Regular Article
Deformation Prediction of Brick Masonry in Coke Oven
2015 Volume 55 Issue 9 Pages 1841-1848
Details
2015 Volume 55 Issue 9 Pages 1841-1848
Various types of brick masonry are used in the handling and treatment of hot materials in steelmaking processes. Although trouble related to damage of the bricks and joints is an important issue, it is difficult to predict and prevent damage of brick masonry because masonry is characterized by heterogeneity, nonlinearity and nonequilibrium. In this paper, the brick masonry in a coke oven is studied as an example, and a method of deformation prediction under external force is developed as a basic study. First, a compression test of a sample consisting of two bricks with one mortar joint is performed. Second, a part of a heating flue of a coke oven made of bricks is constructed as a test sample, and brick masonry deformation under external force is measured experimentally. Third, a model of the same heating flue in the experiment is prepared, and a numerical elasto-plastic analysis is carried out using the total strain rotating crack model based on the measured mechanical properties. Finally, the experimental and numerical deformation results are compared. The results validated this method of predicting masonry deformation.
In a steelmaking process, furnaces and vessels are made of refractory bricks in order to deal with high temperature materials. The blast furnace, coke oven and basic oxygen furnace are typical examples.
The blast furnace and basic oxygen furnace are lined with bricks inside a steel shell. During operation, some bricks may crack or drop and some joints may open. In this case, proper repair, such as relining the bricks, is required in order to prevent damage of the steel shell and leakage of iron pig.
In coke ovens, the main part is built of bricks without a steel shell. A schematic view of a coke oven is shown in Fig. 1. The oven chambers where the coal is carbonized and the heating flues where the combustion gas flows are situated side by side. Coal as a raw material is charged in the oven chamber from charging holes on the oven top. After carbonization, the coke is pushed out horizontally. The heating flues are built of bricks, and the brick wall of oven chamber is called a heating wall. The outside of the coke oven is constrained by H-shaped steel members called “backstays”. With aging of the coke oven, the bricks crack or drop and joints open. Due to the positional shift of loosen bricks, upper part of the heating wall near the oven ends protrudes into the oven chamber,1) which makes it difficult to push out the coke cake after carbonization. Some parts of the heating flues are dismantled and replaced with new bricks in a hot atmosphere, which involves heavy labor under difficult conditions. Therefore, prevention of deterioration damage of brick masonry is an important issue.
Schematic view of coke oven. a) overview, b) enlarged view from oven front, c) enlarged view inside oven.
Many numerical simulation studies have examined masonry walls damaged by seismic events.2,3,4) In the steelmaking process, most numerical studies concerning brick masonry have dealt with improvement of the brick lining design or prediction of cracks in the blast furnace or basic oxygen furnace.5,6,7,8,9,10,11,12) Some studies have investigated deformation of the heating wall in a coke oven. K. Yamamura13) conducted HPM (Hybrid-type Penalty Method)14) simulation for coke oven. Process to the strength reduction and collapse of the wall could be simulated when the force was applied to the center of the wall. I. Shimoyama et al.15) studied the cause of the wall breakage by localized force using DEM simulation. Partial model of the coke oven with preliminarily provided wall damages was used for the simulation. It was found that loss of dowel constraint, wear which reaches the dowel, wide crack and loss of the horizontal constraint decrease allowable limit of the heating wall by localized force.
When performing the simulation of the coke oven, setting the appropriate mechanical property value is an important issue because masonry consisting of bricks and mortar joints is characterized by heterogeneity.
In this study, first, mechanical property value as masonry is investigated. Specifically the compressive strength of the sample consisting of two bricks with one mortar joint is measured. Second, a part of a heating flue of a coke oven is built as a test sample, and its brick masonry deformation behavior under external force is investigated experimentally. For elasto-plastic analysis, the total strain rotating crack model is formulated based on the measured mechanical properties, and deformation of a numerical model with the same structure as the experimental model is numerically simulated. Finally, the experimental and numerical results are compared, and the validity of the numerical analysis method is discussed. As a basic study, all investigations are carried out at room temperature, though an actual coke oven is operated at high temperature.
First, the mechanical properties of the brick and mortar are measured in order to determine the material constants for the elasto-plastic analysis.
