Bearing properties and influence laws of concrete-filled steel tubular arches for underground mining roadway support

2.1 Test scheme design

A total of 25 schemes were considered, which were divided into 5 groups with 5 schemes in each group, as presented in Table 1. The arches in Schemes 1–15 were half circular arches with two straight legs (hereafter defined as straightleg arches, as shown in Figure 2a), and the other schemes involved circular arches (Figure 2b). In the first group, the height of the arch leg H was the variable; the arch radius R was the variable in Schemes 6–10; and the lateral pressure coefficient λ was the variable in Schemes 11–15. The fourth group consisted of Schemes 16–20, in which the arch size (radius R)was the variable. The lateral pressure coefficient λ was the variable in Schemes 21–25.

Figure 2

Models of the tested CFST supporting arch. (a) straight-leg arch; (b) circular arch; (c) cross-section of the arch.

The cross-section of the test arch was the same as that used in the previous laboratory test [8]. The arch was a cold-formed square steel tube (external side length 150 mm, thickness 8 mm) with C40 strength grade concrete (Figure 2c). The load schemes are shown in Figure 2a and 2b. The arch feet were set as two hinges (the laboratory tested arch feet were also set as hinges) to simulate the interacting conditions of the arch in practice as the feet-lock bolts are installed on the arch feet. In the circular arch simulation schemes, the vertical displacement at the arch crown and the horizontal displacement at the right side were restricted to ensure the computational convergence.

Both in this research work and the previous study, the square cross-section arch was selected instead of the circular cross-section arch for the following reasons [8, 12]: First, the bearing capacity of a square cross-section CFST is similar to or slightly higher than that of a circular cross-section CFST with the same steel area. Second, the square section CFST arch has a larger contact area with the surrounding rock compared with that of the circular one, which reduces the stress concentration and plays a positive role in fostering the supporting ability of the CFST arch. In general, we do not believe that any given cross-section is superior than the other because there still remain differences among the different cross-section CFST arches, such as those corresponding to the production technology, on-site installation processes and economic cost, although the bearing capacity and arch-rock contact relation do not change. The square section form is simply a choice for the roadway support against the circular form, and the constructors can choose any cross-section according to the specific conditions.

2.2 Modeling and mechanical parameters

The finite element method software ABAQUS was used as the simulation tool [18, 19]. The C3D8R element was selected for the steel tube and concrete, the “tie restriction” was applied between the inner wall of the steel tube and the core concrete, and the parameters of the steel and concrete were determined through material testing.

2.2.1 Steel parameters

The cold-formed steel tube used in the CFST arch was made of steel sheets through rolling manufacture, and the steel at the corners exhibited reinforcement and hardening. Thus, the cross-section of the square steel tube was distinguished as the corner area or flat area, as shown in Figure 2c.

Adbel-Rahman and Sivakumaran [20] studied this cross-section and presented the following calculation formula to calculate the steel yield strength in the entire corner area:

(1)fy1=0.6×Bc(r/t)m+0.4⋅fy

where

f_y denotes the steel yield strength of the flat area, determined according to the steel tensile test; B_c and m are coefficients,

B_c = 3.69(f_u /f_y)− 0.819(f_u/f_y)² − 1.79,

m = 0.192(f_u/f_y)− 0.068.

where f_u is the tension strength of the flat area.

Based on the relevant research results [21], the weighted average yield strength formula for the cold-formed square steel tube sections is as given in Eq. (2), and this relation was chosen based on the cold-formed steel design rules in North America and Australia/New Zealand:

(2)fya=Cfy1+(1−C)fy

where C is the ratio between the corner area and the entire cross-section area.

Figure 3a shows the strength test of a steel sample taken from the flat area of a steel tube. The mechanical parameters of the steel in the flat area, f_p, f_y and f_u, were, respectively, 285 MPa, 351 MPa and 562 MPa, and the elasticity modulus E_s was 2.04 MPa. Subsequently, the weighted average strength of the tested cold-formed steel tube was calculated: The yield strength f_ya was 409 MPa, the ultimate strength was 594 MPa and the elastic modulus was 2.04 GPa. The abovementioned mechanical parameters were finally applied to the four-stage constitutive model.

Figure 3

Typical results of the strength tests of a steel tube sample and standard concrete cube.

