# Service Life Prediction of Shaft Sidewall Exposed to Sulfate Environment

Authors: Wei He; Xia Meng; Ji-hui Zhao
Journal: Advances in Materials Science and Engineering
 (2018)

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## Abstract

Under the influence of underground water with high concentration of sulfate, several vertical shafts in the Huang-Huai region are seriously corroded but have varying degradation degrees in different parts. Taking the auxiliary shaft of Lin-Huan coal mine as the research subject, the mechanism of this phenomenon was studied. Then, wet-dry alternated and immersion corrosion tests were carried out, and it was found that only the dry-wet alternated accelerate test is representative of the corrosion mechanism that cause the corrosion in the shaft. However, it will cost much time and money for the laboratory test to reach the same degradation depth. To solve this problem, combining with field and laboratory tests, a modified theoretical degradation model was developed to evaluate the residual life of the corroded sidewall. The results indicate that the residual life of the shaft sidewall is 25 years, and the damaged parts have no need for an immediate reinforcement.


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## Body

## 1. Introduction

As the only passage way for transporting workers and equipment, the auxiliary shaft is extremely important to a coal mine, and its designed service life is usually more than 50 years. However, the service performance of shaft lining is degenerated by aggressive groundwater, microorganisms, and other environmental factors [1, 2]. Due to limited coal reserves in a coal mine, there is no need for reinforcement if the corroded shaft sidewall has the ability to service safely until exhausted.Methods that have been used for predicting the service life of an in-service structure generally include predictions based on experience, deductions from a similar structure exposing a similar environment, accelerated testing results, mathematical models based on sulfate ions transportation, and chemical reaction in the corrosion processes [3]. Prediction based on experience is a semiquantitative method; it is built on the accumulated knowledge from laboratory and field testing experience [4]. Because of the variability in materials, geometry, construction practices, and exposure to loads and environments, each structure has certain uniqueness. Thus, deductions from performance of similar structure have not been commonly used [5].The damage of concrete under sulfate attack proceeds from the surface of concrete, the degradation depth is most suitable to represent the degradation degree of the corroded structure. But the specimens in the laboratory are much smaller than the in-service structure; thus, the degradation depth that makes the in-service structure unstable is very difficult to be achieved by the laboratory test. Several mathematic models [6–8] have been built to predict the degradation depth. But as mathematical models have uncertainties related to the model as well as the material and environmental parameters, prediction based on accelerated tests is used more widely [9–11].The vertical shafts of coal mines are usually at great depths, and unavoidable contact some coal measure strata, which contain lots of corrosive ions. In Lin-Huan coal mine, the auxiliary shaft has varying degradation degrees in different parts. The part with aggressive water flow on is protected by a dense layer and is barely corroded. On the contrary, the moist part near the construction joint is seriously corroded. Since this phenomenon has not been fully studied before, the remaining life is hard to evaluate by ordinary methods.


## 2. Field Investigations

The auxiliary shaft is one of the four vertical shafts in Lin-Huan coal mine. Its inner diameter is 7.2 m. The sidewall in surface soil is made of 1.35 m thick double-layer reinforced concrete. The sidewall in bedrock is made of 0.5 m thick C30 plain concrete; the subsection pouring method was adopted. Given the unavoidable placing intermission, the bond between pouring blocks is weak, and a flow conduit had formed. The inner wall near the construction joint is moist but has no obvious flowing water, as shown in Figure1. Several construction holes were drilled at the project acceptance stage, and the flow rate from each construction hole is usually more than 1.5 L/min.Figure 1
A schematic sketch of the field investigation.


### 2.1. Composition Analysis of the Aggressive Water

There are three major damaged parts in the auxiliary shaft, located at −250 m, −271 m, and −280 m. Because of the low flow rate, water was difficult to collect at the construction joints. Thus, water from nearby construction holes was extracted for analysis. The water samples were analyzed by using an ICS-5000 ion chromatographer. The results are presented in Table1.Table 1
Chemical composition of seepage water (mg/L).
Number
Na+
Mg2+
Ca2+
CO32−
Cl−
SO42−
pH
1
362.1
160.6
378.9
95.8
236.9
1748.0
7.60
2
556.4
111.7
291.7
69.9
181.7
1860.2
7.54
3
626.6
101.8
227.7
91.7
176.7
1867.5
7.85
Average
515.0
124.7
299.4
85.8
198.4
1825.2
7.67As the outer wall is soaked in underground water and the inner wall is exposed to the atmosphere, the environment effect can be classified as Class I [12]. Under Class I environment, when the content of SO42− ion is more than 1500 mg/L, the sulfate effect is classified as “Very Strong.”The solubility product constantKsp is the product of the equilibrium molar concentrations of the ions in a saturated solution of a salt in water. When the ion product K of a salt is higher than the solubility product constant Ksp, it is supersaturated. In the water samples, the average ion product K of gypsum is 1.42 × 10−4, and it is obviously higher than the solubility product constant Ksp (3.36 × 10−9 at 25°C).


### 2.2. Chemical Composition Analysis

The most seriously damaged part is located at −271.0 m. At this part, the concrete of the sidewall is obviously bulging and the surface is very loose. As shown in Figure2, the damaged layer is along the construction joint and is approximately 200 mm in height and 55 mm in depth. As shown in Figure 3, under the dense layer, the concrete seems to be very compact. The rebound test indicated that the compressive strength of the concrete protected by the dense layer is 26.7 MPa; it is almost unaffected by corrosion.Figure 2
Corroded concrete (−271 m).
(a)
(b)Figure 3
Compact concrete with a dense layer (−284 m).
(a)
(b)Corroded concrete samples from the −271 m damaged part and a dense layer sample form −284 m were collected for testing. The phases of the samples were measured by X-ray powder diffraction with Cu Kα radiation on a Rigaku Ultima IV type X-ray powder diffractometer operating at 40 kV and 40 mA. An FEI Quanta 250 Environmental Scanning Electron Microscope (SEM) equipped with an EDAX Apollo X silicon drift detector energy-dispersive X-ray spectrometer (EDS) was used to observe the microstructure of the corroded concrete and the dense layer.Figure4(a) shows that the corroded concrete mainly consists of gypsum (CaSO4·2H2O), quartz (SiO2), albite (NaAlSi3O8), margarite (CaAl2(Al2Si2)O10(OH)2), and calcite (CaCO3). The diffraction peak of portlandite (Ca(OH)2), which is one of the major components of normal concrete, was not found. However, gypsum, which is barely contained in normal concrete, is one of the major components. The average concentration of the sulfate ion and pH value in the water samples are 7.67 and 1825.2 mg/L, respectively. According to Bellmann et al. [13], portlandite will react with gypsum at a minimal sulfate concentration of 1400 mg/L (pH = 14.5). With decreasing pH, less concentration of sulfate ions is needed for the reaction to proceed. The reaction formula of this degradation is as follows:(1)CaOH2+SO42−+2H2O⟶CaSO4⋅2H2O+2OH−Figure 4
XRD analysis of the corroded concrete and the dense layer. (a) The corroded sidewall concrete; (b) the dense layer. 1: Gypsum; 2: quartz; 3: albite; 4: margarite; 5 calcite.
(a)
(b)As can be seen from Figure5, Ca2+ in calcium silicate hydrate (C-S-H) gel is partly replaced by Mg2+ to form hydrated magnesium silicate (M-S-H). Biczok [14] found that the corrosion process of concrete in magnesium sulfate usually included two steps: (1) C-S-H gel reacts with SO42− and Mg2+ to produce gypsum, magnesium hydroxide (Mg(OH)2), silica gel, and H2O; (2) Mg2+ reacts with silica gel to form M-S-H and H2O. The structure of M-S-H is much looser than C-S-H, and the adhesion between M-S-H and the aggregate is smaller. Thus, the deterioration degree of concrete in magnesium sulfate solution is much higher than in sodium sulfate solution [15]:(2)Mg2++C‐S‐H⟶M‐S‐H+Ca2+Figure 5
SEM and EDS images of the corroded concrete. (a) SEM; (b) EDS.
(a)
(b)The sidewall in bedrock section was casted by section; therefore, the bond between pouring blocks is weak, and a hydraulic pathway is formed at the construction joint. Because of a small flow of water and a mass of little cracks at the construction joint, the degeneration is aggravated by the internal crystallization of gypsum. As shown in Figure3, the dense layer above the compact concrete is thin (less than 1-2 mm), indicating that the gypsum from the supersaturated water is crystallized in very small amount. Thus, in the damaged part, it can only slightly accelerate the corrosion at the pouring joint and cannot be the main factor causing the degeneration.As the diffraction peak of ordinary aggregates, such as quartz, albite, and margarite, was not found in Figure4(b) and the major components of the dense layer are the same to the supersaturated salt in the aggressive water, the dense layer is supposed to be formed by the precipitation and crystallization from the supersaturated underground water. As shown in Figure 6, due to the compact microstructure of the dense layer, shaft concrete under the dense layer is barely corroded.Figure 6
SEM and EDS images of the dense layer. (a) SEM; (b) EDS.
(a)
(b)