2.1. Experimental Method and ConditionsFor comparison, three kinds of test samples are prepared; A: brick only, B: mortar only, and C: two bricks with one mortar joint. The material properties of the brick and mortar are listed in Table 1. As shown in Table 1, water is added to the mortar at a ratio from 30 to 32 wt%. First, mortar and 60% of the total water weight are mixed for 3 minutes with a mortar mixer, after which the remainder of the water is added gradually while mixing the mortar. After addition of the water, the mortar is mixed for another 10 minutes. Photographs of the test samples are shown in Fig. 2. The size of sample A is about 50×50×100 mm. Sample B is prepared by molding to a size of 50ϕ×100 mm. After three days, the samples are dried at 80°C for 6 hours and demolded. The samples are then dried in the air for an additional 14 days. Regarding sample C, one commercial brick is split into two pieces, the size of which is about 65×100×120 mm, and the sample is prepared using the two pieces. The mortar joint thickness is 4 mm, which is the same size as the actual coke oven. The samples are dried in the air for 9 days.
| a) brick | |
| Chemical component [%] | |
| SiO2 | 96 |
| Al2O3 | 1 |
| CaO | 2 |
| Max. operating temperature [K] | 1623 |
| Apparent porosity [%] | 20 |
| Bulk specific gravity [kg/m3] | 1830 |
| Apparent specific gravity [kg/m3] | 2260 |
| Compressive strength [N/mm2] | 20 |
| Rate of linear change on heating [%] | 1.1 at 1273 K |
| b) mortar | |
| Chemical component [%] | |
| SiO2 | 93 |
| Al2O3 | 2 |
| Fe2O3 | 1 |
| Max. operating temperature [K] | 1623 |
| Grain size [mm] | Max. 1.0 |
| 55% under 0.075 | |
| Addition of water [%] | 30–32 |
Samples used in compression test. a) sample A, b) sample B, c) sample C.
The compressive strength of the test samples is measured in accordance with JIS A 1108. Photographs taken during the measurements are shown in Fig. 3.
Compression test situation. a) sample A, b) sample B, c) sample C.
Examples of the measured stress-strain diagrams are shown in Fig. 4, and the measured values of the three types of samples are listed in Table 2, Tables 3 and 4, respectively. As expected, the compressive strength and elastic modulus of sample A are larger than those of sample B. The compressive strength of sample C is on the intermediate level between those of samples A and B. On the other hand, the elastic modulus of sample C is smaller than those of both samples A and B. Therefore, the elastic modulus of sample C, namely, brick masonry, is difficult to predict from the values of samples A and B, and can be known only by actual measurement.
Measured stress-strain diagrams. a) sample A, b) sample B, c) sample C.
| No. | Density [kg/m3] | Compressive strength [N/mm2] | Elastic modulus [N/mm2] |
|---|---|---|---|
| A-1 | 1910 | 36.33 | 2942.0 |
| A-2 | 1930 | 21.74 | 2502.4 |
| A-3 | 1910 | 30.65 | 2916.2 |
| A-4 | 1940 | 38.70 | 2773.6 |
| A-5 | 1860 | 37.54 | 3233.9 |
| Average | 1910 | 32.99 | 2873.6 |
| No. | Density [kg/m3] | Compressive strength [N/mm2] | Elastic modulus [N/mm2] |
|---|---|---|---|
| B-1 | 1460 | 1.307 | 1289.6 |
| B-2 | 1450 | 1.142 | 1517.8 |
| B-3 | 1470 | 1.446 | 1813.5 |
| B-4 | 1460 | 1.004 | 1557.9 |
| B-5 | 1470 | 1.177 | 1481.3 |
| Average | 1462 | 1.215 | 1532.0 |
| No. | Compressive strength [N/mm2] | Elastic modulus [N/mm2] |
|---|---|---|
| C-1 | 11.32 | 776.4 |
| C-2 | 13.74 | 477.1 |
| Average | 12.53 | 626.8 |
A part of a heating flue of a coke oven is constructed as a test masonry structure. External force is loaded on the test masonry structure to investigate its mechanical behavior, i.e., the deformation of the masonry under external force.
3.1. Experimental Method and ConditionsThe arrangement and dimensions of the test masonry structure are shown in Fig. 5. The one-flue and the four layer of a commercial coke oven are modeled. The materials of the bricks and mortar are the same as in Chapter 2. The mixing procedure of the mortar is also the same as in Chapter 2. The test masonry structure is built on a steel foundation consisting of H-shaped steel and a steel plate. Two Teflon sheets of 1 mm thickness are inserted between the H-shaped steel and the steel plate in order to reduce the friction force. The test masonry structure is dried in the air for 23 days.
Arrangement and dimensions of test masonry structure [mm]. a) plan view of 1st or 3rd layer, b) plan view of 2nd or 4th layer, c) elevation view.
