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Article(id=1240631880379322749, tenantId=1146029695717560320, journalId=1235980550691926019, issueId=1240631872800215183, articleNumber=null, orderNo=null, doi=10.3969/j.issn.0253-6099.2025.01.002, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1721059200000, receivedDateStr=2024-07-16, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773719290107, onlineDateStr=2026-03-17, pubDate=1738339200000, pubDateStr=2025-02-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773719290107, onlineIssueDateStr=2026-03-17, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773719290107, creator=13701087609, updateTime=1773719290107, updator=13701087609, issue=Issue{id=1240631872800215183, tenantId=1146029695717560320, journalId=1235980550691926019, year='2025', volume='45', issue='1', pageStart='1', pageEnd='187', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773719288300, creator=13701087609, updateTime=1773724138257, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1240652215052989235, tenantId=1146029695717560320, journalId=1235980550691926019, issueId=1240631872800215183, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1240652215052989236, tenantId=1146029695717560320, journalId=1235980550691926019, issueId=1240631872800215183, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=7, endPage=13, ext={EN=ArticleExt(id=1240631882027684296, articleId=1240631880379322749, tenantId=1146029695717560320, journalId=1235980550691926019, language=EN, title=Stability Analysis for Soil-Rock Slope Based on Rock Random Distribution Model, columnId=1236276106018484431, journalTitle=Mining and Metallurgical Engineering, columnName=MINING, runingTitle=null, highlight=null, articleAbstract=

In order to conduct more practical stability analysis for soil-rock slope, it was proposed to use Fortran language in a slope model to randomly generate rocks, based on which a soil-rock slope model was established. The stability analysis was conducted respectively for soil-rock slopes with five kinds of rock content. It is found that as the rock content therein increases, the slope stability gradually improves and the potential sliding surface of the slope also changes. The plastic zone penetration presents three typical modes: rock detouring, shunting and rock inclusion. The displacement in X direction is always the largest at the foot of the slope, and the maximum total displacement starts at the foot, moving to the middle of the slope and finally back to the bottom of the slope. The simulation results obtained by this method were compared to the calculation results of models with two typical equivalent strength parameters, and it is concluded that the safety factor calculated by this method is quite different from that obtained by the other two models, and also different in changing trend. In the future, this soil-rock slope model can be further optimized for other complex working conditions based on the mechanical characteristics and laws, with the influence of joints and cracks also taken into consideration.

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为了使土石混合体边坡稳定性分析更加符合实际，提出了一种基于Fortran语言在边坡模型中随机生成块石的方法，建立土石混合体边坡模型，对5种不同含石率的土石混合体边坡进行稳定性研究。结果表明，随着含石率增加，土石混合体边坡稳定性逐渐提高，边坡潜在滑动面发生变化，塑性贯通区呈现“绕石”“分流”“包含”3种典型的破坏模式，边坡X方向位移始终为坡脚最大，最大总位移由坡脚向边坡中部转变，最后回到坡底位置。将本方法仿真结果与2种典型等效强度参数模型计算结果进行对比，得出本方法计算的安全系数与其他2种模型得到的安全系数相差较大，且变化趋势不同。未来，可针对其他复杂工况下的力学特征和规律，以及考虑节理裂隙等影响进一步优化模型。

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付俊（1986—），男，云南昆明人，博士，高级工程师，主要从事矿山岩石力学研究工作。E-mail：
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王希警（1999—），男，湖北仙桃人，硕士研究生，主要从事岩石力学研究。E-mail：

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王希警（1999—），男，湖北仙桃人，硕士研究生，主要从事岩石力学研究。E-mail：

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王希警（1999—），男，湖北仙桃人，硕士研究生，主要从事岩石力学研究。E-mail：