## 2.1. Composition Analysis of the Aggressive Water

There are three major damaged parts in the auxiliary shaft, located at −250 m, −271 m, and −280 m. Because of the low flow rate, water was difficult to collect at the construction joints. Thus, water from nearby construction holes was extracted for analysis. The water samples were analyzed by using an ICS-5000 ion chromatographer. The results are presented in Table1.Table 1
Chemical composition of seepage water (mg/L).
Number
Na+
Mg2+
Ca2+
CO32−
Cl−
SO42−
pH
1
362.1
160.6
378.9
95.8
236.9
1748.0
7.60
2
556.4
111.7
291.7
69.9
181.7
1860.2
7.54
3
626.6
101.8
227.7
91.7
176.7
1867.5
7.85
Average
515.0
124.7
299.4
85.8
198.4
1825.2
7.67As the outer wall is soaked in underground water and the inner wall is exposed to the atmosphere, the environment effect can be classified as Class I [12]. Under Class I environment, when the content of SO42− ion is more than 1500 mg/L, the sulfate effect is classified as “Very Strong.”The solubility product constantKsp is the product of the equilibrium molar concentrations of the ions in a saturated solution of a salt in water. When the ion product K of a salt is higher than the solubility product constant Ksp, it is supersaturated. In the water samples, the average ion product K of gypsum is 1.42 × 10−4, and it is obviously higher than the solubility product constant Ksp (3.36 × 10−9 at 25°C).


## 2.2. Chemical Composition Analysis

The most seriously damaged part is located at −271.0 m. At this part, the concrete of the sidewall is obviously bulging and the surface is very loose. As shown in Figure2, the damaged layer is along the construction joint and is approximately 200 mm in height and 55 mm in depth. As shown in Figure 3, under the dense layer, the concrete seems to be very compact. The rebound test indicated that the compressive strength of the concrete protected by the dense layer is 26.7 MPa; it is almost unaffected by corrosion.Figure 2
Corroded concrete (−271 m).
(a)
(b)Figure 3
Compact concrete with a dense layer (−284 m).
(a)
(b)Corroded concrete samples from the −271 m damaged part and a dense layer sample form −284 m were collected for testing. The phases of the samples were measured by X-ray powder diffraction with Cu Kα radiation on a Rigaku Ultima IV type X-ray powder diffractometer operating at 40 kV and 40 mA. An FEI Quanta 250 Environmental Scanning Electron Microscope (SEM) equipped with an EDAX Apollo X silicon drift detector energy-dispersive X-ray spectrometer (EDS) was used to observe the microstructure of the corroded concrete and the dense layer.Figure4(a) shows that the corroded concrete mainly consists of gypsum (CaSO4·2H2O), quartz (SiO2), albite (NaAlSi3O8), margarite (CaAl2(Al2Si2)O10(OH)2), and calcite (CaCO3). The diffraction peak of portlandite (Ca(OH)2), which is one of the major components of normal concrete, was not found. However, gypsum, which is barely contained in normal concrete, is one of the major components. The average concentration of the sulfate ion and pH value in the water samples are 7.67 and 1825.2 mg/L, respectively. According to Bellmann et al. [13], portlandite will react with gypsum at a minimal sulfate concentration of 1400 mg/L (pH = 14.5). With decreasing pH, less concentration of sulfate ions is needed for the reaction to proceed. The reaction formula of this degradation is as follows:(1)CaOH2+SO42−+2H2O⟶CaSO4⋅2H2O+2OH−Figure 4
XRD analysis of the corroded concrete and the dense layer. (a) The corroded sidewall concrete; (b) the dense layer. 1: Gypsum; 2: quartz; 3: albite; 4: margarite; 5 calcite.
(a)
(b)As can be seen from Figure5, Ca2+ in calcium silicate hydrate (C-S-H) gel is partly replaced by Mg2+ to form hydrated magnesium silicate (M-S-H). Biczok [14] found that the corrosion process of concrete in magnesium sulfate usually included two steps: (1) C-S-H gel reacts with SO42− and Mg2+ to produce gypsum, magnesium hydroxide (Mg(OH)2), silica gel, and H2O; (2) Mg2+ reacts with silica gel to form M-S-H and H2O. The structure of M-S-H is much looser than C-S-H, and the adhesion between M-S-H and the aggregate is smaller. Thus, the deterioration degree of concrete in magnesium sulfate solution is much higher than in sodium sulfate solution [15]:(2)Mg2++C‐S‐H⟶M‐S‐H+Ca2+Figure 5
SEM and EDS images of the corroded concrete. (a) SEM; (b) EDS.
(a)
(b)The sidewall in bedrock section was casted by section; therefore, the bond between pouring blocks is weak, and a hydraulic pathway is formed at the construction joint. Because of a small flow of water and a mass of little cracks at the construction joint, the degeneration is aggravated by the internal crystallization of gypsum. As shown in Figure3, the dense layer above the compact concrete is thin (less than 1-2 mm), indicating that the gypsum from the supersaturated water is crystallized in very small amount. Thus, in the damaged part, it can only slightly accelerate the corrosion at the pouring joint and cannot be the main factor causing the degeneration.As the diffraction peak of ordinary aggregates, such as quartz, albite, and margarite, was not found in Figure4(b) and the major components of the dense layer are the same to the supersaturated salt in the aggressive water, the dense layer is supposed to be formed by the precipitation and crystallization from the supersaturated underground water. As shown in Figure 6, due to the compact microstructure of the dense layer, shaft concrete under the dense layer is barely corroded.Figure 6
SEM and EDS images of the dense layer. (a) SEM; (b) EDS.
(a)
(b)


## 3. Accelerated Corrosion Tests

If the corrosion condition in the laboratory test is completely the same as that in field, the corroded in-service structure will lose carrying capacity before the specimen failure occurs in the laboratory. Therefore, for typical metal and nonmetallic materials, there are corresponding standard accelerated corrosion test methods, by artificially creating more severe conditions, to obtain the degeneration law in a short period of time.


