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Article(id=1226462298227781740, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1226462293408531329, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1731340800000, receivedDateStr=2024-11-12, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1770340998464, onlineDateStr=2026-02-06, pubDate=1761321600000, pubDateStr=2025-10-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770340998464, onlineIssueDateStr=2026-02-06, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770340998464, creator=13701087609, updateTime=1770340998464, updator=13701087609, issue=Issue{id=1226462293408531329, tenantId=1146029695717560320, journalId=1225396423026438145, year='2025', volume='45', issue='10', pageStart='1', pageEnd='288', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1770340997315, creator=13701087609, updateTime=1770341205851, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1226463168155792201, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1226462293408531329, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1226463168155792202, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1226462293408531329, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=279, endPage=288, ext={EN=ArticleExt(id=1226462298567520380, articleId=1226462298227781740, tenantId=1146029695717560320, journalId=1225396423026438145, language=EN, title=Prediction of Compressive Strength for Gold-Tailings-Based Concrete by DP-CNN-GRU Model and its Engineering Application, columnId=null, journalTitle=Mining Research and Development, columnName=null, runingTitle=null, highlight=null, articleAbstract=

As an environmentally friendly material, gold-tailings-based concrete has a wide range of potential applications. However, the complexity of the material composition of gold-tailings-based concrete, traditional prediction methods of compressive strength are often difficult to capture the nonlinear correlation and multivariate coupling characteristics within the material, resulting in insufficient prediction accuracy. Thus, a strength prediction model for gold-tailings-based concrete was proposed based on a deep learning binary fusion model (DP), a fusion Convolutional Neural Network (CNN) and a Gated Recurrent Unit (GRU). Firstly, the mineral, chemical composition and particle size distribution of gold tailings were analyzed, and their leaching toxicity was tested according to relevant standards to ensure their safety and stability as concrete materials. Subsequently, the gold tailings concrete dataset was constructed through experiments and applied to the training and validation of the model. In order to further verify the predictive ability of the model, it was applied to real engineering cases. The results show that the proposed model exhibits high accuracy in both the training and testing process, and is capable of effectively predicting the compressive strength of the gold-tailings-based concrete. The actual engineering cases show that the error range between the predicted and measured compressive strength of concrete with 20%−40% gold tailings is −4.1%−5.7%, which further proves the potential of the model to be applied in engineering practice.

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金尾矿基混凝土作为一种环保型材料，具有广泛的应用潜力。然而，金尾矿基混凝土的材料组成复杂，传统的抗压强度预测方法往往难以捕捉材料内部的非线性关联和多变量耦合特性，导致预测精度不足。提出一种基于深度学习二元融合模型(DP)，融合卷积神经网络(Convolutional Neural Network, CNN)和门控循环网络(Gated Recurrent Unit, GRU)的金属矿基混凝土强度预测模型。首先，对金尾矿的矿物、化学组成及粒度分布进行分析，并依据相关标准检测其浸出毒性，确保其作为混凝土材料的安全性及稳定性。随后，通过试验构建金尾矿混凝土数据集，用于模型的训练和验证。将该模型应用于实际工程案例中，进一步验证了模型的性能。结果表明：所提出的模型在训练和测试阶段均具有较高的精度和较低的误差，能够有效预测金尾矿基混凝土的抗压强度。实际工程案例表明，掺加20%~40%金尾矿的混凝土抗压强度预测值与实测值的误差在−4.1%至5.7%之间，进一步证明了模型在工程实践中的应用潜力。

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刘心中(1963—)，男，山东临沂人，博士，教授，研究方向为深度学习、固废资源化。E-mail:

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刘心中(1963—)，男，山东临沂人，博士，教授，研究方向为深度学习、固废资源化。E-mail:

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刘心中(1963—)，男，山东临沂人，博士，教授，研究方向为深度学习、固废资源化。E-mail:

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Construction and Building Materials, 2018, 180:320-333., articleTitle=A modified firefly algorithm-artificial neural network expert system for predicting compressive and tensile strength of high-performance concrete, refAbstract=null)], funds=[Fund(id=1226549002099934157, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, awardId=2019YFC1904103, language=CN, fundingSource=国家重点研发计划项目(2019YFC1904103), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1226548992268485455, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, xref=null, ext=[AuthorCompanyExt(id=1226548992285262672, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, companyId=1226548992268485455, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=School of Ecological Environment and Urban Construction, Fujian University of Technology, Fuzhou, Fujian 350118, China), AuthorCompanyExt(id=1226548992293651281, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, companyId=1226548992268485455, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=福建理工大学生态环境与城市建设学院，福建　福州　350118)])], figs=[ArticleFig(id=1226548997712692107, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=EN, label=Fig.1, caption=Particle size distribution of gold tailings, figureFileSmall=w4YSLfm+D/ZyKNnp0CwmPg==, figureFileBig=EG4AIVgLu1iGK+7EbTE0BA==, tableContent=null), ArticleFig(id=1226548997800772491, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=图1, caption=金尾矿粒径分布, figureFileSmall=w4YSLfm+D/ZyKNnp0CwmPg==, figureFileBig=EG4AIVgLu1iGK+7EbTE0BA==, tableContent=null), ArticleFig(id=1226548997893047181, 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tableContent=null), ArticleFig(id=1226548998480249751, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=图5, caption=CNN-GRU模型的结构, figureFileSmall=PNVXC2ZQ+3TAW/L8KeaKXg==, figureFileBig=mnkc5O3hmsb9OYukgHbYgg==, tableContent=null), ArticleFig(id=1226548998551552921, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=EN, label=Fig.6, caption=The fitness of DP-CNN-GRU, figureFileSmall=+Aoxq6b+OrkqIupf70WpgQ==, figureFileBig=K5SmwudyC+p6zIR8EMz3Kg==, tableContent=null), ArticleFig(id=1226548998648021914, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=图6, caption=DP-CNN-GRU适应度, figureFileSmall=+Aoxq6b+OrkqIupf70WpgQ==, figureFileBig=K5SmwudyC+p6zIR8EMz3Kg==, tableContent=null), ArticleFig(id=1226548998736102300, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=EN, label=Fig.7, caption=10-fold cross validation of CNN-GRU model on the training set, figureFileSmall=bPGsEerj8gHcZs41lUWmYg==, figureFileBig=nGoqX03piB8AOIzVhbyz6Q==, tableContent=null), ArticleFig(id=1226548998807405470, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=图7, caption=CNN-GRU在训练集上的10折交叉验证, figureFileSmall=bPGsEerj8gHcZs41lUWmYg==, figureFileBig=nGoqX03piB8AOIzVhbyz6Q==, tableContent=null), ArticleFig(id=1226548998870320032, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=EN, label=Fig.8, caption=CNN-GRU model predicted values and actual values, figureFileSmall=5Cyj9ToJTjGU/KPxe7dKNg==, figureFileBig=yGJVKhoeFKKJN/F5jW2D+g==, tableContent=null), ArticleFig(id=1226548998937428898, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=图8, caption=CNN-GRU模型预测值与真实值的对比, figureFileSmall=5Cyj9ToJTjGU/KPxe7dKNg==, figureFileBig=yGJVKhoeFKKJN/F5jW2D+g==, tableContent=null), ArticleFig(id=1226548999000343459, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=EN, label=Fig.9, caption=CNN-GRU model error distribution, figureFileSmall=wMnLR2CX6mP6Qmbj2UqGlg==, figureFileBig=V0An4G8H9P9BM5vteL+tuQ==, tableContent=null), ArticleFig(id=1226548999071646630, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=图9, caption=CNN-GRU模型误差分布, figureFileSmall=wMnLR2CX6mP6Qmbj2UqGlg==, figureFileBig=V0An4G8H9P9BM5vteL+tuQ==, tableContent=null), ArticleFig(id=1226548999151338407, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=EN, label=Table 1, caption=

Main technical specifications of cement

, figureFileSmall=null, figureFileBig=null, tableContent=
强度等级凝结时间/min抗压强度/MPa抗折强度/MPa
初凝终凝3 d28 d3 d28 d
P·O 42.512724027.045.35.78.0
), ArticleFig(id=1226548999235224489, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=表1, caption=

水泥的主要技术指标

, figureFileSmall=null, figureFileBig=null, tableContent=
强度等级凝结时间/min抗压强度/MPa抗折强度/MPa
初凝终凝3 d28 d3 d28 d
P·O 42.512724027.045.35.78.0
), ArticleFig(id=1226548999319110571, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=EN, label=Table 2, caption=

