.011.011.00In this test, the highest free expansion rate is 10.55%; it is found that gypsum rock does not belong to the expansive rock compared with most expansion classification standards, which is obviously contrary to the existing research [16, 17, 28, 39]. At the same time, in the free expansion rate test, it was found that the gypsum rock powder occurred to harden, as shown in Figure 9; the upper anhydrite in the graduated cylinder hydrated into gypsum and hardened, resulting in a weakened reaction between the lower anhydrite and water, which in turn decreased the free expansion rate of gypsum rock. Therefore, it is not accurate to judge the expansion potential of gypsum rock by the free expansion rate.Figure 9
The hardening of Gypsum rock powder.


## 3.2.2. Ultimate Expansion Rate

The test results of the ultimate expansion rate are shown in Table4. The gypsum rock sample before and the confining expansion is shown in Figures 10 and 11.According to the comparison of the top and side views of the sample before and after the expansion, it is found that the upper and lower parts of the ring knife have a prominent expansion of the sample, and the upper part has the most significant expansion and the surface is rich in water, suggesting that the ultimate expansion rate test does not appear phenomenon similar to the free expansion rate test.Table 4
Test results of ultimate expansion rate.
Sample numberThe reading of the dial gauge (mm)Expansion rate (%)Average expansion rate (%)0 days7 days30 days7 days30 days7 days30 daysA-19.009.419.652.053.251.833.05A-29.009.329.571.602.85B-14.005.536.037.6510.156.939.68B-24.005.245.846.209.20C-15.008.269.8516.3024.2515.3524.08C-25.007.889.7814.4023.90D-15.009.3611.5021.8032.5024.2834.08D-25.0010.3512.1326.7535.65E-15.0010.5313.7327.6543.6527.9542.13E-25.0010.6513.1228.2540.60Figure 10
Before the confined expansion.Figure 11
After the confined expansion.According to the ultimate expansion ratio in Table4, it can be seen that on the 7th and 30th days, the expansion ratio of the samples of group A is the smallest, with an average value of 1.83% and 3.05%, respectively; on the 7th and 30th days, the expansion ratio of the samples of group E is the largest, with an average value of 27.95% and 42.13%. The maximum expansion rate and the minimum expansion rate differ by about 14 times; with the deepening of the hydration degree, the expansion rate of the sample decreases. Compared with the free expansion rate, the results of the ultimate expansion rate test are more valuable.During the test of the ultimate expansion rate of gypsum rock, the change of the expansion rate showed a trend of first increasing and then decreasing, with an obvious inflexion point. According to the statistics of 10 groups of data, the inflexion point was basically shown in the range from the 5th day to the 7th day. Therefore, considering the worst case, the 7th day is considered the moment when the inflexion point appears, and its expansion rate is recorded. By analyzing the ultimate expansion rate of the sample on the 7th day and the 30th day, a certain linear relationship is found. The fitting curve is shown in Figure12, and the linear relationship is shown in
(2)δ30t=1.45δ7t+0.41R2=0.964,where δ30t is the expansion rate on the 30th day (%) and δ7t is the expansion rate on the 7th day (%).Figure 12
Fitting curve of expansion rate on the 7th day and the 30th day.In the limit expansion rate test, there is a good fitting relationship between the expansion rate on the 7th day and the expansion rate on the 30th day, and the expansion rate on the 30th day can be predicted by the expansion rate on the 7th day, which greatly saves the test time.


## 3.2.3. Ultimate Expansion Force

The test results of the ultimate expansion force of gypsum rock are shown in Table5; it can be seen that the expansive force of gypsum rock is up to 387.57 kPa, and the lowest is only 15.81 kPa; the difference between the expansive force of group A and group E is about 23 times. Anhydrite content leads to a big difference in swelling force between the two groups. Group A contains less anhydrite after treatment, while group E contains mostly anhydrite after treatment. The ultimate expansion force is negatively correlated with the degree of hydration of the sample.Table 5
Ultimate expansion force test results.
Sample numberTime (d)Expansion force (kPa)Experimental valueAverage valueA-13016.7316.27A-23015.81B-13083.2482.20B-23081.15C-130147.36145.98C-230144.59D-130296.54304.51D-230312.47E-130387.57374.93E-230362.28