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Keyword(id=1240651353505198685, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1240631880379322749, language=CN, orderNo=6, keyword=边坡变形), Keyword(id=1240651353605861991, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1240631880379322749, language=CN, orderNo=7, keyword=位移)], refs=[Reference(id=1240651357946966046, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1240631880379322749, doi=null, pmid=null, pmcid=null, year=2016, volume=37, issue=3, pageStart=50, pageEnd=54, url=null, language=null, rfNumber=[1], rfOrder=0, authorNames=杨继红, 齐丹, 郑珠光, journalName=华北水利水电大学学报(自然科学版), refType=null, unstructuredReference=杨继红, 齐丹, 郑珠光, 等. 土石混合介质堆积体力学特性试验研究[J]. 华北水利水电大学学报(自然科学版), 2016, 37(3): 50-54., articleTitle=土石混合介质堆积体力学特性试验研究, refAbstract=null), Reference(id=1240651358060212266, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1240631880379322749, doi=null, pmid=null, pmcid=null, year=2016, volume=37, 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Large-scale direct shear tests on accumulation body with different stone contents[J]. 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（a）0；（b）10%；（c）20%；（d）30%；（e）40%

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（a）上限安全系数；（b）下限安全系数

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（a）0；（b）10%；（c）20%；（d）30%；（e）40%

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（a）绕石；（b）分流；（c）包含

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（a）X位移监测点；（b）总位移监测点

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（a）X位移（块石分布1）；（b）X位移（块石分布2）；（c）2种块石分布总位移

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（a）下限安全系数；（b）上限安全系数

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Calculation parameters of soil-rock slopes

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材料重度/（kN·m-3）弹性模量/MPa泊松比黏聚力/kPa内摩擦角/（°）
土体201000.31028
块石257 2000.31 00050
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土石混合体边坡的计算参数

, figureFileSmall=null, figureFileBig=null, tableContent=
材料重度/（kN·m-3）弹性模量/MPa泊松比黏聚力/kPa内摩擦角/（°）
土体201000.31028
块石257 2000.31 00050
), ArticleFig(id=1240651356575429522, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1240631880379322749, language=EN, label=Table 2, caption=

Average safety factors of soil-rock slopes with different rock content

, figureFileSmall=null, figureFileBig=null, tableContent=
含石率/%上限安全系数下限安全系数
均值标准差变异系数/%均值标准差变异系数/%
01.586——1.582——
101.7730.20111.341.7400.1056.04
201.9620.1196.061.9580.1125.72
302.3240.0160.692.2920.1004.36
402.6500.1927.242.6360.1917.25
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不同含石率下安全系数均值

, figureFileSmall=null, figureFileBig=null, tableContent=
含石率/%上限安全系数下限安全系数
均值标准差变异系数/%均值标准差变异系数/%
01.586——1.582——
101.7730.20111.341.7400.1056.04
201.9620.1196.061.9580.1125.72
302.3240.0160.692.2920.1004.36
402.6500.1927.242.6360.1917.25
), ArticleFig(id=1240651356877419439, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1240631880379322749, language=EN, label=Table 3, caption=

Models with two equivalent strength parameters

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含石率/%Δφbimrock/（°）Kalender模型Lindquist模型
cbimrock/kPaφbimrock/（°）cbimrock/kPaφbimrock/（°）
0010.0028.01028.0
1008.7028.1928.0
2007.1028.3828.0
301.55.6029.0729.5
404.54.3730.1632.5
), ArticleFig(id=1240651356986471353, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1240631880379322749, language=CN, label=表3, caption=

两种等效模型强度参数

, figureFileSmall=null, figureFileBig=null, tableContent=
含石率/%Δφbimrock/（°）Kalender模型Lindquist模型
cbimrock/kPaφbimrock/（°）cbimrock/kPaφbimrock/（°）
0010.0028.01028.0
1008.7028.1928.0
2007.1028.3828.0
301.55.6029.0729.5
404.54.3730.1632.5
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基于块石随机分布模型的土石混合体边坡稳定性研究
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王希警 1 , 杨溢 1 , 付俊 2 , 韦芊竹 1 , 丁秋月 1
矿冶工程杂志 | 采矿 2025,45(1): 7-13
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矿冶工程杂志 | 采矿 2025, 45(1): 7-13
基于块石随机分布模型的土石混合体边坡稳定性研究
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王希警1 , 杨溢1, 付俊2 , 韦芊竹1, 丁秋月1
作者信息
  • 1.昆明理工大学　公共安全与应急管理学院，云南　昆明　650093
  • 2.中国有色金属工业昆明勘察设计院有限公司，云南　昆明　650051