Basic physical properties of mineral admixtures

, figureFileSmall=null, figureFileBig=null, tableContent=
矿物掺合料比表面积/(m2/kg)密度/(g/cm3)流动度比/%需水量比/%活性指数/%
7 d28 d
S95矿渣微粉3702.82110—8194
Ⅱ级粉煤灰4202.24—91—82
), ArticleFig(id=1226549000602567597, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=表2, caption=

矿物掺合料的基本物理性能

, figureFileSmall=null, figureFileBig=null, tableContent=
矿物掺合料比表面积/(m2/kg)密度/(g/cm3)流动度比/%需水量比/%活性指数/%
7 d28 d
S95矿渣微粉3702.82110—8194
Ⅱ级粉煤灰4202.24—91—82
), ArticleFig(id=1226549000703230895, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=EN, label=Table 3, caption=

Chemical composition of gold tailings

, figureFileSmall=null, figureFileBig=null, tableContent=
SiO2Al2O3K2OFe2O3Na2OCaOZrO2Cr2O3Rb2OZnO其他
73.513.24.05.22.060.60.010.030.020.011.37
), ArticleFig(id=1226549000787116977, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=表3, caption=

金尾矿的化学组成

, figureFileSmall=null, figureFileBig=null, tableContent=
SiO2Al2O3K2OFe2O3Na2OCaOZrO2Cr2O3Rb2OZnO其他
73.513.24.05.22.060.60.010.030.020.011.37
), ArticleFig(id=1226549000875197363, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=EN, label=Table 4, caption=

Results of gold tailings leaching toxicity assay

, figureFileSmall=null, figureFileBig=null, tableContent=
检测项目检测结果《污水综合排放标准》限值
样品1样品2样品3
汞*1.0x10–42.2x10–45x10–50.05
烷基汞NDNDND不得检出
镉NDNDND0.1
铬NDNDND1.5
六价铬NDNDND0.5
砷0.01280.01820.01910.5
铅NDNDND1.0
镍NDNDND1.0
苯并[a]芘NDNDND3x10–5
铍0.0130.0130.0130.005
), ArticleFig(id=1226549000959083445, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=表4, caption=

金尾矿浸出毒性检测结果

, figureFileSmall=null, figureFileBig=null, tableContent=
检测项目检测结果《污水综合排放标准》限值
样品1样品2样品3
汞*1.0x10–42.2x10–45x10–50.05
烷基汞NDNDND不得检出
镉NDNDND0.1
铬NDNDND1.5
六价铬NDNDND0.5
砷0.01280.01820.01910.5
铅NDNDND1.0
镍NDNDND1.0
苯并[a]芘NDNDND3x10–5
铍0.0130.0130.0130.005
), ArticleFig(id=1226549001055552439, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=EN, label=Table 5, caption=

Dataset of gold tailings concrete (600 total, randomly selected 20 sets)

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编号水泥/(kg/m3)高炉矿渣/(kg/m3)粉煤灰/(kg/m3)水/(kg/m3)减水剂/(kg/m3)粗骨料/(kg/m3)细骨料/(kg/m3)金尾矿/(kg/m3)龄期/d抗压强度/MPa
1-0162.00190148.0179.019.0838.0741.00.02833.76
1-1162.00190148.0179.019.0838.0592.8148.22827.20
1-2162.00190148.0179.019.0838.0444.6296.42821.13
1-3162.00190148.0179.019.0838.0294.6444.62815.22
2-0475.00059.0142.01.91 098.0641.00.02857.23
2-1475.00059.0142.01.91 098.0512.8128.22848.76
2-2475.00059.0142.01.91 098.0384.6256.42842.10
2-3475.00059.0142.01.91 098.0256.4384.62836.71
3-0213.500174.2154.611.61 052.3775.50.01433.70
3-1213.500174.2154.611.61 052.3620.4155.11429.3
3-2213.500174.2154.611.61 052.3465.3310.21424.28
3-3213.500174.2154.611.61 052.3310.2465.31416.72
4-0212.000124.8159.07.81 085.4799.50.02838.50
4-1212.000124.8159.07.81 085.4639.6159.92833.21
4-2212.000124.8159.07.81 085.4479.7319.82828.70
4-3212.000124.8159.07.81 085.4319.8479.72822.91
5-0153.10145113.0178.58.0867.28240.02826.23
5-1153.10145113.0178.58.0867.2659.2164.82822.81
5-2153.10145113.0178.58.0867.2494.4329.62819.13
5-3153.10145113.0178.58.0867.2329.6494.42814.64
), ArticleFig(id=1226549001122661305, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=表5, caption=

