As coal resources must be mined from ever deeper seams, highstrength, highperformance concrete shaft linings are required to resist the load of the soil surrounding the deep freezing well. In order to determine the optimal concrete mix for the unique conditions experienced by such highstrength highperformance reinforced concrete shaft lining (HSHPRCSL) structures in deep freezing wells, an experimental evaluation of scaled HSHPRCSL models was conducted using hydraulic pressure load tests. It was observed that as the specimens ruptured, plastic bending of the circumferential reinforcement occurred along the failure surface, generated by compressionshear failure. These tests determined that HSHPRCSL capacity was most affected by the ultimate concrete uniaxial compressive strength and the thicknessdiameter ratio and least affected by the reinforcement ratio. The experimental results were then used to derive fitting equations, which were compared with the results of theoretical expressions derived using the threeparameter strength criterion for the ultimate bearing capacity, stress, radius, and load in the elastic and plastic zones. The proposed theoretical equations yielded results within 8% of the experimentally fitted results. Finally, the finite element analysis method is used to verify the abovementioned results, and all errors are less than 12%, demonstrating reliability for use as a theoretical design basis for deep HSHPRCSL structures.
As the more accessible portions of coal resources near the surface are gradually depleted in large coal producing Chinese provinces such as Hebei, Henan, Shandong, and Anhui, it is necessary to mine deeper coal seams. As mines are constructed deeper, the alluvium traversed by the shaft lining becomes thicker and thicker. For example, the Wanfu Mine, currently under construction at the Juye Coalfield in Shandong, and the Kouzixi Mine, being planned for the Zhangou Coalfield in Anhui, will traverse 600–800 m of overlying ground. This, naturally, results in an increase in the ground pressure acting on the shaft lining. To resist strong frost heave pressure and permanent load acting on the freezing shaft lining in such deep alluvium, it is necessary to provide a highstrength shaft lining structure [
Although C60–C80 grade HSHPC has been used in China in bridge, water conservation, and highrise building projects, the construction environment and performance requirements of these HSHPCs are quite different from those required of deepalluvium freezing shaft lining concrete. Because the thickness of the inner and outer shaft lining increases from about 0.7 m in shallow strata to about 1.2 m in deep strata, the use of HSHPC in these deep structures is classified as a mass concrete project, and accordingly the control of cracking is a significant challenge during the construction process. To ensure the safety of the wellbore as it is sunk to such depths, the average design temperature of the freezing wall is reduced from about −10°C to about −15°C. As the temperature of the freezing wellbore is decreased, the difference between the internal and external temperature of the shaft lining concrete increases, resulting in a deterioration of the concrete curing environment. Generally, when constructing a shaft lining in deep alluvium using a freezing wellbore, the concrete should have high strength, high impermeability, and good workability [
Domestic and foreign scholars alike have conducted a great deal of research into concrete shaft linings [
In view of the current state of HSHPRCSL research and according to the special curing environment and construction conditions of deep freezing shaft linings, in this study, the qualities of different mix ratios are evaluated in preparation tests of C60–C80 HSHPC to obtain an optimal mix. According to the stress characteristics of the inner shaft lining of a deep freezing well, the mechanical properties and failure characteristics of the HSHPRCSL structure are then studied using model tests and theoretical calculations. A threeparameter strength criterion conforming to the strength characteristics of the concrete is then adopted to derive an analytical expression for the ultimate bearing capacity and stress distribution in the elastic and plastic zones of an HSHPRCSL structure. Finally, the finite element analysis method is used to verify the abovementioned results. The resulting conclusions provide a design basis for the engineering application of HSHPC in deep freezing shaft lining structures.
Highstrength, highperformance concrete possesses excellent properties before and after hardening that are provided by mixing a fine active admixture and highefficiency compound waterreducing agent under conditions of low cement content and low watercement ratio. These properties generally include high workability, high impermeability, high volume stability (no cracking during hardening and smaller shrinkage and creep), high strength (above C30 grade), the maintenance of continuous growth in longterm strength, and ultimately excellent durability when subjected to a harsh environment. In view of the special curing environment and construction conditions of the inner shaft lining of a freezing shaft in deep alluvium, the inner shaft lining concrete should possess high strength, crack resistance, seepage prevention, and high early strength to prevent leakage of the shaft lining after the thawing of the frozen wall. Therefore, the preparation of HSHPC for an inner shaft lining should address the following principle qualities:
Ultrahigh early strength with which concrete can be demoulded 10 hours after pouring
Simple preparation process
Good workability and a slump greater than 180 mm, which is convenient for transportation and pouring
Low hydration heat and high durability
High volume stability and high impermeability
Various factors affecting the strength, fluidity, and durability of HSHPC include the variety and dosage of cement, the mix ratio of the concrete, the variety and dosage of admixtures and externally mixed active materials, the aggregate gradation, the construction process, and the environmental conditions at the site. In general, the common mix for grade C60 HSHPC and above consists of a highgrade cement, superplasticiser (with a water reduction rate greater than or equal to 35%), mineral admixture, high quality aggregate, and controlled sand content.
The C60–C80 HSHPC evaluated in this study used Conch brand P.O. 42.5R and P.O. 52.5R early strength ordinary Portland cement with lower relative hydration heats, produced by Ningguo Cement Factory. The early strength and low heat of hydration properties of this cement make it especially suitable for the preparation of HSHPC for use in freezing shaft linings in deep alluvium.
The fine aggregate used in this study was Huaibin medium sand from Henan Province with a fineness modulus of 2.9, a bulk density of 1540 kg/m^{3}, and a mud content of 1.6%. The coarse aggregate used was Shangyao limestone gravel from Huainan City and Mingguang basalt from Chuzhou City, both in Anhui Province, which have a crushing index of 8.3% and 3.3%, respectively, and a continuous grain size grade of 5–31.5 mm.
In consideration of the special use environment of HSHPC in shaft linings, it is critical that an admixture be selected that provides excellent performance with the raw materials in the mix. A compatibility test was accordingly conducted by evaluating eight types of highefficiency composite waterreducing agents (superplasticisers). In the end, an NF naphthalenebased superplasticiser produced by Huainan Mining Group Synthetic Material Co., Ltd., was selected for use in the experiments due to its good compatibility with the other materials in the mix.
The mineral admixtures used in the experiments were a silicon powder produced by Shanxi Dongyi Ferroalloy Factory, a ground slag produced by Hefei Iron and Steel Group of Jinjiang Building Materials Co., Ltd., and a Grade I fly ash produced by Huainan Pingwei Power Plant. The main chemical components of the silicon powder and ground slag are provided in Table
Chemical composition of silicon powder and ground slag (%).
Component  SiO_{2}  Al_{2}O_{3}  Fe_{2}O_{3}  CaO  MgO  SO_{3} 

