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地质岩土英文文献翻译_冶金矿山地质_工程科技_专业资料

地质岩土英文文献翻译_冶金矿山地质_工程科技_专业资料
地质岩土英文文献翻译_冶金矿山地质_工程科技_专业资料

地质岩土英文文献翻译_冶金矿山地质_工程科技_专业资料

International Journal of Rock Mechanics and Mining Sciences

Analysis of geo-structural defects in flexural toppling

failure

Abbas Majdi and Mehdi Amini

Abstract

The in-situ rock structural weaknesses, referred to herein as geo-structural defects, such as naturally induced

micro-cracks, are extremely responsive to tensile stresses. Flexural toppling failure occurs by tensile stress caused by the moment due to the weight of the inclined superimposed cantilever-like rock columns. Hence, geo-structural defects that may naturally exist in rock columns are modeled by a series of cracks in maximum tensile stress plane. The magnitude and location of the maximum tensile stress in rock columns with potential flexural toppling failure are determined. Then, the minimum factor of safety for rock columns are computed by

means of principles of solid and fracture mechanics, independently. Next, a new equation is proposed to determine the length of critical crack in such rock columns. It has been shown that if the length of natural crack is smaller than the length of critical crack, then the result based on solid mechanics approach is more appropriate; otherwise, the result obtained based on the principles of fracture mechanics is more acceptable. Subsequently, for

stabilization of the prescribed rock slopes, some new analytical relationships are suggested for determination the length and diameter of the required fully grouted rock bolts. Finally, for quick design of rock slopes against flexural toppling failure, a graphical approach along with some design curves are presented by which an admissible inclination of such rock slopes and or length of all required fully grouted rock bolts are determined. In addition, a case

study has been used for practical verification of the proposed approaches.

Keywords Geo-structural defects, In-situ rock structural weaknesses, Critical crack length

1.Introduction

Rock masses are natural materials formed in the course of millions of years. Since during their formation and afterwards, they have been subjected to high variable pressures both vertically and horizontally, usually, they are not continuous, and contain numerous cracks and fractures. The exerted pressures, sometimes, produce joint sets. Since these pressures sometimes may not be sufficiently high to create separate joint sets in rock masses, they can produce micro joints and micro-cracks. However, the results cannot be considered as independent joint sets. Although the effects of these micro-cracks are not that pronounced

compared with large size joint sets, yet they may cause a drastic change of in-situ geomechanical properties of rock masses. Also, in many instances, due to dissolution of in-situ rock masses, minute bubble-like cavities, etc., are produced, which cause a severe reduction of in-situ tensile strength. Therefore, one should not replace this in-situ strength by that obtained in the laboratory. On the other hand, measuring the in-situ rock tensile strength due to the interaction of complex parameters is impractical. Hence, an appropriate approach for estimation of the tensile strength should be sought. In this paper, by means of principles of solid and fracture mechanics, a new approach for determination of the effect of geo-structural defects on flexural toppling failure is proposed.

2. Effect of geo-structural defects on flexural toppling failure

2.1. Critical section of the flexural toppling failure

As mentioned earlier, Majdi and Amini [10] and Amini et al. [11] have proved that the accurate factor of safety is equal to that calculated for a series of inclined rock columns, which, by

analogy, is equivalent to the superimposed inclined cantilever beams as shown in Fig. 3. According to the equations of limit equilibrium, the moment M and the shearing force V existing in various cross-sectional areas in the beams can be calculated as follows:

(5)

( 6)

Since the superimposed inclined rock columns are subjected to uniformly distributed loads caused by their own weight, hence, the maximum shearing force and moment exist at the very fixed end, that is, at x=Ψ:

(7)

(8)

If the magnitude of Ψ from Eq. (1) is substituted into Eqs. (7) and (8), then the magnitudes of shearing force and the maximum moment of equivalent beam for rock slopes are computed as follows:

(9)

(10)

where C is a dimensionless geometrical parameter that is related to the inclinations of the rock slope, the total failure plane and the dip of the rock discontinuities that exist in rock masses, and can be determined by means of curves shown in Fig.