2.3 Verification of the numerical simulation

2.3.1 Verification of the basic CFST structures through laboratory tests

Axial compression tests for empty short steel tubes and C40 concrete-filled steel tube columns were conducted. The height of the column was 450 mm, the width of the square steel tube section was 150 mm, and its thickness was 8 mm. The grade of the filled concrete was C40. Furthermore, the corresponding numerical simulation tests were conducted with the same structures.

A wavy buckling appeared on the empty steel tube (Figure 4a), while a waist drum shaped deformation occurred in the CFST specimens (Figure 4b). The deformation type and characteristics of the short column, as obtained from the numerical test, were basically the same as those obtained using the laboratory tests. Figure 4c shows the axial compression load-strain curves of the short column specimens; it can be noted that the curve shapes of the numerical simulation and laboratory test were nearly identical. In addition, the deviations of the ultimate bearing capacity were 0.1% and 1.15% for the empty specimens and CFST specimens, respectively. The compression-bending tests on CFST columns with a length of 1400 mm and the same section were conducted at different eccentricity ratios, as shown in Figure 4d. The numerical simulation results were consistent with the laboratory test, and the obtained load axial strain curve (Figure 4e) indicated that the two curves were nearly identical in terms of the curve shape and peak value. The above comparison results indicate that the selected simulation method and parameters are feasible for simulating the CFST structures.

Figure 4

Mechanical tests on the basic CFST structures performed via laboratory tests and numerical simulations.

2.3.2 Verification of the CFST arch through laboratory tests

Figure 5a illustrates the deformation shapes of a straight-leg CFST arch with a square cross-section (150 mm width and 8 mm thickness with C40 concrete) under uniform loads, both in the laboratory and numerical simulation tests (Scheme 4 in Table 1). Figure 5b shows the deformation curve of the arch at typical sections I and II (the outward deformation is positive, and the inward deformation is negative). The load-displacement curves in the numerical simulation can be divided into three stages: the elastic stage (OA), in which the load and displacement are in a linear relationship and the displacement increases slowly; the elastic-plastic stage (AB), in which the curve slope decreases; and finally, the plastic stage (BC), in which the curve stays horizontal and the load no longer increases.

Figure 5

Full size tests of the CFST arches.

Points A, B and C are considered as the critical loading moments, as described in the following text. The load at Point B is defined as the bearing capacity of the arch, specifically 103.1 kN/m. At point B, the arch legs bent inward, the lateral displacement reached approximately 78 mm, and the roof deformed outward, after which the arch deformation became more intense and unstable. The deformation of the numerical arch, as shown in Figure 9b, is similar to that of the laboratory testing. In summary, the arch deformation form in the numerical simulations is basically consistent with that of the laboratory tests, and the deviation of the arch bearing capacity from the laboratory test results is lower than 5%. The applied numerical simulation method and parameters are thus reliable.

Figure 6

Typical results of Schemes 1–5 with different leg heights. (a)–(c) Stress contours and deformed shapes of the arches; (d) Load-radial displacement curves; (e) Characteristic loads influenced by the leg heights; (f) Axial stress at the dangerous section, influenced by the leg height; (g) Ratio of the axial stress at the inner and outer sides of the dangerous section, influenced by the leg height.

Figure 7

Typical results of Schemes 6–10 with different arch sizes. (a)–(c) Stress contours and deformed shapes of the arches; (d) Load–radial displacement curves; ∈ Characteristic loads influenced by the arch size; (f) Axial stress at the dangerous section, influenced by the arch size; (g) Ratio of the axial stress at the inner and outer sides of the dangerous section, influenced by the arch size.

Figure 8

Typical results for Schemes 11–15 with the different lateral pressure coefficient (a)–(c) Stress contours and deformed shapes of the arches; (d) Load–radial displacement curves; (e) Characteristic loads influenced by the lateral pressure coefficient (f) Axial stress at the dangerous section, influenced by the lateral pressure coefficient (g) Ratio of the axial stress at the inner and outer sides of the dangerous section, influenced by the lateral pressure coefficient

Figure 9

Typical results for Schemes 16–20 with the different arch sizes. (a)–(c) Stress contours and deformed shapes of the arches; (d) Load–radial displacement curves; (e) Characteristic loads influenced by the arch size; (f) Axial stress at the dangerous section, influenced by the arch size; (g) Ratio of the axial stress at the inner and outer sides of the dangerous section, influenced by the arch size.