金尾矿混凝土数据集(总600组，随机节选20组)

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编号水泥/(kg/m3)高炉矿渣/(kg/m3)粉煤灰/(kg/m3)水/(kg/m3)减水剂/(kg/m3)粗骨料/(kg/m3)细骨料/(kg/m3)金尾矿/(kg/m3)龄期/d抗压强度/MPa
1-0162.00190148.0179.019.0838.0741.00.02833.76
1-1162.00190148.0179.019.0838.0592.8148.22827.20
1-2162.00190148.0179.019.0838.0444.6296.42821.13
1-3162.00190148.0179.019.0838.0294.6444.62815.22
2-0475.00059.0142.01.91 098.0641.00.02857.23
2-1475.00059.0142.01.91 098.0512.8128.22848.76
2-2475.00059.0142.01.91 098.0384.6256.42842.10
2-3475.00059.0142.01.91 098.0256.4384.62836.71
3-0213.500174.2154.611.61 052.3775.50.01433.70
3-1213.500174.2154.611.61 052.3620.4155.11429.3
3-2213.500174.2154.611.61 052.3465.3310.21424.28
3-3213.500174.2154.611.61 052.3310.2465.31416.72
4-0212.000124.8159.07.81 085.4799.50.02838.50
4-1212.000124.8159.07.81 085.4639.6159.92833.21
4-2212.000124.8159.07.81 085.4479.7319.82828.70
4-3212.000124.8159.07.81 085.4319.8479.72822.91
5-0153.10145113.0178.58.0867.28240.02826.23
5-1153.10145113.0178.58.0867.2659.2164.82822.81
5-2153.10145113.0178.58.0867.2494.4329.62819.13
5-3153.10145113.0178.58.0867.2329.6494.42814.64
), ArticleFig(id=1226549001189770171, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=EN, label=Table 6, caption=

Particle coding of CNN-GRU hyper-parameters

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变量超参数搜索范围
X1第一层卷积层中的卷积核个数[16,128]
X2第二层卷积层中的卷积核个数[16,128]
X3第一层卷积核尺寸[2×2,3×3]
X4第二层卷积核尺寸[2×2,3×3]
X5GRU层神经元数量[16,64]
X6激活函数[ReLU, sigmoid, tanh]
X7dropout率[0,1]
X8学习率[0.0001,1]
), ArticleFig(id=1226549001265267645, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=表6, caption=

CNN-GRU 超参数的粒子编码

, figureFileSmall=null, figureFileBig=null, tableContent=
变量超参数搜索范围
X1第一层卷积层中的卷积核个数[16,128]
X2第二层卷积层中的卷积核个数[16,128]
X3第一层卷积核尺寸[2×2,3×3]
X4第二层卷积核尺寸[2×2,3×3]
X5GRU层神经元数量[16,64]
X6激活函数[ReLU, sigmoid, tanh]
X7dropout率[0,1]
X8学习率[0.0001,1]
), ArticleFig(id=1226549001353348031, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=EN, label=Table 7, caption=

Parameter settings of the optimization algorithm

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参数名参数值
迭代次数20
群体认知学习因子(c1)1.2
自身认知学习因子(c2)1.2
惯性权重(ωmax)0.4~0.9
差分权重(f)0.5
交叉率(cr)0.7
), ArticleFig(id=1226549001416262593, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=表7, caption=

优化算法的参数设置

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参数名参数值
迭代次数20
群体认知学习因子(c1)1.2
自身认知学习因子(c2)1.2
惯性权重(ωmax)0.4~0.9
差分权重(f)0.5
交叉率(cr)0.7
), ArticleFig(id=1226549001470788547, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=EN, label=Table 8, caption=