Silicon powder  92.6  0.78  0.59  0.8  1.0  0.81 
Ground slag  35.3  8.93  1.26  42.2  6.9  2.0 
The type of silicon powder used in this study contained extremely fine particles consistent with an ultrafine solid material with ultrafine characteristics. The SiO_{2} content of the silicon powder was greater than 90%, its average particle size was 0.1–0.15
According to the specification for the design of concrete mixes, the mixing strengths of C60, C65, C70, C75, and C80 concrete are 69.8, 74.8, 79.8, 84.8, and 89.8 MPa, respectively. Using the orthogonal testing method, the C60–C80 concrete mix proportions shown in Table
Mix ratios of C60, C65, C70, C75, and C80 HSHPC.
Specimen number  Strength grade  Cement : sand : stone : water : mineral admixture (kg)  Cementitious materials (kg)  Waterbinder ratio  Sand ratio (%)  Admixture dosage (%) 

1  C60  410 : 628.0 : 1166.3 : 151.2 : 130  540  0.280  35  NF1.8 
2  C65  410 : 625.5 : 1161.6 : 152.6 : 145  555  0.275  35  NF1.8 
3  C70  410 : 620.0 : 1151.4 : 145.6 : 150  560  0.260  35  NF1.9 
4  C75  420 : 622.5 : 1156.1 : 144.1 : 145  565  0.255  35  NF2.0 
5  C80  430 : 616.6 : 1145.1 : 146.3 : 155  585  0.250  35  NF2.0 
Compressive strength tests were conducted on the mixes detailed in Table
HSHPC strength test results.
Specimen number  Design strength grade  Slump (mm)  Compressive strength of cube specimen (MPa)  