## 3.3. BET-Specific Surface Area

The five groups of gypsum rock samples were tested twice for the BET-specific surface area, and five pairs ofP/P0 and P/VP0−P data were collected each time. The BET-specific surface area curve can be drawn through these 5 pairs of data, as shown in Figure 13.Figure 13
BET-specific surface area curve of gypsum rock samples.
(a)
BET-specific surface area curve of group A(b)
BET-specific surface area curve of group B(c)
BET-specific surface area curve of group C(d)
BET-specific surface area curve of group D(e)
BET-specific surface area curve of group EIt can be seen from Figure13 that the P/VP0−P of the sample A-2 is the largest, which is 1.01; the P/VP0−P of the sample D-2 is the smallest, which is 0.30. The P/P0 of each point in groups A, B, C, D, and E is in the range of 0.05~0.35 and has a good linear relationship with the P/VP0−P, which is in line with the requirements for multipoint determination of BET-specific surface area in the specification [70]. According to the linear relationship between the P/VP0−P and P/P0 of each group in Figure 13, combined with the specification, the specific surface area of gypsum rock can be obtained, as shown in Table 6.Table 6
BET-specific surface area test results of gypsum rock.
Sample numberα (inclination)β (intercept)Specific surface aream2/gExperimental valueAverage valueA-12.120.331.781.73A-22.170.421.68B-10.910.273.693.62B-20.920.313.55C-10.490.384.994.60C-20.520.524.20D-10.570.166.046.31D-20.510.166.57E-10.240.298.217.93E-20.330.247.65It can be seen from Table6 that the BET-specific surface area of sample A-2 is the smallest, which is 1.68 m2/g; the specific surface area of sample E-1 is the largest, which is 8.21 m2/g. According to the change of BET-specific surface area from group A to group E, it can be found that the BET-specific surface area is negatively correlated with the hydration degree; this is because the anhydrite (CaSO4) in gypsum rock converts into gypsum (CaSO4·H2O) after absorbing water, which manifests as an increase in unit cells in microscopic aspect and an increase in the volume of rock powder particles in macroscopic aspect.By analyzing the BET-specific surface area of the gypsum rock, it is concluded that the content of anhydrite affects the BET-specific surface area, indicating that the specific surface area of the gypsum rock is related to its expansion characteristics. Therefore, the expansion potential of gypsum rock samples can also be reflected by the BET-specific surface area.


## 4. Discussion

### 4.1. Expansive Rock Classification

Expansion potential refers to the expansion capacity of expansive rock and soil after absorbing water. The determination of expansion potential is essential in engineering design, and an inaccurate evaluation will affect the structural safety of engineering. Therefore, it is necessary to use suitable methods and indicators to judge the expansion potential of different types of expansive rock and soil.