Hyper-parameters after different iterations of DP

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迭代次数X1X2X3X4X5X6X7X8适应度
169643354Sigmoid0.009 40.168 716.92
21031013355tanh0.010 00.321 113.42
3124163347Sigmoid0.010 00.199 311.44
4128403348tanh0.008 90.000 010.60
8128163264tanh0.008 10.000 010.47
11128163264tanh0.007 50.000 010.00
16128163364tanh0.006 60.000 09.39
), ArticleFig(id=1226549001537897413, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=表8, caption=

不同次数 DP 迭代后的超参数

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迭代次数X1X2X3X4X5X6X7X8适应度
169643354Sigmoid0.009 40.168 716.92
21031013355tanh0.010 00.321 113.42
3124163347Sigmoid0.010 00.199 311.44
4128403348tanh0.008 90.000 010.60
8128163264tanh0.008 10.000 010.47
11128163264tanh0.007 50.000 010.00
16128163364tanh0.006 60.000 09.39
), ArticleFig(id=1226549001613394886, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=EN, label=Table 9, caption=

Index values for 10-fold cross-validation of the optimal model

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迭代次数MSERMSEMAEMAPER2
113.5933.6872.2200.0790.949
26.9942.6451.6570.0570.965
313.0353.6102.3060.0800.952
44.5722.1381.3580.0450.981
58.7612.9601.5440.0560.965
65.2092.2821.3900.0480.979
77.1302.6701.5340.0620.974
85.2082.2821.2450.0430.979
98.5322.9211.4680.0500.970
108.2092.8651.9630.0700.967
平均值8.1242.8061.6680.0590.968
), ArticleFig(id=1226549001676309447, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=表9, caption=

最优模型 10 折交叉验证的指标值

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迭代次数MSERMSEMAEMAPER2
113.5933.6872.2200.0790.949
26.9942.6451.6570.0570.965
313.0353.6102.3060.0800.952
44.5722.1381.3580.0450.981
58.7612.9601.5440.0560.965
65.2092.2821.3900.0480.979
77.1302.6701.5340.0620.974
85.2082.2821.2450.0430.979
98.5322.9211.4680.0500.970
108.2092.8651.9630.0700.967
平均值8.1242.8061.6680.0590.968
), ArticleFig(id=1226549001743418312, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=EN, label=Table 10, caption=

Mix proportion of road pavement concrete

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编号水泥高炉矿渣粉煤灰水减水剂粗骨料细骨料金尾矿
1380756015041 082486.4121.6
2380756015041 082425.6182.4
3380756015041 082364.8243.2
), ArticleFig(id=1226549001797944265, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=表10, caption=

道路路面混凝土配合比

, figureFileSmall=null, figureFileBig=null, tableContent=
编号水泥高炉矿渣粉煤灰水减水剂粗骨料细骨料金尾矿
1380756015041 082486.4121.6
2380756015041 082425.6182.4
3380756015041 082364.8243.2
), ArticleFig(id=1226549001873441738, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=EN, label=Table 11, caption=

Actual and predicted compressive strength of pavement concrete of test road

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编号7 d 强度28 d 强度
预测值/MPa实际值/MPa相对误差/%预测值/MPa实际值/MPa相对误差/%
154.855.92.063.962.1–2.8
252.152.81.356.159.35.7
351.349.2–4.154.254.81.1
), ArticleFig(id=1226549001936356300, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462298227781740, language=CN, label=表11, caption=

试验道路路面抗压强度实际值和预测值

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编号7 d 强度28 d 强度
预测值/MPa实际值/MPa相对误差/%预测值/MPa实际值/MPa相对误差/%
154.855.92.063.962.1–2.8
252.152.81.356.159.35.7
351.349.2–4.154.254.81.1
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基于DP-CNN-GRU模型的金尾矿基混凝土抗压强度预测与工程应用研究
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刘心中 , 马树森 , 葛焰 , 赵津
矿业研究与开发 | 选矿与资源综合利用 2025,45(10): 279-288
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矿业研究与开发 | 选矿与资源综合利用 2025, 45(10): 279-288
基于DP-CNN-GRU模型的金尾矿基混凝土抗压强度预测与工程应用研究
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刘心中 , 马树森, 葛焰, 赵津
作者信息
  • 福建理工大学生态环境与城市建设学院，福建　福州　350118

    • 刘心中(1963—)，男，山东临沂人，博士，教授，研究方向为深度学习、固废资源化。E-mail:

Prediction of Compressive Strength for Gold-Tailings-Based Concrete by DP-CNN-GRU Model and its Engineering Application
Xinzhong LIU , Shusen MA, Yan GE, Jin ZHAO
Affiliations
  • School of Ecological Environment and Urban Construction, Fujian University of Technology, Fuzhou, Fujian 350118, China
出版时间: 2025-10-25
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摘要
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金尾矿基混凝土作为一种环保型材料，具有广泛的应用潜力。然而，金尾矿基混凝土的材料组成复杂，传统的抗压强度预测方法往往难以捕捉材料内部的非线性关联和多变量耦合特性，导致预测精度不足。提出一种基于深度学习二元融合模型(DP)，融合卷积神经网络(Convolutional Neural Network, CNN)和门控循环网络(Gated Recurrent Unit, GRU)的金属矿基混凝土强度预测模型。首先，对金尾矿的矿物、化学组成及粒度分布进行分析，并依据相关标准检测其浸出毒性，确保其作为混凝土材料的安全性及稳定性。随后，通过试验构建金尾矿混凝土数据集，用于模型的训练和验证。将该模型应用于实际工程案例中，进一步验证了模型的性能。结果表明：所提出的模型在训练和测试阶段均具有较高的精度和较低的误差，能够有效预测金尾矿基混凝土的抗压强度。实际工程案例表明，掺加20%~40%金尾矿的混凝土抗压强度预测值与实测值的误差在−4.1%至5.7%之间，进一步证明了模型在工程实践中的应用潜力。

金尾矿  /  混凝土  /  卷积神经网络  /  门控递归单元神经网络  /  混合优化算法  /  抗压强度预测

As an environmentally friendly material, gold-tailings-based concrete has a wide range of potential applications. However, the complexity of the material composition of gold-tailings-based concrete, traditional prediction methods of compressive strength are often difficult to capture the nonlinear correlation and multivariate coupling characteristics within the material, resulting in insufficient prediction accuracy. Thus, a strength prediction model for gold-tailings-based concrete was proposed based on a deep learning binary fusion model (DP), a fusion Convolutional Neural Network (CNN) and a Gated Recurrent Unit (GRU). Firstly, the mineral, chemical composition and particle size distribution of gold tailings were analyzed, and their leaching toxicity was tested according to relevant standards to ensure their safety and stability as concrete materials. Subsequently, the gold tailings concrete dataset was constructed through experiments and applied to the training and validation of the model. In order to further verify the predictive ability of the model, it was applied to real engineering cases. The results show that the proposed model exhibits high accuracy in both the training and testing process, and is capable of effectively predicting the compressive strength of the gold-tailings-based concrete. The actual engineering cases show that the error range between the predicted and measured compressive strength of concrete with 20%−40% gold tailings is −4.1%−5.7%, which further proves the potential of the model to be applied in engineering practice.