3 d  7 d  28 d  
1  C60  206  57.6  63.7  70.4 
2  C65  213  60.7  69.8  75.8 
3  C70  195  64.2  72.7  79.5 
4  C75  210  69.5  78.2  85.3 
5  C80  205  73.2  81.4  90.1 
Given the highstrength and large size of an HSHPRCSL structure, destructive tests on a prototype shaft lining were determined to be prohibitively difficult to implement. As a result, scale models of a shaft lining structure were tested in this study.
The objective of the model tests was not only to determine the stress distribution within the shaft lining section but also to measure the failure load of the shaft lining. Therefore, the shaft lining model design must not only be subjected to scaled stress and deformation but also to a scaled load via a similarity index. Using similarity theory and the basic equations of elasticity, this study applied the equation analysis method [
The similarity conditions of the stress and deformation in the shaft lining model can be obtained from the geometric equations, boundary equations, and physical equations as follows:
The HSHPRCSL is a composite structure composed of two materials, steel and concrete, so in order to ensure that the stress and deformation of each component of the model and the prototype are strictly comparable, it is necessary to maintain geometric similarity between the model and prototype of shaft lining before, throughout, and after loading and deformation; accordingly,
In order to ensure that the load and shape of the shaft lining model are identical to those of the prototype at the time of failure, the stressstrain behaviour of the model in the elastic state must be similar to that of the prototype in the elastic state. Accordingly, the following strength requirements should be met:
The stressstrain curves of the shaft lining model and prototype should be similar throughout the loading process
The strength of the materials in each part of the shaft lining should be similar to each other
The strength criteria for the damage of the model and prototype shaft lining should be similar
To fully meet the required conditions of similarity, it is preferable that the materials proposed for the prototype shaft lining structure be used in the model test. Therefore, the structural material of the shaft lining model was adjusted in the experiment as follows:
In this case, the appropriate geometric similarity constant is the only variable that needs to be determined. In order to make the study results universal, instead of using a specific shaft lining as the simulation object, the simulation was concerned with the effects of the thicknessdiameter ratio
Model parameters.
Model 






A1  380.5  462.5  0.216  0.9  65.3 
A2  380.5  462.5  0.216  1.2  72.2 
A3  380.5  462.5  0.216  0.6  76.8 
A4  385  462.5  0.201  1.38  67.9 
A5  385  462.5  0.201  1.38  74.2 
A6  385  462.5  0.201  1.38  79.3 
A7  379.5  462.5  0.219  0.7  62.2 
A8  379.5  462.5  0.219  0.7  78.3 
Note:
Shaft lining structure model (unit: mm).
To ensure good quality, the shaft lining models were cast using professional formwork. To provide consistent boundary conditions under load, the top and bottom faces of the model were processed using a lathe to obtain a high finish after pouring. The shaft lining model loading tests were conducted using a highload hydraulic loading device, shown in Figure
Shaft lining model loading device.
Schematic diagram of shaft lining model loading device.
The compressive strengths of the HSHPC mixes were determined by three standard cube compression tests for each model mix, with the average values reported in Table
Layout of reinforcing mesh and measurement points of shaft lining model.
Shaft lining model and concrete surface measurement points.
According to the Code for the Design of Concrete Structures [
Normal distribution of concrete compressive strength.
If the total area under the curve in Figure
Coefficient of variation of concrete strength (%) [
Strength grade  C15  C20  C25  C30  C35  C40  C45  C50  C55  C60–C80 


23.3  20.6  18.9  17.2  16.4  15.6  15.6  14.9  14.9  14.1 
Considering the difference between the actual strength of the HSHPRCSL and the concrete strength determined by the cube test, past experience, and test data analysis and in reference to the relevant design code provisions of other countries [
The ratio of prism compressive strength to axial compressive strength,
Because highstrength concrete is more brittle than conventional concrete, in order to ensure the safety of the structure, a brittleness reduction factor,
According these provisions, the standard value of the concrete axial compressive strength can be obtained as follows, with the results shown in Table
Standard value of axial concrete compressive strength (MPa) [
Strength grade  C15  C20  C25  C30  C35  C40  C45  C50  C55  C60  C65  C70  C75  C80 


