An Analytical Elastic Solution for Right-Angle Trapezoidal Opening in Steeply Inclined Coal Seam
Abstract
:1. Introduction
2. Chen-Man-Zhuang Mining Project
3. The Conformal Mapping Representation of Right-Angle Trapezoidal Opening
4. Elastic Solution for Right-Angle Trapezoidal Opening
5. Displacements Analysis for Right-Angle Trapezoidal Opening
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Coefficient | Value | Coefficient | Value |
---|---|---|---|
c−1 | 1.943007098870969 | ||
a0 | 0.123864538423751 | b0 | −0.343130047633050 |
a1 | −0.762775765573139 | b1 | 0.229952727807971 |
a2 | −0.183253154614749 | b2 | −0.108592194784094 |
a3 | −0.210508431449733 | b3 | −0.119129909218219 |
a4 | 0.059058447475317 | b4 | 0.114679930116000 |
a5 | 0.041584641384929 | b5 | 0.012230502784915 |
a6 | 0.009023747775452 | b6 | −0.041311547624255 |
a7 | −0.017357739598054 | b7 | 0.013639095406708 |
a8 | −0.003902025809779 | b8 | −0.013828080675274 |
a9 | −0.002407424676143 | b9 | 0.004481421558265 |
a10 | −0.009939070300865 | b10 | 0.017387660145686 |
dik | Value | dik | Value |
---|---|---|---|
d10 | −0.00613127527563420 − 0.0212816433307378i | d11 | −0.117842059038110 − 0.0680388091648117i |
d12 | 0.0293443760564685 + 0.0707224081150705i | d13 | 0.0274885674993676 + 0.00902292634928232i |
d14 | 0.00303458256474199 − 0.0218746391688664i | d15 | −0.00820945608106655 + 0.00400098771607415i |
d16 | 0.00105898412971797 − 0.0100245445605539i | d17 | −0.00123902001055050 + 0.00230643601913176i |
d18 | −0.00511530313329306 + 0.00894884025683173i | ||
d20 | −0.0190009864787558 − 0.0134533527904577i | d21 | 0.0586887521129370 + 0.141444816230141i |
d22 | 0.0549771349987352 + 0.0180458526985646i | d23 | 0.00606916512948398 − 0.0437492783377329i |
d24 | −0.0164189121621331 + 0.00800197543214830i | d25 | 0.00211796825943594 − 0.0200490891211079i |
d26 | −0.00247804002110100 + 0.00461287203826352i | d27 | −0.0102306062665861 + 0.0178976805136635i |
d30 | −0.00315302474218401 + 0.0351015869896333i | d31 | 0.0824657024981029 + 0.0270687790478470i |
d32 | 0.00910374769422596 − 0.0656239175065993i | d33 | −0.0246283682431996 + 0.0120029631482225i |
d34 | 0.00317695238915391 − 0.0300736336816618i | d35 | −0.00371706003165149 + 0.00691930805739527i |
d36 | −0.0153459093998792 + 0.0268465207704952i | ||
d40 | 0.0243454394191507 + 0.0109132018455532i | d41 | 0.0121383302589680 − 0.0874985566754658i |
d42 | −0.0328378243242662 + 0.0160039508642966i | d43 | 0.00423593651887188 − 0.0400981782422158i |
d44 | −0.00495608004220199 + 0.00922574407652703i | d45 | −0.0204612125331722 + 0.0357953610273269i |
d50 | −0.00804817520189555 − 0.00306491820535773i | d51 | −0.0410472804053327 + 0.0200049385803708i |
d52 | 0.00529492064858985 − 0.0501227228027697i | d53 | −0.00619510005275249 + 0.0115321800956588i |
d54 | −0.0255765156664653 + 0.0447442012841587i | ||
d60 | 0.00434391049468474 − 0.0181115587543296i | d61 | 0.00635390477830782 − 0.0601472673633236i |
d62 | −0.00743412006330299 + 0.0138386161147905i | d63 | −0.0306918187997584 + 0.0536930415409904i |
d70 | 0.0214705733520627 − 0.0203538957756759i | d71 | −0.00867314007385349 + 0.0161450521339223i |
d72 | −0.0358071219330514 + 0.0626418817978221i | ||
d80 | 0 | d81 | −0.0409224250663445 + 0.0715907220546539i |
αk | Real Value | Imaginary Value |
---|---|---|
α0 | 6,048,774.18703198 | −10,298,069.9676466 |
α1 | −31,352,104.1442811 | 9,158,635.93617443 |
α2 | −5,619,295.03514821 | −4,860,490.56892524 |
α3 | −6,630,981.33006717 | −3,869,348.92054447 |
α4 | 1,524,019.59546642 | 4,091,707.21872871 |
α5 | 1,662,297.65768788 | 494,696.756351372 |
α6 | 118,164.270916096 | −1,132,658.59704894 |
α7 | −457,719.446320244 | 172,337.556709757 |
α8 | 132,590.210627846 | −622,630.541593787 |
α9 | −67,708.8190165163 | 126,039.981326195 |
α10 | −279,536.352211837 | 489,027.941597429 |
βk | Real Value | Imaginary Value |
---|---|---|
β0 | −696,738.028633599 | 1,930,106.51793591 |
β1 | 4,290,613.68134891 | −1,293,484.09391984 |
β2 | 1,030,798.99470796 | 610,831.095660530 |
β3 | 1,184,109.92690475 | 670,105.739352481 |
β4 | −332,203.767048660 | −645,074.606902502 |
β5 | −233,913.607790227 | −68,796.5781651473 |
β6 | −50,758.5812369165 | 232,377.455386432 |
β7 | 97,637.2852390529 | −76,719.9116627314 |
β8 | 21,948.8951800059 | 77,782.9537984135 |
β9 | 13,541.7638033033 | −25,207.9962652390 |
β10 | 55,907.2704423675 | −97,805.5883194858 |
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Bu, W.; Xu, H.; Ji, M. An Analytical Elastic Solution for Right-Angle Trapezoidal Opening in Steeply Inclined Coal Seam. Processes 2022, 10, 110. https://doi.org/10.3390/pr10010110
Bu W, Xu H, Ji M. An Analytical Elastic Solution for Right-Angle Trapezoidal Opening in Steeply Inclined Coal Seam. Processes. 2022; 10(1):110. https://doi.org/10.3390/pr10010110
Chicago/Turabian StyleBu, Wankui, Hui Xu, and Ming Ji. 2022. "An Analytical Elastic Solution for Right-Angle Trapezoidal Opening in Steeply Inclined Coal Seam" Processes 10, no. 1: 110. https://doi.org/10.3390/pr10010110
APA StyleBu, W., Xu, H., & Ji, M. (2022). An Analytical Elastic Solution for Right-Angle Trapezoidal Opening in Steeply Inclined Coal Seam. Processes, 10(1), 110. https://doi.org/10.3390/pr10010110