Mmax and Vmax will produce the normal (tensile and compressive) and the shear stresses in critical cross-sectional area, respectively. However, the combined effect of them will cause rock columns to fail. It is well understood that the rocks are very susceptible to tensile stresses, and the effect of maximum shearing force is also negligible compared with the effect of tensile stress. Thus, for the purpose of the ultimate stability, structural defects reduce the

cross-sectional area of load bearing capacity of the rock columns and, consequently, increase the stress concentration in neighboring solid areas. Thus, the in-situ tensile strength of the rock columns, the shearing effect might be neglected and only the tensile stress caused due to maximum bending stress could be used.

2.2. Analysis of geo-structural defects

Determination of the quantitative effect of geo-structural defects in rock masses can be investigated on the basis of the following two approaches.

2.2.1. Solid mechanics approach

In this method, which is, indeed, an old approach, the loads from the weak areas are removed and likewise will be transferred to the neighboring solid areas. Therefore, the solid areas of the rock columns, due to overloading and high stress concentration, will eventually encounter with the premature failure. In this paper, for analysis of the geo-structural defects in flexural toppling failure, a set of cracks in critical cross-sectional area has been modeled as shown in Fig. 5. By employing Eq.

(9) and assuming that the loads from weak areas are transferred to the solid areas with higher load bearing capacity (Fig. 6), the maximum stresses could be computed by the following equation (see Appendix A for

more details):

(11)Hence, with regard to Eq. (11), for determination of the factor of safety against flexural toppling failure in open excavations and underground openings including geo-structural defects the following equation is suggested:

(12)From Eq. (12) it can be inferred that the factor of safety against flexural toppling failure obtained on the basis of principles of solid mechanics is irrelevant to the length of geo-structural defects or the crack length, directly. However, it is related to the dimensionless parameter “joint persistence”, k, as it was defined earlier in this paper. Fig. 2 represents the effect of parameter k on the critical height of the rock slope. This figure also shows the

=1) limiting equilibrium of the rock mass (F

s

with a potential of flexural toppling failure.

Fig. 2. Determination of the critical height of rock slopes with a potential of flexural toppling failure on the basis of principles of solid mechanics.

2.2.2. Fracture mechanics approach

Griffith in 1924 [13], by performing comprehensive laboratory tests on the glasses, concluded that fracture of brittle materials is due to high stress concentrations produced on the crack tips which causes the cracks to extend (Fig. 3). Williams in 1952 and 1957 and Irwin in 1957 had proposed some relations by which the stress around the single ended crack tips subjected to tensile loading at infinite is determined [14], [15] and [16]. They introduced a new factor in their equations called the “stress intensity factor” which indicates the stress condition at the

crack tips. Therefore if this factor could be determined quantitatively in laboratorial, then, the factor of safety corresponding to the failure criterion based on principles of fracture mechanics might be computed.

Fig. 3. Stress concentration at the tip of a single ended crack under tensile loading Similarly, the geo-structural defects exist in rock columns with a potential of flexural toppling failure could be modeled. As it was mentioned earlier in this paper, cracks could be modeled in a conservative approach such that the location of maximum tensile stress at presumed failure plane to be considered as the cracks locations (Fig.

3). If the existing geo-structural defects in a rock mass, are modeled with a series cracks in the total failure plane, then by

means of principles of fracture mechanics, an equation for determination of the factor of safety against flexural toppling failure could be proposed as follows:

(13)where KIC is the critical stress intensity factor. Eq. (13) clarifies that the factor of safety against flexural toppling failure derived based on the method of fracture mechanics is directly related to both the “joint persistence” and the “length of cracks”. As such the length of cracks existing in the rock columns plays important roles in stress analysis. Fig. 10 shows the influence of the crack length on the critical height of rock slopes. This figure represents the limiting equilibrium of the rock mass with the potential of flexural toppling failure. As it can be seen, an increase of the crack length causes a decrease in the critical height of the rock

slopes. In contrast to the principles of solid mechanics, Eq. (13) or Fig. 4 indicates either the onset of failure of the rock columns or the inception of fracture development.

Fig. 4. Determination of the critical height of rock slopes with a potential of flexural toppling failure on the basis of principle of fracture mechanics.

3. Comparison of the results of the two approaches

The curves shown in Fig. represent Eqs.

(12) and (13), respectively. The figures reflect the quantitative effect of the geo-structural defects on flexural toppling failure on the basis of principles of solid mechanics and fracture mechanics accordingly. For the sake of comparison, these equations are applied to one kind of rock mass (limestone) with the following physical and mechanical properties [16]: , , γ=20kN/m3, k=0.75.

In any case studies, a safe and stable slope height can be determined by using Eqs.