10.0  13.4  16.7  20.1  23.4  26.8  29.6  32.4  35.5  38.5  41.5  44.5  47.4  50.2 
The standard axial tensile strength
Standard value of axial concrete tensile strength (MPa) [
Strength grade  C15  C20  C25  C30  C35  C40  C45  C50  C55  C60  C65  C70  C75  C80 


1.27  1.54  1.78  2.01  2.20  2.39  2.51  2.64  2.74  2.85  2.93  2.99  3.05  3.11 
The biaxial strength envelope of the concrete is a closed curve composed of four segments, shown in Figure
Strength envelope diagram of biaxial stress in concrete.
For convenience of calculation, the biaxial compressive strengths indicated in Figure
Compressive strength of concrete under biaxial compression [

1.0  1.05  1.10  1.15  1.20  1.25  1.29  1.25  1.20  1.16 

0  0.07  0.16  0.25  0.36  0.50  0.88  1.03  1.11  1.16 
The experimentally determined ultimate bearing capacities (
Comparison of theoretically, experimentally, and numerically determined HSHPRCSL plastic ultimate bearing capacity.
Model 









A1  65.3  49.19  31.85  2.62  40.26  17.0  17.51  18.72 
A2  72.2  54.98  35.44  2.74  44.79  19.5  20.25  21.82 
A3  76.8  58.87  37.82  2.83  47.80  21.0  22.08  22.40 
A4  67.9  51.38  33.21  2.67  41.98  16.8  16.99  17.50 
A5  74.2  56.67  36.48  2.78  46.11  19.0  19.29  20.87 
A6  79.3  61.01  39.12  2.87  49.45  21.0  21.21  23.01 
A7  62.2  46.45  30.13  2.55  38.08  15.5  16.58  16.95 
A8  78.3  60.14  38.59  2.85  48.78  21.5  23.13  23.88 
Note:
In order to provide a reasonable and economic shaft lining design, the relationships between bearing capacity and reinforcement ratio and between bearing capacity and concrete compressive strength (Figures
Relationship curve between ultimate bearing capacity and reinforcement ratio.
Relationship between ultimate bearing capacity and concrete compressive strength.
The ultimate bearing capacity of the HSHPRCSL model was found to be significantly influenced by the strength grade of the concrete. Figure
Figure
Shaft lining model failure mode.
The failure surface of the threeparameter strength criterion, shown in Figure
Parabolic threeparameter strength criterion.
For the yield plane of the threeparameter strength criterion shown in Figure
Because the shaft lining is under external pressure, the principle stress components
Mechanical model of concrete shaft lining.
Mine shaft lining can be analysed as a plane axially symmetric problem in which the radial stress
As
When the external load
When the plastic zone (
The relationship between the ultimate bearing capacity of the HSHPRCSL,
According to the Code for the Design of Concrete Structures [
According to the analysis of model test results, the ultimate bearing capacities of the HSHPRCSL models were found to be significantly influenced by the concrete strength to the extent that the ultimate bearing capacity of a HSHPRCSL is most effectively improved by increasing the strength of the concrete during the design stage. To analyse the degree of correlation between the experimentally derived fitted equation and the theoretically derived equation based on the threeparameter strength criterion for the ultimate bearing capacity of the shaft lining, specimens with thicknessdiameter ratios of
The relationship between ultimate bearing capacity and compressive strength when
The relationship between ultimate bearing capacity and compressive strength when
From Figures
The above analysis demonstrates that the difference between the ultimate bearing capacity of the HSHPRCSL calculated using the proposed equation based on the threeparameter strength criterion and calculated using the fitting equation based on experimental results is very small, with errors around about ±5%. Thus, the calculation of the ultimate bearing capacity of HSHPRCSL by equations (
It is well known that reasonable and accurate numerical approach could be implemented as an alternative to costly and timeconsuming fullscale experimental tests, allowing an extensive parametric investigation of composite joints and possible design optimizations [
In the finite element model, the concrete is simulated by SOLID65 threedimensional solid element, the steel bar is simulated by LINK8 bar element, and the reinforcedconcrete separated model is adopted. Displacement coordination is achieved by sharing joint between concrete elements and steel elements. The constitutive relationship of concrete is determined by the multilinear kinematic hardening model (bilinear kinematic), as well as the uniaxial compressive test results of HSHPC blocks. The failure criterion of concrete is Willam and Warnke’s fiveparameter failure criterion [
Finite element model of HSHPRCSL.
The force parameter table of concrete.
Model 