### 4.2. Expansion Potential Determination of Gypsum Rock

#### 4.2.1. Selection of Judgment Indicators

According to the test results of the free expansion rate, combined with Table7, it is judged that the gypsum rock is not an expansive rock. This is because, in the test, the hydration of the upper anhydrite results in a weakened reaction between the lower anhydrite and water, which in turn causes a low free expansion rate of gypsum rock. Therefore, although the free expansion [25] rate is one of the most widely used judging indicators for expansive rock and soil, it is not suitable for judging the expansion potential of gypsum rock.Table 7
Main classification standards of expansive rock [13, 14, 18, 39].
IndicatorNonexpansive rockSlight expansive rockWeak expansive rockStrong expansive rockFree expansive rate (%)<3030~5050~70>70Dry saturated water absorption (%)<1010~3030~50>50Linear shrinkage (%)<55~88~12.5>12.5Ultimate expansive rate (%)<55~1010~20>20Ultimate expansive force (kPa)<100100~300300~500>500Specific surface area (m2/g)<5050~100100~300>300Exchanging volume (mL/g)<0.10.1~0.20.2~0.5>0.5Strength of surrounding rock (MPa)>10.7~10.4~0.7<0.4In the ultimate expansion rate test [26], the samples did not show the phenomenon of surface hardening agglomeration hindering the water absorption of the internal sample, and the ultimate expansion rate was as high as 43.65%, indicating that the ultimate expansion rate can be used as a grading index of the expansion potential of gypsum rocks. However, the classification standard in Table 6 is mainly based on the expansion mechanism of the second type of expansive rock, while gypsum rock belongs to the first type of expansive rock, and their expansion mechanism is completely different; therefore, it needs to be corrected when the limit expansion coefficient is used as the judgment index of the expansion potential of gypsum rock.The ultimate expansion force [13, 14, 39] is not only the most important index for judging the expansion potential of expansive soil but also the most important parameter for structural design. No matter the reason for the expansion, its ultimate expansion force corresponds to the same expansion potential grade; the mineral composition and expansion mechanism only affect the expansion rate and do not affect the expansion potential grade. Therefore, the expansion potential grade of gypsum rock concerning the ultimate expansion force can be judged regarding Table 7.For the first type of expansive rock and the second type of expansive rock, the meaning of the specific surface area is different. For the first type of expansive rock, the change in the specific surface area is due to the hydration of anhydrite, and the number of unit cells increases from 4 to 8, resulting in a larger specific surface area of the rock sample before expansion [18]. For the second type of expansive rock, the specific surface area affects the range of the contact surface between hydrophilic minerals and water. In the test of the specific surface area of gypsum rock, it is found that the specific surface area is related to the expansion potential of gypsum rock, but the current expansion potential judgment based on specific surface area is based on the range determined by the second type of expansive rock, which is not suitable for gypsum rock. Therefore, when the BET-specific surface area is used as the evaluation index of the expansion potential of gypsum rock, it is necessary to redivide its grade range.In this paper, the ultimate expansion ratio, ultimate expansion force, and specific surface area are selected to divide the expansion potential of gypsum rock based on laboratory tests.


#### 4.2.2. The Relationship between the Ultimate Expansion Rate and the Ultimate Expansion Force

The relationship curve between the ultimate expansion rate of gypsum rock (Table4) and the test results of the ultimate expansion force (Table 5) can be drawn from the test results, as shown in Figure 14. It can be seen from Figure 14 that the ultimate expansion rate of gypsum rock is positively correlated with the ultimate expansion force, and there is a certain functional relationship as follows:
(3)Ps=9.05δ30t−19.83R2=0.961,where Ps is the ultimate expansion force (kPa) and δ30t is the 30th day ultimate expansion rate (%).Figure 14
Relation curve between ultimate expansion rate and ultimate expansion force.From Equation (3), it can be seen that the fitting degree between the ultimate expansion ratio and the ultimate expansion force is relatively high, and the ultimate expansion force of the specimen can be estimated from the ultimate unloaded expansion ratio of the sample through this formula.


#### 4.2.3. Relationship between Specific Surface Area and Ultimate Expansion Force

The BET-specific surface area test results of gypsum rock (Table6) and the ultimate expansion force test results (Table 5) are analyzed, and their relationship curve is obtained, as shown in Figure 15. Figure 15 shows that the expansion force increases synchronically with the BET-specific surface area increase, showing a good linear relationship, and the fitting formula of the primary function can be obtained:
(4)Ps=61.48As−112.54R2=0.963,where Ps is the ultimate expansion force (kPa) and As is the BET-specific surface area (m2/g).Figure 15
The relationship between BET-specific surface area and expansion force.