### 3.1. Experimental Procedure

#### 3.1.1. Materials and Specimen Preparation

Each pouring block needs to carry the gravity loads of the upper sidewall immediately after concrete mould is removed, so the NaCl-NaNO3-TEOA compound component was used as an early strength agent. Table 2 shows the mix proportion of the C30 shaft concrete.Table 2
Mix proportion of the shaft concrete (kg/m3).
Material
Water
Cement
Sand
Rock
NaCl
NaNO3
TEOA (triethanolamine)
Weight
176
400
620
1224
4
4
0.2PO 42.5R Portland cement, continuous grading crushed stone in size of 5–20 mm, and river sand of fineness modulus of 2.8 were adopted. The major performance of the cement is shown in Table3. NaCl, NaNO3, and TEOA were analytically pure, produced by Sinopharm Group Co. Ltd. Drinking water supply was used in the preparation of the samples.Table 3
The major performance of the PO 42.5R cement.
80μm sieve residue
Water requirement
Initial setting time
Final setting time
Flexural strength
Compressive strength
3 d
28 d
3 d
28 d
0.6%
0.268
180 min
320 min
3.5
7.5
25.2
48.4The specimens are 400 × 100 × 100 mm3 cuboids. A plastic board with 2 mm thickness, 100 mm width, and 40 mm height was used to create a notch in the middle of the specimens. The dimension of the concrete specimen is shown in Figure 7. The plastic board was removed in 6 hours. Form removal was carried out after 24 hours. Then, the specimens were cured at 20 ± 2°C and 95% relative humidity until the age of 28 days.Figure 7
Size of the specimens.


#### 3.1.2. Condition of the Accelerated Tests

Three accelerated corrosion tests were carried out including (1) immersion test with 9% sulfate solution; (2) immersion test with 15% sulfate solution; (3) wet-dry alternated test with 15% sulfate solution. In the immersion tests, the specimens were fully immersed in a sulfate solution. In the wet-dry alternated test, the NELD-LSC automatic sulfate dry-wet cycle testing machine was adopted. Each dry-wet cycle includes soaking in water for 16 h, drying at 80°C for 6 h, and cooling at room temperature for 2 h. Sulfate solutions were made by mixing sodium sulfate (Na2SO4) and magnesium sulfate (MgSO4). The mass ratio of sodium sulfate and magnesium sulfate is 4 : 1. The sulfate solution was replaced every 30 days to maintain full immersion and to ensure that the sulfate concentration was maintained.


#### 3.1.3. Characterization

The grouping and testing arrangements are shown in Table4. At each testing age, three specimens from each group were taken out for ultrasonic tests first, and then three-point bending tests were conducted. The surface of the broken samples was mechanically crushed and ground into a powder of about 300-mesh size. XRD measurements were performed on a Rigaku Ultima IV type X-ray powder diffractometer. Then, the external small pieces of the crushed samples were analyzed by using SEM and EDS.Table 4
Grouping and testing arrangement.
Group
Corrosion condition
Sulfate content (by mass)
Corrosion time (days)
0
60
90
120
150
A
Immerged in sulfate solution
9%
3
3
3
3
3
B
Immerged in sulfate solution
15%
—
3
3
3
3
C
Wet-dry alternated
15%
—
3
3
3
3In the three-point bending test, fracture strength testing machine manufactured by Toni Technik Co., Ltd., JM3840 dynamic and static collect system manufactured by Jing Ming Technology Co., Ltd., and YYJ-5/10 electronic extensometer manufactured by NCS Testing Technology Co., Ltd. were adopted. The load speed of loading was controlled by displacement (0.05 mm/min). Five strain gauges were placed on one side of the specimen to monitor the process of crack initiation, as shown in Figure8.Figure 8
Schematic diagram of the three-point bending test.
(a)
(b)Based on linear elastic fracture mechanics, Xu and Zhao [16] proposed a double-K fracture model, which has received the recommendation of China Electricity Council [17]. In double-K fracture model, two fracture parameters (initial fracture toughness KICQ and unstable fracture toughness KICS) were defined to capture the three stages of the fracture process in concrete. The initial fracture toughness KICQ is defined as the ability of a body to resist an external load before the appearance of crack propagation and the unstable fracture toughness. KICQ is defined as the ability to resist a maximum external load at critical fracture condition [18]. The unstable fracture toughness KICS and the elastic modules E of the concrete specimens could be calculated as follows:(3)KICS=1.5Pmax+mg/2×10−2×10−3⋅S⋅ac1/2th2fα,(4)fα=1.99−α1−α2.15−3.93α+2.7α21+2α1−α1.5,(5)α=ach,(6)ac=2πh+h0arctantECMODc32.6Pmax−0.11351/2−h0,(7)E=1tci3.70+32.60tan2π2a0+h0h+h0,where Pmax is the maximum load, kN; m is the weight of the specimen between the two supports, kg; t and h are the width and depth, respectively, of the specimen, m; a is the height to width ratio of the crack, constant; ac is the maximum crack opening displacement, m; a0 is the length of the crack, m; h0 is the blade thickness of electronic extensometer, m; CMODc is critical crack mouth opening displacement, μm; and ci is the slope at any point of linear segment, μm/kN.The NM-4B nonmetallic ultrasonic detector manufactured by Koncrete Co., Ltd. was adopted to obtain the degradation thickness of the specimens. The ultrasonic time is determined by the ultrasonic single side test method, as shown in Figure9. One of the ultrasonic transducers was fixed at a certain position. When the other one was placed at 50, 100, 150, 200, and 250 mm away, and the corresponding ultrasonic time was recorded.Figure 9
Diagram of the ultrasonic single side test method.Then, the degradation depth can be calculated as follows [19]:(8)dfc=L02va−vfva+vf,where vf is the ultrasonic velocity in the corroded layer, mm/μm; va is the ultrasonic velocity in the internal uncorroded concrete, mm/μm; and L0 is the turning point in the “ultrasonic time-distance” diagram, mm. Figure 10 is an example.Figure 10
Calculation chart forL0 (Group B, 60 days).


### 3.2. Corrosion Mechanism Analysis

Sulfate solution transports through the pore of concrete, resulting in chemical reactions between sulfate and cement hydration products. Expansive reaction products, such as ettringite and gypsum, generate high stress in the pore, causing spalling and cracking of the concrete. Some reaction products, such as M-S-H and magnesium hydroxide, are not expansive products, but are nonbinders. As concrete specimens with different corrosion mechanisms have different corrosion products and have different degeneration law, the degradation mechanism in the accelerated corrosion test should be the same as that responsible for the in-service deterioration [20]. XRD, SEM, and EDS analyses were performed on the corroded samples to analyze their corrosion mechanism, as shown in Figures 11 and 12.Figure 11
XRD results of corroded concrete (150 days). 1: Gypsum; 2: AFT; 3: quartz.Figure 12
SEM and EDS images of the specimen in the wet-dry alternated test (150 days). (a) SEM (50,000x magnification); (b) EDS.
(a)
(b)As shown in Figure11, the content of gypsum from high to low is Groups C, B, and A. A small amount of ettringite was found in Groups B and A. In the wet-dry alternated test, due to the adoration of sulfate solution in the pores during the “wet” process and the evaporation of the solution during the “dry” process, sulfate concentration in concrete pores is actually higher than that in the solution, which not only accelerates the corrosion rate of sulfate but also inhibits the occurrence of ettringite crystalline sulfate corrosion. But ettringite was not found in the field investigations. As can be seen from Figure 12, in the wet-dry alternated test, Ca2+ in C-S-H gel is also partly replaced by Mg2+ to form M-S-H, which is similar to field corrosion. Thus, wet-dry alternated accelerated corrosion experiment is more representative to the field corrosion.