Gold tailings  /  Concrete  /  Convolutional neural network  /  Gated recurrent unit neural network  /  Hybrid optimization algorithm  /  Compressive strength prediction
刘心中, 马树森, 葛焰, 赵津. 基于DP-CNN-GRU模型的金尾矿基混凝土抗压强度预测与工程应用研究. 矿业研究与开发, 2025 , 45 (10) : 279 -288 .
Xinzhong LIU, Shusen MA, Yan GE, Jin ZHAO. Prediction of Compressive Strength for Gold-Tailings-Based Concrete by DP-CNN-GRU Model and its Engineering Application[J]. Mining Research and Development, 2025 , 45 (10) : 279 -288 .
正文
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0　引言
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随着全球城市化和基础设施建设的快速发展，混凝土在建筑和道路工程中的应用愈发广泛。抗压强度作为混凝土力学性能的关键指标，直接关系到结构的安全性和耐久性。传统的抗压强度测试方法往往依赖于大量试验，测试成本高且耗时长。与此同时，随着工业活动的不断发展，工业固废的处理问题日益严峻。作为矿业废弃物的金属矿，长期被堆存处置，带来了环境污染和资源浪费的双重问题。近年来，研究人员开始探索将金尾矿等工业废弃物资源化利用的可行性，将其掺入到混凝土中，不仅可以有效降低废弃物堆放对环境的影响，还能提高混凝土材料的性能。然而，金尾矿复杂的物化特性和掺量对混凝土力学性能的影响尚未完全明确，特别是在抗压强度预测方面缺乏系统性研究。因此，针对金尾矿基混凝土抗压强度的精确预测，建立一种“组分-强度”的高效预测模型，已成为工程界的现实需求。
在过去的几十年，研究人员一直致力于探索各种机器学习（Machine Learning, ML）算法来解决许多具有挑战性的土木工程问题[1-3]。ML方法的准确性和简单性促使许多研究人员使用这些算法，ABUNASSAR N等[4]利用人工神经网络(Artificial Neural Network, ANN)和支持向量机（Support Vector Machine, SVM)对粉煤灰和硅灰改性混凝土抗压强度进行建模，成功建立了“组分-强度”的预测模型。随着机器学习技术在土木工程领域的不断发展和应用，研究人员逐渐开始探索将传统模型与优化算法相结合的方法，以构建更为准确和高效的模型。WU Yanqi 等[5]结合支持向量回归(Support Vector Regression, SVR)模型与网格搜索(Grid Search, GS)优化，提出了预测混凝土抗压强度的GS-SVR模型，通过对559个数据集的分析，证明了该模型在预测精度上显著优于原始SVR模型。众所周知，混凝土的力学性能绝大多数由其成分决定[6-7]，且其力学性能与成分之间的关系是高度非线性的，这使得传统模型在面对混凝土复杂组分和高度非线性关系时较为困难。
与传统机器学习方法相比，深度学习（Deep Learning, DL)模型具有较高的预测精度和强大的特征学习能力，因而得到了研究人员的广泛认可。其中卷积神经网络（Convolutional Neural Network, CNN)和门控循环网络(Gated Recurrent Unit, GRU)因其强大的特征提取和时序处理能力，已经被广泛应用于多种预测模型中。ISLAM N等[8]采用4种深度学习技术来预测高性能混凝土的抗压强度。结果显示，4个模型在训练阶段的R2均值约为0.960，测试阶段达到了0.940。ZENG Ziyue等[9]不再局限于一些非解释特征（如水泥、粗骨料、水等），而是聚焦于多个可解释特征（如水泥强度等级、水胶比、砂率等），提出了一种基于可解释特征的深度学习(CNN)模型，显著提高了模型的理论可信度和实际适用性。然而，单一模型在处理复杂工程问题时，往往面临预测精度和泛化能力的平衡问题。