The method of loading the test masonry structure is shown in Fig. 6. Initially, the H-shaped steel as a dead weight is placed on top of the test masonry structure in order to prevent slipping of the masonry on the foundation. Next, a constraint force parallel to the test brick masonry wall, “axial force”, is loaded, corresponding to the restraint of the “backstay”. A load perpendicular to the test brick masonry wall, “horizontal force”, is then added with a force-applied beam in the second and third layers of the masonry, and this load is gradually increased. The “horizontal force” corresponds to the coking pressure during carbonization, the contact pressure pushing out after carbonization or other undesirable forces in a commercial coke oven. The experiment is completed when the bricks crack partially and the horizontal force goes down. During loading, force and displacement are measured both in the horizontal and the axial directions. The measured positions of displacement are shown in Figs. 5 and 6. Assuming an actual coke oven, when the constraint force of the coke oven by a pair of backstays is 125.4 kN and the height of coke oven is 6.4 m, the constraint force per unit height is 19.6 kN/m. As the height of the test masonry structure is 0.532 m, the constraint force is calculated to be 10.4 kN. Therefore, the axial force is set to be 5.2 kN for each test brick masonry wall. The dead weight is set to be 2.2 kN/m2. The four ends of the test masonry are pin-supported conditions using cylindrical surfaces both parallel and perpendicular to the test brick masonry wall in order to prevent the bending moment at the supporting points. As shown in Fig. 6, the wall faces are labeled face A, B, C and D for convenience of the explanation.
Method of loading test masonry (plan view).
The measured horizontal force-deformation diagram is shown in Fig. 7 with a thick line. Measured point is moved forward by the applied horizontal force. The maximum strength is 14.1 kN at 10.8 mm. This strength is converted to stress by dividing surface of the force-applied beam (0.25 m in height, 0.8 m in width), with a result of 70 kPa. It is noted that coking pressure during carbonization in an actual coke oven is controlled so as to become several kPa or less16) assuming it to be averagely exerted on the whole heating wall, which is smaller than collapse stress of the test brick masonry wall. On the other hand, it is reported that contact force generated between a coke lump and a heating wall during coke pushing is 600 N or less and the receiving area of contact force is around 2 cm2 as results from laboratory experiments.17) Although the stress obtained by converting contact force is 3 MPa and much larger than collapse stress of the test brick masonry wall, the stress is localized in a few cm2 and contact force is smaller than collapse strength of the test brick masonry wall.
Horizontal force-deformation diagram.
Photographs of the masonry at the end of the experiment are shown in Fig. 8. The joints of the wall at face D have opened slightly. Looking at face A and B, cracks developed at the edge of the force-applied beam.
Test masonry after experiment. a) face D side, b) face A side, c) face B and C side.
The measured axial elongation-horizontal deformation diagram is shown in Fig. 9 with lines marked “exp.”. Although the test brick masonry wall is constrained by the axial force corresponds to the “backstay”, the test masonry is elongated in the axial direction during loading. The elongation is 4.7 mm and 4.0 mm at axial measured Position 1 and 2, respectively, when the horizontal deformation reaches the maximum, 38.6 mm. Experimental result shows that axial force by the backstay is not so strong to fix the coke oven length. Instead, it is considered that bricks in the coke oven are fixed mainly by the surrounding bricks.18) It is known that coke ovens become superannuated and the coke oven length is elongated during the long-term operation.19) Generally it is explained as follows: When the coal is charged, the temperature at the heating wall of oven chamber side decreases and bricks thermally shrink. This causes the joint openings between shrunken bricks or cracks in shrunken bricks at the heating wall. During carbonization, hydrocarbon-based gas generated from the coal intruded into the joint openings or cracks. Pyrolysis of the hydrocarbon-based gas progresses in the high temperature atmosphere and deposited carbon adheres to the joint openings or cracks at the heating wall. The heating wall liner bricks with deposited carbon expand thermally. These thermal shrinkage and expansion of bricks lead to the elongation of the coke oven, as backstay constraint is not strong enough.20)
Axial elongation-horizontal deformation diagram.
Based on the mechanical properties of the masonry discussed in Chapter 2, the finite element three dimensional elasto-plastic analysis of the test masonry structure discussed in Chapter 3 was carried out.