### 3.3. Performance Degradation in Different Accelerated Tests

As shown in Figure13, the surfaces of the specimens immersed in 15% sulfate solution for 150 days are uneven and rough, the edges are slightly damaged, and some of the coarse aggregates are exposed. The specimen placed in the dry-wet cycle testing machine for 150 days is seriously corroded, especially at the edges, and the internal aggregates are exposed.Figure 13
Appearances of the corroded specimens (150 days). (a) Immersion test (15%); (b) wet-dry alternated test.
(a)
(b)


#### 3.3.1. Degradation Depth

During the process of sulfate corrosion, a series of corrosion reactions occur, causing the concrete surface loose. If the ultrasonic wave encounters the defect regions, such as cracks and holes, the propagation path will increase, resulting in the increase of ultrasonic time and the decrease of calculated ultrasonic velocity. Thus, the calculated ultrasonic velocity can be used to reflect the degradation degree of the corroded specimen.Figure14(a) shows the surface ultrasonic velocity of the concrete specimens. As the corrosion time is increased, the surface ultrasonic velocity of Group C exhibits a decreasing trend and it is much lower compare to the results from Groups A and B. At the corrosion time of 150 days, the surface velocities of Groups A, B, and C are 3.82, 3.56, and 2.14 km/s, respectively, decreased by 21.6%, 26.9%, and 43.9%. It seems that the corrosion degree of the corrosion layer in the wet-dry alternated experiment is much more serious than that in immersion tests.Figure 14
Surface ultrasonic velocity and degradation depth at different corrosion time. (a) Surface ultrasonic velocity; (b) degradation depth.
(a)
(b)Figure14(b) shows the degradation depth of the corroded specimens. In immersion tests, due to the filling of corrosion products in concrete pores, there is no obvious corrosion before 90 days. Then, the degradation depth increased steadily to the end the experiment. However, in the wet-dry alternated accelerated corrosion test, the degradation depth increased rapidly before 90 days. Then, with the corrosion time increasing, the growth started to flatten.


#### 3.3.2. Elastic Module and Unstable Fracture Toughness

Figure15 illustrates the results of elastic module E and unstable fracture toughness KICS of corroded specimens at different corrosion time.Figure 15
Elastic module and unstable fracture toughness at different corrosion time. (a) Elastic module; (b) unstable fracture toughness.
(a)
(b)It can be seen from Figure15(a) that, with corrosion time increasing, the elastic module of Group A and Group B increases at first and then gradually declines. Due to the high degradation rate, the elastic module of Group C has no increasing stage, and its decline speed is more rapid than Groups A and B. As shown in Figure 15(b), the unstable fracture toughness of Groups A, B, and C shows a similar decreasing trend during the early stages of corrosion. But after 90 days of corrosion, the decreasing trend of Group C is remarkable obvious, whereas, Groups A and B are slow.


## 3.1. Experimental Procedure

### 3.1.1. Materials and Specimen Preparation

Each pouring block needs to carry the gravity loads of the upper sidewall immediately after concrete mould is removed, so the NaCl-NaNO3-TEOA compound component was used as an early strength agent. Table 2 shows the mix proportion of the C30 shaft concrete.Table 2
Mix proportion of the shaft concrete (kg/m3).
Material
Water
Cement
Sand
Rock
NaCl
NaNO3
TEOA (triethanolamine)
Weight
176
400
620
1224
4
4
0.2PO 42.5R Portland cement, continuous grading crushed stone in size of 5–20 mm, and river sand of fineness modulus of 2.8 were adopted. The major performance of the cement is shown in Table3. NaCl, NaNO3, and TEOA were analytically pure, produced by Sinopharm Group Co. Ltd. Drinking water supply was used in the preparation of the samples.Table 3
The major performance of the PO 42.5R cement.
80μm sieve residue
Water requirement
Initial setting time
Final setting time
Flexural strength
Compressive strength
3 d
28 d
3 d
28 d
0.6%
0.268
180 min
320 min
3.5
7.5
25.2
48.4The specimens are 400 × 100 × 100 mm3 cuboids. A plastic board with 2 mm thickness, 100 mm width, and 40 mm height was used to create a notch in the middle of the specimens. The dimension of the concrete specimen is shown in Figure 7. The plastic board was removed in 6 hours. Form removal was carried out after 24 hours. Then, the specimens were cured at 20 ± 2°C and 95% relative humidity until the age of 28 days.Figure 7
Size of the specimens.


### 3.1.2. Condition of the Accelerated Tests

Three accelerated corrosion tests were carried out including (1) immersion test with 9% sulfate solution; (2) immersion test with 15% sulfate solution; (3) wet-dry alternated test with 15% sulfate solution. In the immersion tests, the specimens were fully immersed in a sulfate solution. In the wet-dry alternated test, the NELD-LSC automatic sulfate dry-wet cycle testing machine was adopted. Each dry-wet cycle includes soaking in water for 16 h, drying at 80°C for 6 h, and cooling at room temperature for 2 h. Sulfate solutions were made by mixing sodium sulfate (Na2SO4) and magnesium sulfate (MgSO4). The mass ratio of sodium sulfate and magnesium sulfate is 4 : 1. The sulfate solution was replaced every 30 days to maintain full immersion and to ensure that the sulfate concentration was maintained.