    • 王希警（1999—），男，湖北仙桃人，硕士研究生，主要从事岩石力学研究。E-mail：

通讯作者:

付俊（1986—），男，云南昆明人，博士，高级工程师，主要从事矿山岩石力学研究工作。E-mail：
Stability Analysis for Soil-Rock Slope Based on Rock Random Distribution Model
Xijing WANG1 , Yi YANG1, Jun FU2 , Qianzhu WEI1, Qiuyue DING1
Affiliations
  • 1.Faculty of Public Security and Emergency Management, Kunming University of Science and Technology, Kunming 650093, Yunnan, China
  • 2.Kunming Prospecting Design Institute of China Nonferrous Metals Industry Co., Ltd., Kunming 650051, Yunnan, China
出版时间: 2025-02-01 doi: 10.3969/j.issn.0253-6099.2025.01.002
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摘要
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为了使土石混合体边坡稳定性分析更加符合实际，提出了一种基于Fortran语言在边坡模型中随机生成块石的方法，建立土石混合体边坡模型，对5种不同含石率的土石混合体边坡进行稳定性研究。结果表明，随着含石率增加，土石混合体边坡稳定性逐渐提高，边坡潜在滑动面发生变化，塑性贯通区呈现“绕石”“分流”“包含”3种典型的破坏模式，边坡X方向位移始终为坡脚最大，最大总位移由坡脚向边坡中部转变，最后回到坡底位置。将本方法仿真结果与2种典型等效强度参数模型计算结果进行对比，得出本方法计算的安全系数与其他2种模型得到的安全系数相差较大，且变化趋势不同。未来，可针对其他复杂工况下的力学特征和规律，以及考虑节理裂隙等影响进一步优化模型。

边坡稳定性  /  土石混合体边坡  /  块石随机分布  /  强度折减  /  安全系数  /  边坡变形  /  位移

In order to conduct more practical stability analysis for soil-rock slope, it was proposed to use Fortran language in a slope model to randomly generate rocks, based on which a soil-rock slope model was established. The stability analysis was conducted respectively for soil-rock slopes with five kinds of rock content. It is found that as the rock content therein increases, the slope stability gradually improves and the potential sliding surface of the slope also changes. The plastic zone penetration presents three typical modes: rock detouring, shunting and rock inclusion. The displacement in X direction is always the largest at the foot of the slope, and the maximum total displacement starts at the foot, moving to the middle of the slope and finally back to the bottom of the slope. The simulation results obtained by this method were compared to the calculation results of models with two typical equivalent strength parameters, and it is concluded that the safety factor calculated by this method is quite different from that obtained by the other two models, and also different in changing trend. In the future, this soil-rock slope model can be further optimized for other complex working conditions based on the mechanical characteristics and laws, with the influence of joints and cracks also taken into consideration.