4.1. Calculation Method and ConditionsThe numerical simulation grid is shown in Fig. 10. Due to the symmetric shape, loading and boundary conditions, the calculations are performed in only half of the whole region to save computation time. The element used for the analysis is a hexahedron and a twenty-node isoparametric solid brick.21) It is based on quadratic interpolation and Gauss integration.21) The simulation considers not only the material nonlinearity but also geometrical nonlinearity. The number of nodes and elements are 1181 and 176, respectively.
Numerical simulation grid.
The total strain rotating crack model22) is used as the elasto-plastic property of the element. Compressive and tensile behaviors used in simulation are shown in Fig. 11. Based on the measurement of the mechanical properties of sample C discussed in Chapter 2, the parameters used for the simulation are listed in Table 5. When fc and ft are set as a compressive strength and a tensile strength of material, respectively, concrete is known that tensile strength is around ft = fc/10.23) On the other hand, tensile strength of the brick masonry building is greatly changed from ft = fc/100 to ft = fc/10 depending on the object.24,25) In this study, as the shape of the dowel is not modeled, tensile strength is set at ft = fc/20 considering the effect of the dowel, which is smaller than that of concrete and relatively larger in the range of the data for the brick masonry building.
Compressive and tensile behaviors used in simulation. a) compressive behavior, b) tensile behavior.
| Density [kg/m3] | 1910 |
| Elastic modulus E [N/mm2] | 626.75 |
| Poison ratio [–] | 0.2 |
| Compressive strength fc [N/mm2] | 12.53 |
| Tensile strength ft [N/mm2] | 0.6265 |
| Ultimate compressive strain εuc [–] | 0.02 |
| Ultimate tensile strain εut [–] | 0.3 |
| Tensile rigidity parameter α [–] | 0.4 |
The calculated horizontal force-deformation diagram is shown in Fig. 7 with a thin line. The maximum strength is 14.2 kN at 8.8 mm. Compared with the experimental horizontal force-deformation diagram, the simulation results fit the experimental ones. Axial elongation is also checked. The calculated axial elongation-horizontal deformation diagram is shown in Fig. 9 with lines marked “cal.”. The elongation values of Position 1 and 2 are calculated considering the both ends of the whole test masonry structure. The specimen is elongated 6.7 mm and 5.8 mm at the same points as measured Position 1 and 2, respectively, when the horizontal deformation is 38.6 mm corresponding to the maximum value in the experiment. The elongation results are similar to the experimental ones.
Figure 12 shows the calculated results at the displacement of 10 mm at the horizontal measured point. The extent of the deformation is displayed ten times larger than the actual one to make it easier to follow. High compressive stress is observed in the area of the force-applied beam at face A, and high tensile stress is observed at faces B and D. Cracks are observed mainly in the area corresponding to the high tensile force. Figure 13 shows the principal crack strain over 0.04. Same as Fig. 12, the extent of the deformation is displayed ten times larger than the actual one. First, the specimen is cracked vertically at faces B and D, after which it is found that the vertical cracks develop toward faces A and C. Horizontal cracks appeared at the displacement of 30 mm at the horizontal measured point. The cracks penetrated from face B to face A and from face D to face C at the horizontal displacement of 40 mm. As this crack pattern is in good agreement with the experimental result, it can be said that the numerical simulation model discussed here is appropriate for prediction of deformation of the brick masonry structure.
Calculated results at displacement of 10 mm at measured point. a) deformation, b) principal stress over 1.5 and under –4.5 [N/mm2], c) principal crack strain over 0.04.
Principal crack strain over 0.04. a) 10 mm, b) 20 mm, c) 30 mm, d) 40 mm at measured point.
In order to predict deformation of heating wall of the coke oven, the finite element three dimensional elasto-plastic analysis of a test brick masonry structure under external force was carried out using the mechanical properties of a sample of two bricks with one mortar joint. Concurrently with the simulation, the deformation of a test brick masonry structure under external force was measured. From the results, the following conclusions were obtained.
(1) Measurement of the mechanical properties of a sample consisting of two bricks with one mortar joint and use of those properties in numerical simulation are effective, because the macroscopic property can be determined from this measurement. Therefore, it is not necessary to model the brick or the mortar joint individually. Based on a comparison with the experimental results, the numerical simulation method discussed in this paper is found to be applicable to evaluation of the deformation of the coke oven.
(2) When a horizontal force is loaded to the test brick masonry wall in a state to be constrained by the axial force equivalent to actual backstays, opposite side of the test brick masonry wall is deformed with joint openings and cracks. In addition, the test masonry is elongated in the axial direction during loading of the horizontal force. It is indicated that the axial force corresponding to the backstays is not enough to fix the coke oven length.