### 3.1.3. Characterization

The grouping and testing arrangements are shown in Table4. At each testing age, three specimens from each group were taken out for ultrasonic tests first, and then three-point bending tests were conducted. The surface of the broken samples was mechanically crushed and ground into a powder of about 300-mesh size. XRD measurements were performed on a Rigaku Ultima IV type X-ray powder diffractometer. Then, the external small pieces of the crushed samples were analyzed by using SEM and EDS.Table 4
Grouping and testing arrangement.
Group
Corrosion condition
Sulfate content (by mass)
Corrosion time (days)
0
60
90
120
150
A
Immerged in sulfate solution
9%
3
3
3
3
3
B
Immerged in sulfate solution
15%
—
3
3
3
3
C
Wet-dry alternated
15%
—
3
3
3
3In the three-point bending test, fracture strength testing machine manufactured by Toni Technik Co., Ltd., JM3840 dynamic and static collect system manufactured by Jing Ming Technology Co., Ltd., and YYJ-5/10 electronic extensometer manufactured by NCS Testing Technology Co., Ltd. were adopted. The load speed of loading was controlled by displacement (0.05 mm/min). Five strain gauges were placed on one side of the specimen to monitor the process of crack initiation, as shown in Figure8.Figure 8
Schematic diagram of the three-point bending test.
(a)
(b)Based on linear elastic fracture mechanics, Xu and Zhao [16] proposed a double-K fracture model, which has received the recommendation of China Electricity Council [17]. In double-K fracture model, two fracture parameters (initial fracture toughness KICQ and unstable fracture toughness KICS) were defined to capture the three stages of the fracture process in concrete. The initial fracture toughness KICQ is defined as the ability of a body to resist an external load before the appearance of crack propagation and the unstable fracture toughness. KICQ is defined as the ability to resist a maximum external load at critical fracture condition [18]. The unstable fracture toughness KICS and the elastic modules E of the concrete specimens could be calculated as follows:(3)KICS=1.5Pmax+mg/2×10−2×10−3⋅S⋅ac1/2th2fα,(4)fα=1.99−α1−α2.15−3.93α+2.7α21+2α1−α1.5,(5)α=ach,(6)ac=2πh+h0arctantECMODc32.6Pmax−0.11351/2−h0,(7)E=1tci3.70+32.60tan2π2a0+h0h+h0,where Pmax is the maximum load, kN; m is the weight of the specimen between the two supports, kg; t and h are the width and depth, respectively, of the specimen, m; a is the height to width ratio of the crack, constant; ac is the maximum crack opening displacement, m; a0 is the length of the crack, m; h0 is the blade thickness of electronic extensometer, m; CMODc is critical crack mouth opening displacement, μm; and ci is the slope at any point of linear segment, μm/kN.The NM-4B nonmetallic ultrasonic detector manufactured by Koncrete Co., Ltd. was adopted to obtain the degradation thickness of the specimens. The ultrasonic time is determined by the ultrasonic single side test method, as shown in Figure9. One of the ultrasonic transducers was fixed at a certain position. When the other one was placed at 50, 100, 150, 200, and 250 mm away, and the corresponding ultrasonic time was recorded.Figure 9
Diagram of the ultrasonic single side test method.Then, the degradation depth can be calculated as follows [19]:(8)dfc=L02va−vfva+vf,where vf is the ultrasonic velocity in the corroded layer, mm/μm; va is the ultrasonic velocity in the internal uncorroded concrete, mm/μm; and L0 is the turning point in the “ultrasonic time-distance” diagram, mm. Figure 10 is an example.Figure 10
Calculation chart forL0 (Group B, 60 days).


## 3.1.1. Materials and Specimen Preparation

Each pouring block needs to carry the gravity loads of the upper sidewall immediately after concrete mould is removed, so the NaCl-NaNO3-TEOA compound component was used as an early strength agent. Table 2 shows the mix proportion of the C30 shaft concrete.Table 2
Mix proportion of the shaft concrete (kg/m3).
Material
Water
Cement
Sand
Rock
NaCl
NaNO3
TEOA (triethanolamine)
Weight
176
400
620
1224
4
4
0.2PO 42.5R Portland cement, continuous grading crushed stone in size of 5–20 mm, and river sand of fineness modulus of 2.8 were adopted. The major performance of the cement is shown in Table3. NaCl, NaNO3, and TEOA were analytically pure, produced by Sinopharm Group Co. Ltd. Drinking water supply was used in the preparation of the samples.Table 3
The major performance of the PO 42.5R cement.
80μm sieve residue
Water requirement
Initial setting time
Final setting time
Flexural strength
Compressive strength
3 d
28 d
3 d
28 d
0.6%
0.268
180 min
320 min
3.5
7.5
25.2
48.4The specimens are 400 × 100 × 100 mm3 cuboids. A plastic board with 2 mm thickness, 100 mm width, and 40 mm height was used to create a notch in the middle of the specimens. The dimension of the concrete specimen is shown in Figure 7. The plastic board was removed in 6 hours. Form removal was carried out after 24 hours. Then, the specimens were cured at 20 ± 2°C and 95% relative humidity until the age of 28 days.Figure 7
Size of the specimens.


## 3.1.2. Condition of the Accelerated Tests

Three accelerated corrosion tests were carried out including (1) immersion test with 9% sulfate solution; (2) immersion test with 15% sulfate solution; (3) wet-dry alternated test with 15% sulfate solution. In the immersion tests, the specimens were fully immersed in a sulfate solution. In the wet-dry alternated test, the NELD-LSC automatic sulfate dry-wet cycle testing machine was adopted. Each dry-wet cycle includes soaking in water for 16 h, drying at 80°C for 6 h, and cooling at room temperature for 2 h. Sulfate solutions were made by mixing sodium sulfate (Na2SO4) and magnesium sulfate (MgSO4). The mass ratio of sodium sulfate and magnesium sulfate is 4 : 1. The sulfate solution was replaced every 30 days to maintain full immersion and to ensure that the sulfate concentration was maintained.


## 3.1.3. Characterization

The grouping and testing arrangements are shown in Table4. At each testing age, three specimens from each group were taken out for ultrasonic tests first, and then three-point bending tests were conducted. The surface of the broken samples was mechanically crushed and ground into a powder of about 300-mesh size. XRD measurements were performed on a Rigaku Ultima IV type X-ray powder diffractometer. Then, the external small pieces of the crushed samples were analyzed by using SEM and EDS.Table 4
Grouping and testing arrangement.
Group
Corrosion condition
Sulfate content (by mass)
Corrosion time (days)
0
60
90
120
150
A
Immerged in sulfate solution
9%
3
3
3
3
3
B
Immerged in sulfate solution
15%
—
3
3
3
3
C
Wet-dry alternated
15%
—
3
3
3
3In the three-point bending test, fracture strength testing machine manufactured by Toni Technik Co., Ltd., JM3840 dynamic and static collect system manufactured by Jing Ming Technology Co., Ltd., and YYJ-5/10 electronic extensometer manufactured by NCS Testing Technology Co., Ltd. were adopted. The load speed of loading was controlled by displacement (0.05 mm/min). Five strain gauges were placed on one side of the specimen to monitor the process of crack initiation, as shown in Figure8.Figure 8
Schematic diagram of the three-point bending test.
(a)
(b)Based on linear elastic fracture mechanics, Xu and Zhao [16] proposed a double-K fracture model, which has received the recommendation of China Electricity Council [17]. In double-K fracture model, two fracture parameters (initial fracture toughness KICQ and unstable fracture toughness KICS) were defined to capture the three stages of the fracture process in concrete. The initial fracture toughness KICQ is defined as the ability of a body to resist an external load before the appearance of crack propagation and the unstable fracture toughness. KICQ is defined as the ability to resist a maximum external load at critical fracture condition [18]. The unstable fracture toughness KICS and the elastic modules E of the concrete specimens could be calculated as follows:(3)KICS=1.5Pmax+mg/2×10−2×10−3⋅S⋅ac1/2th2fα,(4)fα=1.99−α1−α2.15−3.93α+2.7α21+2α1−α1.5,(5)α=ach,(6)ac=2πh+h0arctantECMODc32.6Pmax−0.11351/2−h0,(7)E=1tci3.70+32.60tan2π2a0+h0h+h0,where Pmax is the maximum load, kN; m is the weight of the specimen between the two supports, kg; t and h are the width and depth, respectively, of the specimen, m; a is the height to width ratio of the crack, constant; ac is the maximum crack opening displacement, m; a0 is the length of the crack, m; h0 is the blade thickness of electronic extensometer, m; CMODc is critical crack mouth opening displacement, μm; and ci is the slope at any point of linear segment, μm/kN.The NM-4B nonmetallic ultrasonic detector manufactured by Koncrete Co., Ltd. was adopted to obtain the degradation thickness of the specimens. The ultrasonic time is determined by the ultrasonic single side test method, as shown in Figure9. One of the ultrasonic transducers was fixed at a certain position. When the other one was placed at 50, 100, 150, 200, and 250 mm away, and the corresponding ultrasonic time was recorded.Figure 9
Diagram of the ultrasonic single side test method.Then, the degradation depth can be calculated as follows [19]:(8)dfc=L02va−vfva+vf,where vf is the ultrasonic velocity in the corroded layer, mm/μm; va is the ultrasonic velocity in the internal uncorroded concrete, mm/μm; and L0 is the turning point in the “ultrasonic time-distance” diagram, mm. Figure 10 is an example.Figure 10
Calculation chart forL0 (Group B, 60 days).