(12) and (13), independently. The two equations yield two different slope heights out of which the minimum height must be taken as the most acceptable one. By equating Eqs.

(12) and (13), the following relation has been derived by which a crack length, in this paper called critical length of crack, can be computed:

(14a)where ac is the half of the average critical length of the cracks. Since ac appears on both sides of Eq. (14a), the critical length of the crack could be computed by trial and error method. If the length of the crack is too small with respect to rock column thickness, then the ratio t/(t?2ac) is slightly greater than one. Therefore one may ignore the length of crack in denominator, and then this ratio becomes

1. In this case Eq. (14a) reduces to the following equation, by which the critical length of the crack can be computed directly:

(14b)

It must be born in mind that Eq. (14b) leads to underestimate the critical length of the crack compared with Eq. (14a). Therefore, for an appropriate determination of the quantitative effect of

geo-structural defects in rock mass against flexural toppling failure, the following 3 conditions must be considered: (1) a=0; (2) aac.

In case 1, there are no geo-structural defects in rock columns and so Eq. (3) will be used for flexural toppling analysis. In case 2, the lengths of geo-structural defects are smaller than the critical length of the crack. In this case failure of rock column occurs due to tensile stresses for

which Eq. (12), based on the principles of solid mechanics, should be used. In case 3, the lengths of existing geo-structural defects are greater than the critical length. In this case failure will occur due to growing cracks for which Eq. (13), based on the principles of fracture mechanics, should be used for the analysis.

The results of Eqs. (12) and (13) for the limiting equilibrium both are shown in Fig. 11. For the sake of more accurate comparative studies the results of Eq. (3), which represents the rock columns with no geo-structural defects are also shown in the same figure. As it was mentioned earlier in this paper, an increase of the crack length has no direct effect on Eq. (12), which was derived based on principles of solid mechanics, whereas according to the principles of fracture mechanics, it causes to reduce the value of factor of safety. Therefore, for more in-depth comparison,

the results of Eq. (13), for different values of the crack length, are also shown in Fig. As can be seen from the figure, if the length of crack is less than the critical length (dotted curve shown in Fig. 11), failure is considered to follow the principles of solid mechanics which results the least slope height. However, if the length of crack increases beyond the critical length, the rock column fails due to high stress concentration at the crack tips according to the principles of fracture mechanics, which provides the least slope height. Hence, calculation of critical length of crack is of paramount importance.

4. Estimation of stable rock slopes with a potential of flexural toppling failure

In rock slopes and trenches, except for the soil and rock fills, the heights are dictated by the natural topography. Hence, the desired slopes must be designed safely. In rock masses with the potential of

flexural toppling failure, with regard to the length of the cracks extant in rock columns the slopes can be computed by Eqs.

(3), (12), and (13) proposed in this paper. These equations can easily be converted into a series of design curves for selection of the slopes to replace the lengthy manual computations as well. [Fig. 12], [Fig. 13], [Fig. 14] and [Fig. 15] show several such design curves with the potential of flexural topping failures. If the lengths of existing cracks in the rock columns are smaller than the critical length of the crack, one can use the design curves, obtained on the basis of principles of solid mechanics, shown in [Fig. 12] and [Fig. 13], for the rock slope design purpose. If the lengths of the cracks existing in rock columns are greater than the critical length of the crack, then the design curves derived based on principles of fracture mechanics and shown in [Fig. 14] and [Fig. 15] must be used for the slope

design intention. In all, these design curves, with knowing the height of the rock slopes and the thickness of the rock columns, parameter (H2/t) is computed, and then from the design curves the stable slope is calculated. It must be born in mind that all the aforementioned design curves are valid for the equilibrium condition only, that is, when FS=1. Hence, the calculated slopes from the above design curves, for the final safe design purpose must be reduced based on the desired factor of safety. For example, if the information regarding to one particular rock slope are given [17]: k=0.25, φ=10°, σt=10MPa, γ=20kN/m3, δ=45°,

H=100 m, t=1 m, ac>a=0.1 m, and then according to Fig. 12 the design slope will be 63°, which represents the condition of equilibrium only. Hence, the final and safe slope can be taken any values less than the above mentioned one, which is solely dependent on the desired factor of safety.

Fig. 5. Selection of critical slopes for rock columns with the potential of flexural toppling failure on the basis of principles of solid mechanics when k=0.25.