#### 4.2.4. Expansion Potential Classification

According to the ultimate expansion force in Table7, the classification range of the expansion potential is divided into non, slight, weak, and strong, and the corresponding ultimate expansion force ranges are <100 kPa, 100~300 kPa, 300~500 kPa, and >500 kPa. According to Formula (3), the limit expansion rate ranges are obtained as <13.3%, 13.3~35.3%, 35.3~57.4%, and >57.4%. According to Formula (4), the range of BET-specific surface area is <3.5m2/g, 3.5~6.7 m2/g, 6.7~10.0 m2/g, and >10.0m2/g. Thus, the classification standard of gypsum rock expansion potential can be obtained, as shown in Table 8.Table 8
Classification of the expansion potential of gypsum rocks.
Judgement indicatorsNonexpansive rockWeak expansive rockIntermediate expansive rockStrong expansive rockUltimate expansive rate (%)<13.313.3~35.335.3~57.4>57.4Ultimate expansive force (kPa)<100100~300300~500>500BET-specific surface area (m2/g)<3.53.5~6.76.7~10.0>10.0The BET-specific surface area of the sample was tested indoors for 2 to 3 hours; at the same time, the expansion ratio test was carried out for 7 days, and then, the expansion ratio for 30 days was converted using Equation (1). Combined with Table 8, the expansion potential of gypsum rock can be quickly and accurately analyzed. Compared with the traditional method of judging the expansion potential which lasts for several months, the criterion in this paper can greatly save time and ensure the rapid and safe construction of the project. The ultimate expansion rate, ultimate expansion force, and BET-specific surface area of the gypsum rock in the Wuzhishan Tunnel are 34.08%, 304.51 kPa, and 6.31 m2/g, respectively. According to the standards in this paper, the rock is judged to be intermediate expansive rock.The division of expansion potential is for reference to engineering practice. In the future research, the expansion potential should be adjusted after observing the expansion force changes of the field engineering structures.


## 4.1. Expansive Rock Classification

Expansion potential refers to the expansion capacity of expansive rock and soil after absorbing water. The determination of expansion potential is essential in engineering design, and an inaccurate evaluation will affect the structural safety of engineering. Therefore, it is necessary to use suitable methods and indicators to judge the expansion potential of different types of expansive rock and soil.


## 4.2. Expansion Potential Determination of Gypsum Rock

### 4.2.1. Selection of Judgment Indicators

According to the test results of the free expansion rate, combined with Table7, it is judged that the gypsum rock is not an expansive rock. This is because, in the test, the hydration of the upper anhydrite results in a weakened reaction between the lower anhydrite and water, which in turn causes a low free expansion rate of gypsum rock. Therefore, although the free expansion [25] rate is one of the most widely used judging indicators for expansive rock and soil, it is not suitable for judging the expansion potential of gypsum rock.Table 7
Main classification standards of expansive rock [13, 14, 18, 39].
IndicatorNonexpansive rockSlight expansive rockWeak expansive rockStrong expansive rockFree expansive rate (%)<3030~5050~70>70Dry saturated water absorption (%)<1010~3030~50>50Linear shrinkage (%)<55~88~12.5>12.5Ultimate expansive rate (%)<55~1010~20>20Ultimate expansive force (kPa)<100100~300300~500>500Specific surface area (m2/g)<5050~100100~300>300Exchanging volume (mL/g)<0.10.1~0.20.2~0.5>0.5Strength of surrounding rock (MPa)>10.7~10.4~0.7<0.4In the ultimate expansion rate test [26], the samples did not show the phenomenon of surface hardening agglomeration hindering the water absorption of the internal sample, and the ultimate expansion rate was as high as 43.65%, indicating that the ultimate expansion rate can be used as a grading index of the expansion potential of gypsum rocks. However, the classification standard in Table 6 is mainly based on the expansion mechanism of the second type of expansive rock, while gypsum rock belongs to the first type of expansive rock, and their expansion mechanism is completely different; therefore, it needs to be corrected when the limit expansion coefficient is used as the judgment index of the expansion potential of gypsum rock.The ultimate expansion force [13, 14, 39] is not only the most important index for judging the expansion potential of expansive soil but also the most important parameter for structural design. No matter the reason for the expansion, its ultimate expansion force corresponds to the same expansion potential grade; the mineral composition and expansion mechanism only affect the expansion rate and do not affect the expansion potential grade. Therefore, the expansion potential grade of gypsum rock concerning the ultimate expansion force can be judged regarding Table 7.For the first type of expansive rock and the second type of expansive rock, the meaning of the specific surface area is different. For the first type of expansive rock, the change in the specific surface area is due to the hydration of anhydrite, and the number of unit cells increases from 4 to 8, resulting in a larger specific surface area of the rock sample before expansion [18]. For the second type of expansive rock, the specific surface area affects the range of the contact surface between hydrophilic minerals and water. In the test of the specific surface area of gypsum rock, it is found that the specific surface area is related to the expansion potential of gypsum rock, but the current expansion potential judgment based on specific surface area is based on the range determined by the second type of expansive rock, which is not suitable for gypsum rock. Therefore, when the BET-specific surface area is used as the evaluation index of the expansion potential of gypsum rock, it is necessary to redivide its grade range.In this paper, the ultimate expansion ratio, ultimate expansion force, and specific surface area are selected to divide the expansion potential of gypsum rock based on laboratory tests.