Poisson ratio 






A1  3.66  0.2  39.2  65.3  7.18  0.45  0.9 
A2  3.72  0.2  43.3  72.2  8.10  0.45  0.9 
A3  3.77  0.2  46.1  76.8  8.35  0.45  0.9 
A4  3.59  0.2  40.7  67.9  7.45  0.45  0.9 
A5  3.67  0.2  44.5  74.2  8.21  0.45  0.9 
A6  3.75  0.2  47.6  79.3  8.42  0.45  0.9 
A7  3.62  0.2  37.3  62.2  6.71  0.45  0.9 
A8  3.78  0.2  47.0  78.3  8.39  0.45  0.9 
Note:
The force parameter table of rebar.

Poisson ratio 


2.1  0.3  340 
Through finite element calculation, the ultimate bearing capacity of 8 HSHPRCSLs is obtained. From Table
In this study, a series of highstrength, highperformance concrete (HSHPRC) mix tests were first conducted to determine the optimal mix ratio for use in deep freezing shaft linings. Then, a series of highstrength, highperformance reinforced concrete shaft lining (HSHPRCSL) models were tested to determine their mechanical properties and failure characteristics. And then, a theoretical analysis based on the threeparameter strength criterion was undertaken to determine the ultimate bearing capacity of the HSHPRCSL models, providing analytical expressions for elastic and plastic zone radii, stress, and load. Finally, the finite element analysis method is used to verify the abovementioned results. The following conclusions were obtained:
According to the special curing environment and construction conditions to which deep freezing shaft linings are subjected, an optimised concrete mix was proposed for concrete strengths in the range of C60 to C80, providing important information to promote improved design and construction of deep alluvium freezing shaft linings.
When the HSHPRCSL models ruptured, large chunks of concrete were observed to fall, inclined broken cracks appeared, plastic bending of the circumferential reinforcement occurred along the failure surface, and compressiveshear failure occurred with an angle between the failure surface and the maximum principle stress of 25–30°.
Results of the HSHPRCSL model tests indicated a high ultimate bearing capacity. The factors that influenced the ultimate bearing capacity were, in order of decreasing influence, the ultimate uniaxial compressive strength of the concrete, the thicknessdiameter ratio, and the reinforcement ratio. Under a uniform externally applied load, when the concrete strength grade was increased by 10 MPa, the ultimate bearing capacity of the model increased by 6.29 MPa. For the same concrete strength grade, an increase in the reinforcement ratio from 0.3% to 0.8% only improved the ultimate bearing capacity of the shaft lining by about 0.85 MPa.
The theoretical HSHPRCSL ultimate bearing capacities, calculated based on the threeparameter strength criterion, were basically consistent with the experimental results, showing an error of less than 8%. Clearly, the proposed method for the theoretical calculation of the ultimate bearing capacity of HSHPRCSL structures is reliable, providing a theoretical basis for the design of HSHPRCSL structures in deep alluvium freezing wells.
Due to the constraints of the finite element model fully reflecting the threedimensional compression state of the borehole lining, the finite element calculation results of the ultimate bearing capacity of HSHPRCSL are slightly higher than those of the model test and theoretical formula. However, the errors are less than 12%, which verifies the rationality of the finite element model.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was financially supported by the National Natural Science Foundation of China (Grant nos. 51374010, 51474004, 51874005, 51878005, and 51804006) and The Key project of Anhui Provincial Natural Science Research in Colleges and Universities (Grant nos. KJ2010A094 and KJ2011A093).