slope stability  /  soil-rock slope  /  random distribution of rock  /  strength reduction  /  safety factor  /  slope deformation  /  displacement
王希警, 杨溢, 付俊, 韦芊竹, 丁秋月. 基于块石随机分布模型的土石混合体边坡稳定性研究. 矿冶工程杂志, 2025 , 45 (1) : 7 -13 . DOI: 10.3969/j.issn.0253-6099.2025.01.002
Xijing WANG, Yi YANG, Jun FU, Qianzhu WEI, Qiuyue DING. Stability Analysis for Soil-Rock Slope Based on Rock Random Distribution Model[J]. Mining and Metallurgical Engineering, 2025 , 45 (1) : 7 -13 . DOI: 10.3969/j.issn.0253-6099.2025.01.002
正文
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土石混合体是一种由土和块状物质混合而成的岩土体，通常是具有一定尺寸孔隙的松散岩土，其中土的强度较低，而块状物质的强度较高，因此其力学性质相对于单一的岩石和土体更加复杂而多变[1-3]。受松散物料的影响，土石混合体在降雨、振动、自重等条件下极易发生滑坡、泥石流等地质灾害[4-5]。许多学者针对土石混合体与均质边坡的力学特性以及大块石对混合体边坡稳定性的影响进行了一系列试验和理论探讨[6-13]。在这些研究中，实地试验的取样可能会受到混合物中颗粒大小分布的影响从而导致力学性能出现差异。另外，不同取样位置可能会导致颗粒大小分布的差异，进而影响试验数据的准确性。部分数值模拟研究尝试简化土石混合体边坡模型，将整体边坡视为均质体进行计算。然而，在许多土石混合体边坡中，会存在分布不规则的石块，岩土体的宏观力学性质在很大程度上由内部微观结构的特征所决定。这些特征包括块状物体的空间分布和排列方式、形状、粒度分布以及岩土之间的相互作用等，在研究土石混合体的力学特性时，需要综合考虑内部微观结构的各个方面，以确保对其整体力学行为有准确的认识和描述[6,10]。
在土石混合体中，石块通常呈现多面体形状。二维数值模拟不能完全展现石块对土石混合体边坡的影响，存在一定局限性，而三维数值模拟则更加全面，但三维有限元分析存在网格划分的难题，因此关于三维土石混合体边坡的研究较少。为解决这一难点，本文提出了一种在边坡内随机生成块石的方法，并通过网格映射的方法进行网格划分，选取坡高10 m，坡角30°，含石率（体积分数）分别为0、10%、20%、30%、40%的土石混合体边坡为研究对象，研究块石分布及含量对边坡的影响以及边坡破坏形态。
1　块石随机生成系统
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1.1　模型的选取
构建土石混合体边坡模型时，应遵循选择适当边界位置的准则，文献[14]提出了一种建立边坡分析有限元模型的理论，其原则是将距离坡脚1.5倍坡高的位置作为左边界，将距离坡顶2.5倍坡高的位置作为右边界，同时整体模型高度为坡高的2倍。据此理论，本文建立的边坡模型坡高10.0 m，坡角30°，边坡左边界距离坡脚15.0 m，坡顶到右边界距离25.0 m，坡脚到下边界距离10.0 m，如图1所示。
1.2　块石的生成
块石的生成主要使用Fortran语言联合ANSYS/LS-DYNA有限元软件进行模拟，具体步骤如下：
1）首先确定所选块石体积、含量等参数，利用Fortran语言进行代码编写，对块石参数进行描述。
2）建立边坡基本模型，在坡体内部随机投放块石，块石体积范围为0.05～0.1 m3，随机生成块石圆心点，除第一个块石圆心点以外，后面每生成一个点都需要与其他点进行距离判定，避免块石互相侵入，并根据块石尺寸计算块石总体积，直至已生成块石累计体积率达到设定值。块石生成过程中，对块石进行侵入判定至关重要，判定方法主要有向量面积法[15]、夹角之和测试法[16]等。本文采用的侵入判定方法如下：
如果在三维土石混合体边坡内部已经生成的块石圆心坐标与当前正在检查的块石圆心坐标之间的距离超过2个块石的半径之和，那么这2个块石被视为不侵入。反之，如果距离小于等于2个块石的半径之和，则这2个块石被视为侵入，据此确定块石侵入判断公式如下：
式中：X为块石在X轴的距离；Y为块石在Y轴的距离；Z为块石在Z轴的距离；R为块石半径。
3）使用Fortran编程输出块石的圆心坐标，将土石混合边坡细观模型直接映射到ANSYS/LS-DYNA或HyperMesh软件中，生成均质有限元模型，并导出为k文件格式。随后，将该模型导入FLAC3D中进行模拟与后处理，以实现土石混合体边坡的仿真分析。