3.1 Main results

Table 2 presents the results of the straight-leg arches (Schemes 1–15). In the table, ‘high-risk section’ is the cross-section corresponding to the highest steel stress on the arch at the critical loading moment B (Point B on the load-displacement curve); ‘Load’ is the total load on the arch divided by the complete length of the arch axis line, unit: kN/m; and ‘Bearing capacity’ is the load on the arch at loading moment B, unit: kN/m.

3.2 Influence laws of the leg height

Figure 6 shows the typical results of Schemes 1–5 with different leg heights.

1. The arch crown in Schemes 2–5 deformed outwardly and the legs bent inward, which is contrary to the state in Scheme 1 (H=0 m). The leg height within a certain range thus influences the deformation model of the arch.

2. The load-displacement curves in each scheme basically exhibit the same shape (Figure 6d), all of which can be divided into three stages, similar to those in Scheme 4, as described in Section 1.3. In addition, a higher arch leg corresponds to a flatter linear section of the curve.

3. Figure 6e shows the critical load curves influenced by the leg height. The elastic critical loads (Point A) are slightly smaller than the elastoplastic critical loads (Point B), which is basically the same as the extreme load. The bearing capacity curve presents an early peak followed by a decrease, and the bearing capacity of the arch with a leg height of 0 m is smaller than that of the arch with a leg height of 0.5 m. Furthermore, the bearing capacity decreases as the height of the arch leg increases when the height of the arch leg is greater than 0.5 m; a longer leg corresponds to a lower influence.

4. As the height of the arch leg increases, the position of the dangerous section of the arch gradually moves downward from the leg top-end.

5. The steel stress at the dangerous section of the arch at the critical loading moments A and B is shown in Figures 6f and 6g. The signs of the stress values on the inner and outer sides on the dangerous section are opposite, which indicates that the dangerous section is subjected to a compression-bending inner force. When the arch leg height is larger than 0.5 m, the absolute value of the stress ratio increases as the arch leg becomes longer, which indicates that the bending moment acting on the dangerous section increases as the arch leg becomes longer. The steel stress exceeds the yield strength at critical loading moment A and ranged from −3300μ∈ −6000μ∈ at critical loading moment B. This result indicates that the failure modes of the tested arches correspond to the instability at the extreme point caused by the strength deterioration.

6. Overall, the arch leg height (0–3 m) has an influence on the arch deformation form but not on the arch failure mode.

3.3 Influence laws of the arch size

Figure 7 shows the main results for Schemes 6–10 with different arch sizes.

1. All the deformation forms of the tested arches (R=1.0–4.0 m) are the same, the arch legs are bent inward, and the crown is deformed outward.

2. The forms of the load-radial displacement curve of each scheme are basically the same and can be divided into three stages, which is the same as that for Scheme 4 described in Section 1.3. A larger arch size corresponds to a smaller slope of the linear stage (OA) of the curve.

3. Figure 7e shows the critical load curves influenced by the arch size. The bearing capacity constantly decreases as the arch size increases, which is reflected in the form of an approximately inverse function. A smaller arch size corresponds to a larger influence.

4. The position of the dangerous section gradually deviates downward from the leg top-end as the arch size increases.

5. The steel stress values at the dangerous section on the arch at critical loading moments A and B are shown in Figures 7f and 7g. The stress on the outer side of the dangerous section is compressive, and that on the inner side is tensile, which indicates that the dangerous section is subjected to a compression-bending load with a large eccentricity. The absolute value of the stress ratio in Figure 7g increases as the arch size increases, and the ratios in both schemes with R=3 m and R=4 m are larger than 1, which indicates that a larger arch size corresponds to a larger bending moment acting on the dangerous section. The steel stress exceeds the yield strength at critical loading moment A and ranges from −3200μ∈ to −4200μ∈ (except for in Scheme 6) at critical loading moment B. This finding indicates that the failure modes of the tested arches (R=1.0–4.0 m) correspond to the instability at the extreme point caused by the strength deterioration.

3.4 Influence laws of the lateral pressure coefficient

Figure 8 shows the main results of Schemes 6–10 with the different arch sizes.