## 3.2. Corrosion Mechanism Analysis

Sulfate solution transports through the pore of concrete, resulting in chemical reactions between sulfate and cement hydration products. Expansive reaction products, such as ettringite and gypsum, generate high stress in the pore, causing spalling and cracking of the concrete. Some reaction products, such as M-S-H and magnesium hydroxide, are not expansive products, but are nonbinders. As concrete specimens with different corrosion mechanisms have different corrosion products and have different degeneration law, the degradation mechanism in the accelerated corrosion test should be the same as that responsible for the in-service deterioration [20]. XRD, SEM, and EDS analyses were performed on the corroded samples to analyze their corrosion mechanism, as shown in Figures 11 and 12.Figure 11
XRD results of corroded concrete (150 days). 1: Gypsum; 2: AFT; 3: quartz.Figure 12
SEM and EDS images of the specimen in the wet-dry alternated test (150 days). (a) SEM (50,000x magnification); (b) EDS.
(a)
(b)As shown in Figure11, the content of gypsum from high to low is Groups C, B, and A. A small amount of ettringite was found in Groups B and A. In the wet-dry alternated test, due to the adoration of sulfate solution in the pores during the “wet” process and the evaporation of the solution during the “dry” process, sulfate concentration in concrete pores is actually higher than that in the solution, which not only accelerates the corrosion rate of sulfate but also inhibits the occurrence of ettringite crystalline sulfate corrosion. But ettringite was not found in the field investigations. As can be seen from Figure 12, in the wet-dry alternated test, Ca2+ in C-S-H gel is also partly replaced by Mg2+ to form M-S-H, which is similar to field corrosion. Thus, wet-dry alternated accelerated corrosion experiment is more representative to the field corrosion.


## 3.3. Performance Degradation in Different Accelerated Tests

As shown in Figure13, the surfaces of the specimens immersed in 15% sulfate solution for 150 days are uneven and rough, the edges are slightly damaged, and some of the coarse aggregates are exposed. The specimen placed in the dry-wet cycle testing machine for 150 days is seriously corroded, especially at the edges, and the internal aggregates are exposed.Figure 13
Appearances of the corroded specimens (150 days). (a) Immersion test (15%); (b) wet-dry alternated test.
(a)
(b)


### 3.3.1. Degradation Depth

During the process of sulfate corrosion, a series of corrosion reactions occur, causing the concrete surface loose. If the ultrasonic wave encounters the defect regions, such as cracks and holes, the propagation path will increase, resulting in the increase of ultrasonic time and the decrease of calculated ultrasonic velocity. Thus, the calculated ultrasonic velocity can be used to reflect the degradation degree of the corroded specimen.Figure14(a) shows the surface ultrasonic velocity of the concrete specimens. As the corrosion time is increased, the surface ultrasonic velocity of Group C exhibits a decreasing trend and it is much lower compare to the results from Groups A and B. At the corrosion time of 150 days, the surface velocities of Groups A, B, and C are 3.82, 3.56, and 2.14 km/s, respectively, decreased by 21.6%, 26.9%, and 43.9%. It seems that the corrosion degree of the corrosion layer in the wet-dry alternated experiment is much more serious than that in immersion tests.Figure 14
Surface ultrasonic velocity and degradation depth at different corrosion time. (a) Surface ultrasonic velocity; (b) degradation depth.
(a)
(b)Figure14(b) shows the degradation depth of the corroded specimens. In immersion tests, due to the filling of corrosion products in concrete pores, there is no obvious corrosion before 90 days. Then, the degradation depth increased steadily to the end the experiment. However, in the wet-dry alternated accelerated corrosion test, the degradation depth increased rapidly before 90 days. Then, with the corrosion time increasing, the growth started to flatten.


### 3.3.2. Elastic Module and Unstable Fracture Toughness

Figure15 illustrates the results of elastic module E and unstable fracture toughness KICS of corroded specimens at different corrosion time.Figure 15
Elastic module and unstable fracture toughness at different corrosion time. (a) Elastic module; (b) unstable fracture toughness.
(a)
(b)It can be seen from Figure15(a) that, with corrosion time increasing, the elastic module of Group A and Group B increases at first and then gradually declines. Due to the high degradation rate, the elastic module of Group C has no increasing stage, and its decline speed is more rapid than Groups A and B. As shown in Figure 15(b), the unstable fracture toughness of Groups A, B, and C shows a similar decreasing trend during the early stages of corrosion. But after 90 days of corrosion, the decreasing trend of Group C is remarkable obvious, whereas, Groups A and B are slow.


## 3.3.1. Degradation Depth

During the process of sulfate corrosion, a series of corrosion reactions occur, causing the concrete surface loose. If the ultrasonic wave encounters the defect regions, such as cracks and holes, the propagation path will increase, resulting in the increase of ultrasonic time and the decrease of calculated ultrasonic velocity. Thus, the calculated ultrasonic velocity can be used to reflect the degradation degree of the corroded specimen.Figure14(a) shows the surface ultrasonic velocity of the concrete specimens. As the corrosion time is increased, the surface ultrasonic velocity of Group C exhibits a decreasing trend and it is much lower compare to the results from Groups A and B. At the corrosion time of 150 days, the surface velocities of Groups A, B, and C are 3.82, 3.56, and 2.14 km/s, respectively, decreased by 21.6%, 26.9%, and 43.9%. It seems that the corrosion degree of the corrosion layer in the wet-dry alternated experiment is much more serious than that in immersion tests.Figure 14
Surface ultrasonic velocity and degradation depth at different corrosion time. (a) Surface ultrasonic velocity; (b) degradation depth.
(a)
(b)Figure14(b) shows the degradation depth of the corroded specimens. In immersion tests, due to the filling of corrosion products in concrete pores, there is no obvious corrosion before 90 days. Then, the degradation depth increased steadily to the end the experiment. However, in the wet-dry alternated accelerated corrosion test, the degradation depth increased rapidly before 90 days. Then, with the corrosion time increasing, the growth started to flatten.


## 3.3.2. Elastic Module and Unstable Fracture Toughness

Figure15 illustrates the results of elastic module E and unstable fracture toughness KICS of corroded specimens at different corrosion time.Figure 15
Elastic module and unstable fracture toughness at different corrosion time. (a) Elastic module; (b) unstable fracture toughness.
(a)
(b)It can be seen from Figure15(a) that, with corrosion time increasing, the elastic module of Group A and Group B increases at first and then gradually declines. Due to the high degradation rate, the elastic module of Group C has no increasing stage, and its decline speed is more rapid than Groups A and B. As shown in Figure 15(b), the unstable fracture toughness of Groups A, B, and C shows a similar decreasing trend during the early stages of corrosion. But after 90 days of corrosion, the decreasing trend of Group C is remarkable obvious, whereas, Groups A and B are slow.