### 4.2.2. The Relationship between the Ultimate Expansion Rate and the Ultimate Expansion Force

The relationship curve between the ultimate expansion rate of gypsum rock (Table4) and the test results of the ultimate expansion force (Table 5) can be drawn from the test results, as shown in Figure 14. It can be seen from Figure 14 that the ultimate expansion rate of gypsum rock is positively correlated with the ultimate expansion force, and there is a certain functional relationship as follows:
(3)Ps=9.05δ30t−19.83R2=0.961,where Ps is the ultimate expansion force (kPa) and δ30t is the 30th day ultimate expansion rate (%).Figure 14
Relation curve between ultimate expansion rate and ultimate expansion force.From Equation (3), it can be seen that the fitting degree between the ultimate expansion ratio and the ultimate expansion force is relatively high, and the ultimate expansion force of the specimen can be estimated from the ultimate unloaded expansion ratio of the sample through this formula.


### 4.2.3. Relationship between Specific Surface Area and Ultimate Expansion Force

The BET-specific surface area test results of gypsum rock (Table6) and the ultimate expansion force test results (Table 5) are analyzed, and their relationship curve is obtained, as shown in Figure 15. Figure 15 shows that the expansion force increases synchronically with the BET-specific surface area increase, showing a good linear relationship, and the fitting formula of the primary function can be obtained:
(4)Ps=61.48As−112.54R2=0.963,where Ps is the ultimate expansion force (kPa) and As is the BET-specific surface area (m2/g).Figure 15
The relationship between BET-specific surface area and expansion force.


### 4.2.4. Expansion Potential Classification

According to the ultimate expansion force in Table7, the classification range of the expansion potential is divided into non, slight, weak, and strong, and the corresponding ultimate expansion force ranges are <100 kPa, 100~300 kPa, 300~500 kPa, and >500 kPa. According to Formula (3), the limit expansion rate ranges are obtained as <13.3%, 13.3~35.3%, 35.3~57.4%, and >57.4%. According to Formula (4), the range of BET-specific surface area is <3.5m2/g, 3.5~6.7 m2/g, 6.7~10.0 m2/g, and >10.0m2/g. Thus, the classification standard of gypsum rock expansion potential can be obtained, as shown in Table 8.Table 8
Classification of the expansion potential of gypsum rocks.
Judgement indicatorsNonexpansive rockWeak expansive rockIntermediate expansive rockStrong expansive rockUltimate expansive rate (%)<13.313.3~35.335.3~57.4>57.4Ultimate expansive force (kPa)<100100~300300~500>500BET-specific surface area (m2/g)<3.53.5~6.76.7~10.0>10.0The BET-specific surface area of the sample was tested indoors for 2 to 3 hours; at the same time, the expansion ratio test was carried out for 7 days, and then, the expansion ratio for 30 days was converted using Equation (1). Combined with Table 8, the expansion potential of gypsum rock can be quickly and accurately analyzed. Compared with the traditional method of judging the expansion potential which lasts for several months, the criterion in this paper can greatly save time and ensure the rapid and safe construction of the project. The ultimate expansion rate, ultimate expansion force, and BET-specific surface area of the gypsum rock in the Wuzhishan Tunnel are 34.08%, 304.51 kPa, and 6.31 m2/g, respectively. According to the standards in this paper, the rock is judged to be intermediate expansive rock.The division of expansion potential is for reference to engineering practice. In the future research, the expansion potential should be adjusted after observing the expansion force changes of the field engineering structures.