1. Arches with lateral pressure coefficients from 0.75 to 1.5 share the same deformation form; the arch crown deforms outward, and the legs bend inward, whichis in contrast to the trend for the arches with a lateral pressure coefficient of 0.5.

2. The load-radial displacement curves of each scheme have basically the same form, and all of them can be divided into three stages, which is the same as the curve defined in Section 1.3.

3. Figure 8e shows the critical load curves influenced by the lateral pressure coefficient. The arch bearing capacity first increases and later decreases as the pressure coefficient increases, and this capacity reaches the maximum value when the lateral pressure coefficient reaches 0.75.

4. The dangerous section is located above the leg top-end when the lateral pressure coefficient is 0.5. This section gradually moves downward as the coefficient increases, and this section moves below the leg top-end when the coefficient reaches 0.75.

5. The steel stress values at the dangerous section of the arch at critical loading moments A and B are shown in Figures 8f and 8g. All the stress ratios are approximately −1, and the stress signs on the inner and outer sides of the dangerous section are opposite, indicating that the dangerous section is subjected to a compression-bending load with a large eccentricity. The steel stress exceeds the yield strength at critical loading moment A and ranges from −2700μ∈ to −3900μ∈ (except in Scheme 11) at critical loading moment B. The abovementioned results indicate that the deformation form changes as the lateral pressure coefficient changes from 0.5 to 0.75. However, the failure mode does not change, and all the failure modes correspond to the instability at the extreme point caused by the deterioration in the section strength.

4.1 Main results

Table 3 presents the results of the circular arches (Schemes 16–25).

4.2 Influence laws of the arch size

Figure 9 shows the main results for Schemes 16–20 with the different arch sizes.

1. The arch deformation form changes remarkably as the arch size changes. Except the case of Scheme R=1.0, the roofs of all the other arches exhibit an inward deformation.

2. The forms of the load–radial displacement curve in each scheme are basically the same, and they can all be divided into three stages, which is the same trend as the curves in Scheme 4, as described in Section 1.3. One difference pertaining to the semicircular straight leg schemes is that the distance between Points A and B is considerably smaller, which indicates the failure instantaneity.

3. Figure 9e shows the critical load curves influenced by the arch size. The arch bearing capacity decreases remarkably as the arch size increases, which corresponds to an approximate inverse function style.

4. The stress values of the crown and bottom sections are, respectively, similar and higher than those for the other sections, and they are both dangerous sections for the arch.

5. The comparison between Schemes 18 (R=2.0 m) and 8 (R=2.0 m, H=1.2 m) indicates that for a CFST arch with the same section under a uniform pressure, the bearing capacity of the circular arch is approximately 4.3 times that of a straight-leg arch.

6. The steel stress values at the dangerous section of an arch at critical loading moments A and B are shown in Figures 9f and 9g. The stress on the inner and outer sides of the dangerous section are all compressive stresses, which indicates that the critical section is subjected to a compression-bending inner force with a lower eccentricity, which is different from the state for the straight-leg arch. The axial stress of the steel tube in the crown section at critical loading moment A decreases rapidly as the arch radius increases, and the stress values in Schemes 19 and 20 are considerably lower than the steel yield strength,which is still in the elastic state. The above-mentioned results indicate that the arch failure form of a circular arch can be recognized as the instability at the branch point; Schemes 16–18 exhibit elasto-plastic or plastic instability, and Schemes 19–20 exhibit elastic instability.

4.3 Influence law of the lateral pressure coefficient

Figure 10 shows the main results for Schemes 21–25 with the different lateral pressure coefficients.

Figure 10

Typical results for Schemes 21–25 with the different lateral pressure coefficient (a)–(c) Stress contours and deformed shapes of the arches; (d) Load-displacement curves; (e) Characteristic loads influenced by the lateral pressure coefficient (f) Axial stress at the dangerous section, influenced by the lateral pressure coefficient (g) Ratio of the axial stress at the inner and outer sides of the dangerous section, influenced by the lateral pressure coefficient

1. The deformation forms of each arch with a lateral pressure coefficient larger than 1 are basically the same, and the shape corresponds to a vertical ellipse.