## 4. Service Life Prediction

Damage of concrete under sulfate attack proceeds from the surface, thus the damage degree of a structure can be expressed as a function of the degradation depth [21]. The acceleration corrosion factor (ACF) is the ratio of service time to accelerated time corresponding to the same degradation depth [22]. Accelerated testing programs, if properly designed, performed, and interpreted, can help predict the performance and service life of concrete [20, 23, 24].As described in Section2, for the wet-dry alternated accelerated test, not only the degradation rate is much faster than immersion test but also the degradation process is more similar to the field corrosion. However, due to limited specimen size and test condition, after 150 days of corrosion, the degradation depth in the wet-dry alternated test is just 17 mm and is much lower than the current corrosion depth of the sidewall (55 mm at −271 m). It will take too much time and money in the laboratory to reach the same degradation depth that causes the failure of the sidewall. Therefore, combing with limited corrosion data, a modified theoretical model was applied to develop a long-run degradation depth function to estimate the residual life of the corroded sidewall.The three major damaged parts are not far from one another, and the properties of nearby strata are similar. Thus, the computation of shaft sidewall reliability can be transferred to compute the most dangerous structure member reliability.


### 4.1. Degradation Depth Prediction Function

Based on Fick’s law of diffusion, Li et al. [25] proposed a time-varying model to represent the degradation process:(9)d0=2DCstn,where d0 is degradation depth, mm; D is diffusion coefficient of internal concrete, mm2/d; Cs is concentration of sulfate at the surface of the concrete, mol/L; t is corrosion time, d; and n is sulfate absolute capacity, mol/L.In a report from the US Bureau of Reclamation [24], the rate of the performance deterioration of concrete caused by the wet-dry alternated accelerated test was eight times that of the concrete caused by pure soaking. Zhou et al. [26] proposed that the acceleration effect of wet-dry cycles on the rate of sulfate diffusion can be simply equivalent to the amplification adjustment of the diffusion coefficient. Thus, we define η as the coefficient of influence of wet-dry cycles on the diffusion coefficient of concrete. Substituting it in (7), it yields(10)d0=2ηDCstn.Thus, the long-term degradation depth function of the wet-dry alternated tests is(11)d0=1.818t.The acceleration corrosion factor, ACF, which can be assumed to be a constant, can be obtained from [20]:(12)ACF=RATRLT,where RAT is the degradation rate of the specimens in accelerated tests, mm/d, and RLT is the degradation rate of the in-service structure, mm/d.As the shaft sidewall has been in-service for 26 years (9490 d) and the degradation depth at −271 m is 55 mm, the ACF is 5.702. The relationship between the degradation depth of shaft sidewalldc in mm and service time T in days is as follows:(13)dc=0.319T.


### 4.2. Limit State Function of Shaft Sidewall

The external forces on the shaft sidewall mainly contain horizontal forcePh and vertical force Pv: (1) Ph includes formation and water pressure, and (2) Pv includes the deadweight of the superstructure and additional force caused by soil settling [27].The radial pressure on the outer shaft wall can be calculated with the following formula [28]:(14)P=∑i=1nγighiAi,where γi is the bulk density of ith strata, kg/m3; g is gravitational acceleration, 10 N/kg; hi is the thickness of ith strata, m; and Ai is the lateral pressure coefficient of ith strata.According to Ni [29] and Zhang [30], the average bulk density and the lateral pressure coefficient can be assumed to be 2300 kg/m3 and 0.164, respectively. Thus, the lateral pressure on the sidewall at −271 m is 1.06 MPa.Compared with the gravity of the shaft sidewall, the equipment weight is very small and can be generally ignored. Bedrock is hard to be compressed, and the vertical pressure is as follows:(15)Pv=γgH,where γ is the bulk density of shaft sidewall, kg/m3, and H is the depth, m.The average bulk density is assumed to be 2400 kg/m3, thus the vertical pressure on the sidewall at −271 m is 6.50 MPa.Only when the ratio of vertical and horizontal stress,Pv/Ph, is greater than 10, the failure of the shaft wall is dominated by the vertical stress [31]. As the Pv/Ph is 6.13, the performance function can be simplified to consist of horizontal resistance and horizontal load.The cross section of the shaft wall is symmetrical in shape and forces, the relationship between radial forceσr and circumferential force σθ can be described as dσr/dr+σr−σθ/r=0. Thus,(16)σr=1−r1rσθ.The sidewall concrete is reinforced by the confining pressure. According to lots of test data, the ultimate strength of the shaft sidewall can be described as follows [32]:(17)σθ−Kσr=fc,where fc is the axial compressive strength of concrete, MPa, and K is strengthening coefficient. It can be calculated from the formula K=0.8896λ−1.2708fc0.2639 or chosen based on experience (2.2–3.0).By substituting (17) in (16), the radial force σr can be calculated as follows:(18)σr=1−r1/rfc1−1−r1/rK.When the radial force reaches the ultimate bearing capacity of the shaft sidewall, the load-carrying resistance is(19)R=1−r1/r2fc1−1−r1/r2K,where r1 is the inner radius of the shaft sidewall, m, and r2 is the outer radius of the shaft sidewall, m.We assume that the strengthening coefficientK is 2.5, and the limit state function can be calculated as follows:(20)Z=fc1−r1+dc/r21−2.51−r1+dc/r2−γghA,where dc is the degradation depth, mm.


### 4.3. Reliability Index of Corroded Sidewall

The limit state can been expanded using Taylor’s series, and if only the first order terms are retained, ifX = [fc, dc, γ, A]T, we get(21)Z=gX≈gμX+∂g∂XX=μXTX−μX.The variablesfc, dc, γ, and A can be assumed to be statistically independent, and then the mean and variance of Z are then approximated by(22)μZ=gμfc,μdc,μγ,μA,σZ=bT∑Xb1/2,b=∂g∂XX=μX.Then, the reliability index of the shaft sidewall at −271 m is(23)β=μZσZ.The analysis of the reservation test block shows that the strength of the shaft concrete is distributed normally, the average axial compressive strength is 17.00 MPa, and the variation coefficient is 0.1374 [33]. The variation coefficient of the degradation depth is assumed to be 0.1 [34]. The mean values of the lateral pressure coefficient and bulk density are 0.164 and 2300 kg/m3, respectively. As the geotechnical mechanics parameters are hard to calculate accurately [35], the variation coefficients of the lateral pressure coefficient and bulk density are assumed to be 0.20 and 0.15, respectively.After calculation, the reliability indexes and degradation depths at different corrosion time are shown in Figure16. The target reliability index of bearing capacity limited state, which is recommended by MOHURD (Ministry of Housing and Urban-Rural Development of the People’s Republic of China), is shown in Table 5 [36].Figure 16
Reliability index and degradation depth at different service time.Table 5
Target reliability index of bearing capacity limit state.
Importance of structure
Class I
Class II
Class III
Ductile failure
3.7
3.2
2.7
Brittle failure
4.2
3.7
3.2The sidewall is subjected to a multidirectional pressure, so the failure mode of the shaft sidewall can be assumed to be ductile failure. The auxiliary shaft undergoes a routine check on a daily basis, and the failure risk can be identified with a timely fashion. As the lives of thousands of workers depend on it, the target reliability is set as 3.2. At present, the service time of the shaft sidewall is 26 years, and the reliability index is 3.50. It is safe now, but with the service time increasing, the reliability index will unavoidably decrease. When the reliability index reduces to 3.20, the service time will be 51 years. It is obvious that there is no need to reinforce in the next 25 years.