## 4.2.1. Selection of Judgment Indicators

According to the test results of the free expansion rate, combined with Table7, it is judged that the gypsum rock is not an expansive rock. This is because, in the test, the hydration of the upper anhydrite results in a weakened reaction between the lower anhydrite and water, which in turn causes a low free expansion rate of gypsum rock. Therefore, although the free expansion [25] rate is one of the most widely used judging indicators for expansive rock and soil, it is not suitable for judging the expansion potential of gypsum rock.Table 7
Main classification standards of expansive rock [13, 14, 18, 39].
IndicatorNonexpansive rockSlight expansive rockWeak expansive rockStrong expansive rockFree expansive rate (%)<3030~5050~70>70Dry saturated water absorption (%)<1010~3030~50>50Linear shrinkage (%)<55~88~12.5>12.5Ultimate expansive rate (%)<55~1010~20>20Ultimate expansive force (kPa)<100100~300300~500>500Specific surface area (m2/g)<5050~100100~300>300Exchanging volume (mL/g)<0.10.1~0.20.2~0.5>0.5Strength of surrounding rock (MPa)>10.7~10.4~0.7<0.4In the ultimate expansion rate test [26], the samples did not show the phenomenon of surface hardening agglomeration hindering the water absorption of the internal sample, and the ultimate expansion rate was as high as 43.65%, indicating that the ultimate expansion rate can be used as a grading index of the expansion potential of gypsum rocks. However, the classification standard in Table 6 is mainly based on the expansion mechanism of the second type of expansive rock, while gypsum rock belongs to the first type of expansive rock, and their expansion mechanism is completely different; therefore, it needs to be corrected when the limit expansion coefficient is used as the judgment index of the expansion potential of gypsum rock.The ultimate expansion force [13, 14, 39] is not only the most important index for judging the expansion potential of expansive soil but also the most important parameter for structural design. No matter the reason for the expansion, its ultimate expansion force corresponds to the same expansion potential grade; the mineral composition and expansion mechanism only affect the expansion rate and do not affect the expansion potential grade. Therefore, the expansion potential grade of gypsum rock concerning the ultimate expansion force can be judged regarding Table 7.For the first type of expansive rock and the second type of expansive rock, the meaning of the specific surface area is different. For the first type of expansive rock, the change in the specific surface area is due to the hydration of anhydrite, and the number of unit cells increases from 4 to 8, resulting in a larger specific surface area of the rock sample before expansion [18]. For the second type of expansive rock, the specific surface area affects the range of the contact surface between hydrophilic minerals and water. In the test of the specific surface area of gypsum rock, it is found that the specific surface area is related to the expansion potential of gypsum rock, but the current expansion potential judgment based on specific surface area is based on the range determined by the second type of expansive rock, which is not suitable for gypsum rock. Therefore, when the BET-specific surface area is used as the evaluation index of the expansion potential of gypsum rock, it is necessary to redivide its grade range.In this paper, the ultimate expansion ratio, ultimate expansion force, and specific surface area are selected to divide the expansion potential of gypsum rock based on laboratory tests.


## 4.2.2. The Relationship between the Ultimate Expansion Rate and the Ultimate Expansion Force

The relationship curve between the ultimate expansion rate of gypsum rock (Table4) and the test results of the ultimate expansion force (Table 5) can be drawn from the test results, as shown in Figure 14. It can be seen from Figure 14 that the ultimate expansion rate of gypsum rock is positively correlated with the ultimate expansion force, and there is a certain functional relationship as follows:
(3)Ps=9.05δ30t−19.83R2=0.961,where Ps is the ultimate expansion force (kPa) and δ30t is the 30th day ultimate expansion rate (%).Figure 14
Relation curve between ultimate expansion rate and ultimate expansion force.From Equation (3), it can be seen that the fitting degree between the ultimate expansion ratio and the ultimate expansion force is relatively high, and the ultimate expansion force of the specimen can be estimated from the ultimate unloaded expansion ratio of the sample through this formula.