2　土石混合体参数模型
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2.1　等效土石混合体强度参数
根据大量的人工双岩体试验，比较可靠的等效强度参数模型主要为Lindquist模型[17]和Kalender模型[18]。
Lindquist模型：
式中：τp为土石混合体抗剪强度；cmatrix为土石混合体中土体黏聚力；φmatrix为土石混合体中土体内摩擦角；b为含石率；Δφbimrock为土石混合体随着含石率增加而增加的内摩擦角，当b>25%时，b每增加10%，Δφbimrock增加3°。
Kalender模型：
式中：φbimrock为土石混合体的内摩擦角；α为块石的休止角；σbimrock为土石混合体的单轴压缩强度；σmatrix为土石混合体中土体的单轴压缩强度；A为由土体单轴压缩强度及块石的休止角共同确定的系数；cbimrock为土石混合体的黏聚力。
2.2　强度折减法
为了有效处理土石混合坡体的复杂情况，采用强度折减法来评估边坡的稳定性状况。在强度折减法中，岩土体在边坡失稳时所对抗的剪切力减弱程度被定义为安全系数。强度折减法计算如下：
式中：ctrial、φtrial分别为土体折减后的黏聚力、内摩擦角；Ftrial为折减系数；c、φ分别为岩土体折减前的黏聚力、内摩擦角。
2.3　不同含石率土石混合体边坡及参数设置
含石率是指坡体中块石的总体积在边坡总体积中的占比，不同含石率土石混合体边坡如图2所示。
本文采用莫尔-库仑本构模型。为了更好地与均质边坡的破坏形态对比，本文土石混合体边坡的2种组成材料在力学特性上应有明显差异，需满足弹性模量Erock/Ematrix>2和tanφrock/tanφmatrix>2，具体计算参数见表1。
3　不同含石率下边坡模拟结果分析
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3.1　土石混合体边坡稳定性分析
利用有限差分法，对不同含石率的土石混合体边坡进行稳定性评估，研究块石的随机分布及含量变化对边坡稳定性的影响。每个含石率生成多个随机模型，共创建了25个不同的三维土石混合体边坡。在筛选数据后，6个土石混合体边坡在不同分布和含石率条件下的上、下限安全系数如图3所示，统计各组数据平均值见表2。
从图3（a）可以看出，含石率从10%增加至20%时，边坡上限安全系数的增长不显著，但含石率30%时，边坡上限安全系数比较集中，基本分布于同一点，偏差较小，说明含石率30%的边坡比较稳定，受块石扰动较小。土石混合体边坡平均上限安全系数随着含石率增加逐渐提高，相较均质土边坡（含石率为0）分别增加了11.79%、23.71%、46.53%和67.09%，这表明边坡稳定性得到显著提高。这主要是因为土石混合体边坡的滑动面受块石影响而发生偏移，不再呈现均质土边坡滑动面的圆弧状特征。
从图3（b）中可以看出，土石混合体边坡的下限安全系数在不同含石率下表现出不同的变化趋势。含石率10%～20%时，安全系数增长比较平稳；含石率20%～40%时，安全系数增长加快，这说明含石率对边坡下限安全系数的影响具有一定规律性。相比于均质土边坡（含石率为0），土石混合体边坡含石率从10%增加至40%时，其下限安全系数平均值分别提高了9.99%、23.77%、44.88%和66.62%，明显增加。
从表2可以看出，含石率相同时，由于块石位置分布的多样性，土石混合体边坡的上、下限安全系数存在较大差异。含石率10%～40%时，变异系数出现波动，无规律性。由此可以推断，土石混合体边坡存在多种不确定因素，不宜采用确定性分析方法。
3.2　土石混合体边坡塑性区云图分析
不同含石率土石混合体边坡塑性区云图如图4所示。从图4可以看出，含石率不断增加，边坡的潜在滑动面发生变化，呈现复杂的曲线和不规则特征。随着坡体内部块石分布的改变，混合体边坡内部出现3种典型滑动破坏模式，分别为：“绕石”模式，导致斜坡上某些部位发生偏移，形成了一种特殊的切割模式；“分流”模式，促使塑性区范围扩大，使得剪切带增长；“包含”模式，导致土石混合体边坡出现多个滑动面。3种破坏模式示意图如图5所示，数值模拟中剪切带的真实情况如图6所示。
3.3　土石混合体边坡变形特征分析
为了研究含石率对土石混合体边坡变形和稳定性的影响，在坡脚至坡顶的剪切带上等距分布5个监测点监测X位移，布置2个监测点监测总位移，如图7所示。由于篇幅限制，随机选择2种块石分布情况进行位移分析，土石混合体边坡位移变化结果如图8所示。