## 4.1. Degradation Depth Prediction Function

Based on Fick’s law of diffusion, Li et al. [25] proposed a time-varying model to represent the degradation process:(9)d0=2DCstn,where d0 is degradation depth, mm; D is diffusion coefficient of internal concrete, mm2/d; Cs is concentration of sulfate at the surface of the concrete, mol/L; t is corrosion time, d; and n is sulfate absolute capacity, mol/L.In a report from the US Bureau of Reclamation [24], the rate of the performance deterioration of concrete caused by the wet-dry alternated accelerated test was eight times that of the concrete caused by pure soaking. Zhou et al. [26] proposed that the acceleration effect of wet-dry cycles on the rate of sulfate diffusion can be simply equivalent to the amplification adjustment of the diffusion coefficient. Thus, we define η as the coefficient of influence of wet-dry cycles on the diffusion coefficient of concrete. Substituting it in (7), it yields(10)d0=2ηDCstn.Thus, the long-term degradation depth function of the wet-dry alternated tests is(11)d0=1.818t.The acceleration corrosion factor, ACF, which can be assumed to be a constant, can be obtained from [20]:(12)ACF=RATRLT,where RAT is the degradation rate of the specimens in accelerated tests, mm/d, and RLT is the degradation rate of the in-service structure, mm/d.As the shaft sidewall has been in-service for 26 years (9490 d) and the degradation depth at −271 m is 55 mm, the ACF is 5.702. The relationship between the degradation depth of shaft sidewalldc in mm and service time T in days is as follows:(13)dc=0.319T.


## 4.2. Limit State Function of Shaft Sidewall

The external forces on the shaft sidewall mainly contain horizontal forcePh and vertical force Pv: (1) Ph includes formation and water pressure, and (2) Pv includes the deadweight of the superstructure and additional force caused by soil settling [27].The radial pressure on the outer shaft wall can be calculated with the following formula [28]:(14)P=∑i=1nγighiAi,where γi is the bulk density of ith strata, kg/m3; g is gravitational acceleration, 10 N/kg; hi is the thickness of ith strata, m; and Ai is the lateral pressure coefficient of ith strata.According to Ni [29] and Zhang [30], the average bulk density and the lateral pressure coefficient can be assumed to be 2300 kg/m3 and 0.164, respectively. Thus, the lateral pressure on the sidewall at −271 m is 1.06 MPa.Compared with the gravity of the shaft sidewall, the equipment weight is very small and can be generally ignored. Bedrock is hard to be compressed, and the vertical pressure is as follows:(15)Pv=γgH,where γ is the bulk density of shaft sidewall, kg/m3, and H is the depth, m.The average bulk density is assumed to be 2400 kg/m3, thus the vertical pressure on the sidewall at −271 m is 6.50 MPa.Only when the ratio of vertical and horizontal stress,Pv/Ph, is greater than 10, the failure of the shaft wall is dominated by the vertical stress [31]. As the Pv/Ph is 6.13, the performance function can be simplified to consist of horizontal resistance and horizontal load.The cross section of the shaft wall is symmetrical in shape and forces, the relationship between radial forceσr and circumferential force σθ can be described as dσr/dr+σr−σθ/r=0. Thus,(16)σr=1−r1rσθ.The sidewall concrete is reinforced by the confining pressure. According to lots of test data, the ultimate strength of the shaft sidewall can be described as follows [32]:(17)σθ−Kσr=fc,where fc is the axial compressive strength of concrete, MPa, and K is strengthening coefficient. It can be calculated from the formula K=0.8896λ−1.2708fc0.2639 or chosen based on experience (2.2–3.0).By substituting (17) in (16), the radial force σr can be calculated as follows:(18)σr=1−r1/rfc1−1−r1/rK.When the radial force reaches the ultimate bearing capacity of the shaft sidewall, the load-carrying resistance is(19)R=1−r1/r2fc1−1−r1/r2K,where r1 is the inner radius of the shaft sidewall, m, and r2 is the outer radius of the shaft sidewall, m.We assume that the strengthening coefficientK is 2.5, and the limit state function can be calculated as follows:(20)Z=fc1−r1+dc/r21−2.51−r1+dc/r2−γghA,where dc is the degradation depth, mm.


## 4.3. Reliability Index of Corroded Sidewall

The limit state can been expanded using Taylor’s series, and if only the first order terms are retained, ifX = [fc, dc, γ, A]T, we get(21)Z=gX≈gμX+∂g∂XX=μXTX−μX.The variablesfc, dc, γ, and A can be assumed to be statistically independent, and then the mean and variance of Z are then approximated by(22)μZ=gμfc,μdc,μγ,μA,σZ=bT∑Xb1/2,b=∂g∂XX=μX.Then, the reliability index of the shaft sidewall at −271 m is(23)β=μZσZ.The analysis of the reservation test block shows that the strength of the shaft concrete is distributed normally, the average axial compressive strength is 17.00 MPa, and the variation coefficient is 0.1374 [33]. The variation coefficient of the degradation depth is assumed to be 0.1 [34]. The mean values of the lateral pressure coefficient and bulk density are 0.164 and 2300 kg/m3, respectively. As the geotechnical mechanics parameters are hard to calculate accurately [35], the variation coefficients of the lateral pressure coefficient and bulk density are assumed to be 0.20 and 0.15, respectively.After calculation, the reliability indexes and degradation depths at different corrosion time are shown in Figure16. The target reliability index of bearing capacity limited state, which is recommended by MOHURD (Ministry of Housing and Urban-Rural Development of the People’s Republic of China), is shown in Table 5 [36].Figure 16
Reliability index and degradation depth at different service time.Table 5
Target reliability index of bearing capacity limit state.
Importance of structure
Class I
Class II
Class III
Ductile failure
3.7
3.2
2.7
Brittle failure
4.2
3.7
3.2The sidewall is subjected to a multidirectional pressure, so the failure mode of the shaft sidewall can be assumed to be ductile failure. The auxiliary shaft undergoes a routine check on a daily basis, and the failure risk can be identified with a timely fashion. As the lives of thousands of workers depend on it, the target reliability is set as 3.2. At present, the service time of the shaft sidewall is 26 years, and the reliability index is 3.50. It is safe now, but with the service time increasing, the reliability index will unavoidably decrease. When the reliability index reduces to 3.20, the service time will be 51 years. It is obvious that there is no need to reinforce in the next 25 years.


## 5. Conclusions

(1)
In the aggressive underground water of Lin-Huan coal mine, gypsum is supersaturated. When the aggressive water flows on the compact concrete, a dense layer formed by the crystallized precipitations protects it against sulfate attack. By contrast, the degradation of the part where water flows through pouring joints is aggravated by the internal crystallization of gypsum.
(2)
Apart from the internal crystallization of gypsum, the degradation of the damaged part is caused by the formation of expansive gypsum and incohesive M-S-H. The wet-dry alternated and immersion tests indicate that not only the degradation rate of the wet-dry alternated test is much faster than immersion test but also its degradation process is more similar to the corroded sidewall.
(3)
For an in-service structure exposed to sulfate environment, degradation depth is best suited for evaluating the damage degree and calculating the residual life. Since the specimens in the laboratory are smaller than the field structure, the corrosion degree that makes the in-service structure unstable is very difficult to be achieved in the laboratory test.To solve this problem, in this paper, based on a modified theoretical model, combining with the limit data form the wet-dry alternated tests and field investigations, the remaining service life of the shaft sidewall is estimated. The results indicate that the service life of the auxiliary shaft of Lin-Huan coal mine is 51 years, and there is no need to reinforce in the next 25 years.



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*Source: 3038685-2018-07-03.xml*