## 4.2.3. Relationship between Specific Surface Area and Ultimate Expansion Force

The BET-specific surface area test results of gypsum rock (Table6) and the ultimate expansion force test results (Table 5) are analyzed, and their relationship curve is obtained, as shown in Figure 15. Figure 15 shows that the expansion force increases synchronically with the BET-specific surface area increase, showing a good linear relationship, and the fitting formula of the primary function can be obtained:
(4)Ps=61.48As−112.54R2=0.963,where Ps is the ultimate expansion force (kPa) and As is the BET-specific surface area (m2/g).Figure 15
The relationship between BET-specific surface area and expansion force.


## 4.2.4. Expansion Potential Classification

According to the ultimate expansion force in Table7, the classification range of the expansion potential is divided into non, slight, weak, and strong, and the corresponding ultimate expansion force ranges are <100 kPa, 100~300 kPa, 300~500 kPa, and >500 kPa. According to Formula (3), the limit expansion rate ranges are obtained as <13.3%, 13.3~35.3%, 35.3~57.4%, and >57.4%. According to Formula (4), the range of BET-specific surface area is <3.5m2/g, 3.5~6.7 m2/g, 6.7~10.0 m2/g, and >10.0m2/g. Thus, the classification standard of gypsum rock expansion potential can be obtained, as shown in Table 8.Table 8
Classification of the expansion potential of gypsum rocks.
Judgement indicatorsNonexpansive rockWeak expansive rockIntermediate expansive rockStrong expansive rockUltimate expansive rate (%)<13.313.3~35.335.3~57.4>57.4Ultimate expansive force (kPa)<100100~300300~500>500BET-specific surface area (m2/g)<3.53.5~6.76.7~10.0>10.0The BET-specific surface area of the sample was tested indoors for 2 to 3 hours; at the same time, the expansion ratio test was carried out for 7 days, and then, the expansion ratio for 30 days was converted using Equation (1). Combined with Table 8, the expansion potential of gypsum rock can be quickly and accurately analyzed. Compared with the traditional method of judging the expansion potential which lasts for several months, the criterion in this paper can greatly save time and ensure the rapid and safe construction of the project. The ultimate expansion rate, ultimate expansion force, and BET-specific surface area of the gypsum rock in the Wuzhishan Tunnel are 34.08%, 304.51 kPa, and 6.31 m2/g, respectively. According to the standards in this paper, the rock is judged to be intermediate expansive rock.The division of expansion potential is for reference to engineering practice. In the future research, the expansion potential should be adjusted after observing the expansion force changes of the field engineering structures.


## 5. Conclusions

In this research, the expansion characteristics and BET-specific surface area of gypsum rock are analyzed, and the standard for judging the expansion potential of gypsum rock is established. The main conclusions are as follows:(1)
Through XPS and XRF analysis, it was confirmed that the surrounding rock of the Wuzhishan Tunnel is gypsum rock, and the content of anhydrite is much higher than that of gypsum(2)
In the test, the maximum expansion rate is 42.13%, the maximum expansion force is 374.93 kPa, and the maximum specific surface area is 7.93 m2/g. The hydration degree of gypsum rocks is negatively correlated with free expansion rate, ultimate expansion rate, ultimate expansion force, and BET-specific surface area(3)
It is found that the free expansion rate is not suitable to judge the expansion potential of gypsum rock. The criteria for judging the expansion potential of gypsum rock by the ultimate expansion force, ultimate expansion ratio, and BET-specific surface area are established. This criterion can more accurately judge the real expansion potential of gypsum rock. According to this standard, the gypsum rock of the Wuzhishan tunnel is determined as the weak expansive rock



---

*Source: 6921150-2022-10-14.xml*