2. The forms of the load–radial displacement curve of each scheme are nearly identical and can be divided into three stages, which is the same as that for Scheme 4, as described in Section 1.3. The distance between Points A and B in Scheme 21 (λ = 1) is considerably smaller than those of the other schemes.

3. Figure 10e shows the critical load curves influenced by the lateral pressure coefficient. The comparison indicates a small difference in the load values at points A, B and C. The arch bearing capacity decreases as the lateral pressure coefficient increases, and the bearing capacity when the lateral pressure coefficient is not 1 is considerably smaller than those of the arches under a uniform pressure.

4. The stress values of the crown and bottom sections are, respectively, similar and higher than those for the other sections, and they are both dangerous sections for the arch.

5. The steel stress values of the dangerous section of an arch at critical loading moments A and B are shownin Figures 10f and 10g. Except in the case of Scheme 21, the stresses on the outer and inner sides of the dangerous section are all tensile and compressive stresses, respectively, which indicates that the dangerous sections are subjected to the compression-bending inner forces with a large eccentricity,which is similar to the case for a straight leg arch and considerably different from the case of a circular arch under a uniform pressure. The steel stress is similar to the yield strength when the arch reaches the elastic limit, which indicates that the steel on the compressed side of the dangerous section yields before the arch reaches the elastic limit. At Point B, the axial strain on the steel tube in the above position ranges from −3100μ∈ to −6900μ∈. The abovementioned analysis results indicate that the arch failure modes of the circular arch correspond to the instability at the extreme point caused by the deterioration of the section strength under a load when the lateral pressure coefficient is not 1.

5.0.1 Straight-leg arch

All the failure modes of the straight-leg arches correspond to the instability at the extreme point caused by the strength deterioration of the dangerous sections. Because the test parameters (150 ×8-C40, R=1.0–4.0 m, H=0–3.0 m, and evenly distributed load or lateral pressure coefficient 0.5–1.5) basically correspond to the parameters of the field practice, we can conclude that the failure modes of the straight-leg arches are all due to instability at the extreme point caused by the strength deterioration.

5.0.2 Circular arch

The failure modes of the circular arches (150×8-C40) when the lateral pressure coefficient is not 1 all correspond to the instability at the extreme point caused by the strength deterioration of the critical sections. The failure mode of a circular arch under a uniform load is typically the instability at the branch point; however, the failure mode is elastic instability when the arch radius is larger than 2 m, and elastoplastic or plastic instability serve as the failure modes in other cases.

Based on the abovementioned results, the following suggestions are proposed for the optimization of the arch support design.

1. The height of the straight wall should be reduced as much as possible for the straight-wall semicircular roadways.

2. The arch locking rock bolts should be set on the dangerous sections (generally near the leg top-end) for the straight-wall semicircular roadways to prevent local failure, thus ensuring the global bearing capacity of the arches.

3. Because the rock roadways with high stresses or a weak cementation are always subjected to a large surrounding rock pressure, the cross-section shape of the roadway should be first optimized according to the roadway demands and ground stress conditions. The circular shape, three-core arch shape and curved-leg semicircular shape are preferable under the above conditions.

4. For the circular soft rock roadways under an approximate water pressure, more attention should be focused on the global stability than on the local strength of the supporting arch.

The Zhaolou coal mine is a typical 1000 m deep mine in China. The objective roadway of this mine was excavated, and it was composed primarily of mudstone with an inferior rock quality; this roadway was further weakened by a fault. The roadway was originally supported with a U-steel arch + rock bolts + shotcrete support system, and it experienced a critical deformation failure. To solve this problem, the following CFST support scheme was designed: the width of the supporting arch was 5 m, and the height was 4.3 m; the height of the leg was 1.8 m, the row spacing was 1 m, and the arch cross-section parameters were the same as those in the simulation tests. The preceding studies indicated that an arch with high legs has a high risk of leg bending failure. Therefore, the arch locking bolts were set at the leg top-end point of the arch in this scheme, as shown in Figures 11a and 11b. Figures 11c and 11d show the roadway 1.5 y after the excavation and support, and the monitoring data shows that the average deformation of the roadway in the new arch supporting system after157 days was 15.7 mm, which is only 28% that of the original supported roadway.

Figure 11

Field practice of the CFST arch support with the arch locking bolts.