由图8可知，含石率从0增大到40%，土石混合体边坡位移分布并不均匀，这种不均匀性主要是由于块石加入坡体中，改变了边坡结构。块石的存在决定了坡体的变形特征，使得坡体从密实结构逐渐转变为孔隙结构，同时也增加了坡体内部的节理。随着含石率增加，总位移变化与X位移变化不同，2种块石分布的X位移始终为坡脚最大，而总位移均由坡脚向边坡中部转变，最后回到坡底位置。当含石率增加到一定比例时，会逐渐由块石来主导边坡的力学特性，这与文献[19-20]的研究结果大概一致，证明了本文方法的可行性。
3.4　等效强度参数模型的结果分析
为了验证本文方法的可行性，将仿真结果与随机分布模型计算结果进行对比，应用Lindquist和Kalender等效强度参数模型分析土石混合体边坡的稳定性，计算采用式（2）～（5），式中α取40°，A取0.25，σmatrix取35 kPa，其他参数取值见表1。2种等效强度参数模型计算得到的cbimrock、φbimrock值见表3。最终，计算得到不同模型上、下限安全系数的对比曲线如图9所示。
由图9可知，含石率10%时，采用2种等效强度参数模型计算的安全系数差异不明显，但与本文方法的计算结果相差较大，是因为块石的加入从整体上增加了土石混合体边坡的节理裂隙，但该节理裂隙会通过自然沉降或人工挤压进行压缩，因此，虽然存在较大差异，但本文方法仍具有一定可行性。等效强度参数模型计算方法仅从抗滑参数上进行拟合，并未考虑块石在边坡中实际变化过程及本文所提到的3种破坏模式，采用2种等效强度参数模型分析土石混合体边坡时不能准确得到边坡实际的滑动面，从侧面反映了本文提出的土石混合体边坡稳定性的分析方法是可行的。
4　结论
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1）随着含石率变化，土石混合体结构发生改变。含石率增加时，边坡安全性提升，但内部应力和位移分布变得更加不均匀。整体边坡位移趋势开始减缓并逐渐趋于稳定，边坡最大位移区域逐渐向上移动。
2）随着含石率改变，边坡的潜在剪切滑动面会逐渐发生变化，从最初的光滑连贯的单一圆弧形滑动面逐渐演变成多个曲折的次滑动面，次滑动面与主滑动面相互连接。随着块石含量增加，土石混合体边坡整体稳定性升高。
3）在土石混合边坡中，由于块石的空间分布情况不同，同等含石率下的上限安全系数、下限安全系数存在较大差异。
4）随着含石率增加以及空间分布改变，坡体塑性区由圆弧形变为不规律甚至不连贯的滑动面，出现“绕石”“包含”“分流”3种典型的扩展模式。
5）将本文方法与Lindquist模型和Kalender模型所得的安全系数进行对比分析，从侧面验证了本文方法分析土石混合体边坡的可行性。
6）本文假设土石混合体边坡中2种力学性能的物料存在较大差异，但仅考虑重力影响，未考虑其他复杂工况下的力学特征，也未考虑到加入块石后产生的节理裂隙，因此模型有待进一步优化。
基金
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  • 国家自然科学基金(41861134008)
  • 云南省重点研发计划项目(202003AC100002)
  • 云南省院士专家工作站科研项目(202405AF140045)
  • 昆明市中青年学术和技术带头人科技专项(202405B040035)
文献
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2025年第45卷第1期
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doi: 10.3969/j.issn.0253-6099.2025.01.002
  • 接收时间：2024-07-16
  • 首发时间：2026-03-17
  • 出版时间：2025-02-01
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  • 收稿日期：2024-07-16
基金
国家自然科学基金(41861134008)
云南省重点研发计划项目(202003AC100002)
云南省院士专家工作站科研项目(202405AF140045)
昆明市中青年学术和技术带头人科技专项(202405B040035)
作者信息
    1.昆明理工大学　公共安全与应急管理学院，云南　昆明　650093
    2.中国有色金属工业昆明勘察设计院有限公司，云南　昆明　650051

通讯作者:

付俊（1986—），男，云南昆明人，博士，高级工程师，主要从事矿山岩石力学研究工作。E-mail：
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2种不同金属材料的力学参数
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Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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