Fig. 6. Selection of critical slopes for rock columns with the potential of flexural toppling failure based on principles of solid mechanics when k=0.75..

Fig. 7. Selection of critical slopes for rock columns with the potential of flexural toppling failure based on principles of fracture mechanics when k=0.25.

Fig. 8. Selection of critical slopes for rock columns with the potential of flexural toppling failure based on principles of fracture mechanics when k=0.75.

5. Stabilization of the rock mass with the potential of flexural toppling failure

In flexural toppling failure, rock columns slide over each other so that the tensile loading induced due to their

self-weighting grounds causes the existing cracks to grow and thus failure occurs. Hence, if these slides, somehow, are prevented then the expected instability will be reduced significantly. Therefore, employing fully grouted rock bolts, as a useful tool, is great assistance in increasing the degree of stability of the rock columns as shown in Fig. 16 [5] and [6]. However, care must be taken into account that employing fully grouted rock bolts is not the only approach to stabilize the rock mass with potential of flexural toppling failure. Therefore, depending up on the case, combined methods such as decreasing the slope inclination, grouting, anchoring, retaining walls, etc., may even have more

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Abstract: A supporting body of diatomite-based porous ceramics was prepared by a solid-phase sintering process and low-temperature calcination process. A nano-TiO2 compound membrane was loaded on the supporting body by the hydrolysis precipitation method and using TiCl4 as the forerunner body, and the TiO2/diatomite-based porous ceramic composite structure was characterized by X-ray diffraction and scanning electron microscopy and so on. The photocatalytic activities of TiO2 films were investigated by the degradation of formaldehyde. The results indicate that the TiO2 films in TiO2/diatomite-based porous ceramic composite calcined at 550 ℃are anatase, and the average grain size of TiO2 is 10.9 nm. The elimination rate of the composites for formaldehyde reaches 96.8% in 6 h under an ultraviolet lamp irradiation of 8 W, and the concentration of formaldehyde drops to 0.015 mg/m3 from 0.463 mg/m3. Key words: diatomite-based porous ceramics; nano-titania compound membrane; water solution precipitation method; formaldehyde; photocatalytic activity 摘要:采用固相烧结法和低温煅烧工艺,制备了硅藻土基多孔陶瓷支承体。以四氯化钛为前驱体,采用水解沉淀法在支承体上负载纳米TiO2复合膜。用X射线衍射仪和扫描电子显微镜等对TiO2复合膜/多孔陶瓷支承体的复合结构进行了表征;并以甲醛为降解对象,考察了TiO2复合膜的光催化性能。结果表明:纳米TiO2/硅藻土基多孔陶瓷复合膜在550℃煅烧后TiO2为锐钛矿型,平均晶粒粒径为10.9 nm。在紫外光照射240min后,甲醛气体初始浓度由0.463 mg/m3 降至0.015 mg /m3,复合材料对甲醛的去除率达到96.8%。 关键词:硅藻土基多孔陶瓷;纳米二氧化钛复合膜; 水解沉淀法;甲醛;光催化性能Abstrac:t Photocatalytic ceramic foam filter, the composite of high photo active TiO2 nano mate rials and three dimensional porous ceramic foam materials, has been widely applied in the field of air /water purification, owing to its characteristics of high photoactivity, large surface area, large flowing flux and ceramic heat/ chemical resistance, recycling probability. Applications have been in the fields of industrial exhaust deodorization, agriculture pesticide degradation using sunlight, sterilization of laboratories and hospitals, high-speed train air purification, and so on. The application research progress, problem and future prospect of photo catalytic ceramic foam filter are summarized. Key words: photo catalyst; ceramic foam filter; application; air /water purification 摘要: 高活性的光催化二氧化钛纳米材料与高气孔率的三维多孔泡沫陶瓷材料复合, 得到的光催化泡沫陶瓷过滤器, 具备高活性、大表面积、大通量、以及陶瓷的耐高温、耐化学腐蚀、循环适用性, 在大气/水净化领域率先得到了广泛应用。在工业领域的废气脱臭处理、在农业领域的农药废水太阳光降解、在医疗卫生领域的实验室医院空气杀菌处理、在交通领域的高速列车空气净化等, 已经展开应用。综述了国内外光催化泡沫陶瓷过滤器的应用研究现状、问题及其发展趋势。 关键词: 光催化; 泡沫陶瓷过滤器; 应用研究; 大气/水净化

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