深度学习模型的性能高度依赖于超参数配置[10]，传统的人工调参方法耗时且不稳定。因此，采用优化算法来确定合适的模型参数变得至关重要。粒子群优化算法[11]（Particle Swarm Optimization, PSO)作为一种经典的群优化算法，已被学者用于优化各种CNN架构，以提高风险预测、物体识别、图像分类等的精度[12-17]。LI Tianyang等[18]提出了一种基于粒子群优化的CNN微调算法，可以帮助CNN以较少的训练数据走出停滞状态。但是，传统PSO在多峰和高维优化问题中容易出现早熟收敛、陷入局部最优等问题。为了解决这些问题，研究者们对惯性权重的调节方法展开了深入研究，LIMi等[19]提出了一种基于单个粒子最优适应的惯性权重调整算法，使粒子具有不同的惯性权重，从而增加惯性权重的多样性。由于不同的优化方法可能具有不同的强度，研究人员很自然地将它们融合起来进行互补。BEED R等[20]将PSO与人工蜂群算法(Artificial Bee Colony, ABC)结合起来。PSO具有较强的全局搜索性能，而ABC在局部搜索方面表现更优，通过结合两者的优势，来提高优化性能。然而，大多数的研究采用优化算法对单一模型进行超参数调整，未能充分挖掘模型融合的潜力。为解决传统PSO算法在复杂优化问题中存在的不足，本研究引入差进化算法(Differential Evolution, DE)与PSO的混合优化算法(DP)，用于改进CNN-GRU模型的超参数搜索过程。其中，利用DE来增强种群的多样性，避免早期陷入局部最优；利用PSO的快速收敛特性来提高搜索效率。
本文的研究旨在为金尾矿的资源化利用及金尾矿混凝土的性能预测提供理论基础和实践支持，推动工业废弃物在绿色建筑材料中的应用。为解决传统方法在预测精度和泛化能力上的不足，提出了一种基于改进深度学习模型的金尾矿基混凝土抗压强度预测模型（DP-CNN-GRU）。本文将该模型应用于实际工程案例，进一步验证模型的理论优势，以及金尾矿在工程应用中的可行性与有效性，并深入研究了掺合金尾矿的混凝土在道路工程中的力学性能表现，通过现场道路铺设试验对其性能进行了验证。
1　材料与方法
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1.1　原材料
试验采用P⋅O 42.5硅酸盐水泥，主要技术指标见表1。细骨料为普通河砂，细度模数2.82，含水量0.3%。粗骨料为当地石料厂生产的石子，粒径范围为5~20 mm，压碎指标为5.8%，表观密度为2 890 kg/m3。试验采用Ⅱ级粉煤灰和S 95矿渣微粉，以及粉体聚羧酸减水剂，减水率达到25%。矿物掺合料的基本物理性能见表2。
金尾矿(Gold Tailings, GT)来源于山东黄金源鑫矿业有限公司，其主要化学组成见表3，粒径分布见图1。
由表3可以看出，金尾矿中的主要成分为SiO2、Al2O3、Fe2O3、CaO和MgO。其中CaO、Al2O、Fe2O3等均具有一定的活性，能够与无机结合料产生固化反应，形成具有刚度、耐久性和抗水性的产物。此外，金尾矿还含有较高比例的硅和铝，为其在基层材料中的应用奠定了基础。金尾矿的矿物组成主要包括石英、赤铁矿、方解石、白云石、长石等，这些与天然砂石相比没有明显差异。从图1可以看出，金尾矿的大部分颗粒粒径分布在100 μm以下，存在5 μm和20 μm两个峰值。
金尾矿可能含有重金属和其他有害化学物质，因此为保证金尾矿作为混凝土材料的安全性，避免对环境和人体健康造成潜在风险，本研究依据《一般工业固体废物贮存和填埋污染控制标准》（GB 18599—2020），按照《固体废物浸出毒性浸出方法水平振荡法》（HJ 557—2010）规定方法制备金尾矿样品的浸出液，并检测浸出液中的特征污染物浓度。本次检测共检测了64种特征污染物，银、镉、铬、铜、镍、铅、六价铬等42种特征污染物均未检出。汞、锰、砷、铍等虽被检出，但远低于标准的限值。部分特征污染物的检测结果见表4。
1.2　试验方法
本次研究用金尾矿替代原有配比中的部分细骨料，并进行试验，从而构建金尾矿混凝土数据集，进一步对模型进行训练和验证，探讨尾矿掺合对高性能混凝土力学性能的影响。
按照《混凝土物理力学性能试验方法标准》(GB/T 50081—2019)制定金尾矿混凝土试验，随机选取原数据集中的50组配合比，替代20%、40%、60%的细骨料，模具均采用100 mm立方体非标准试件，换算系数为0.95。混凝土试块制备成型并养护至规定龄期时，按照标准要求，根据强度等级选择加载速度连续均匀加载。
1.3　算法理论
1.3.1　卷积神经网络(CNN)
卷积神经网络是深度学习的代表算法之一，主要被用于深度挖掘数据之间的特征关系。CNN的基本架构如图2所示，通常由输入层、卷积层、池化层、全连接层和输出层组成。
在卷积神经网络中，其核心在于通过卷积层有效捕捉数据空间特征，减少参数数量和计算量，同时保持局部信息的连续性，使得网络具有平移不变性和层级结构，能够在连续的卷积层中逐级提取输入数据的层次化特征，进一步提高了模型的泛化能力[21]。
1.3.2　门控循环单元神经网络(GRU)
GRU可以识别数据中的长期关系，通过引入门控机制，能够有效缓解梯度消失问题，使网络能够捕捉数据中的长期依赖特征。GRU的核心优势在于其创新的门控结构，该结构通过动态更新来维护和调节信息流，进而保留重要的历史信息和当前输入信息。GRU的结构如图3所示。
GRU公式如式(1)所示。更新门(Zt)和重置门(Rt)在GRU网络中共同协调信息流动和记忆保留，其中更新门管理着遗忘旧信息与整合新信息的平衡，而重置门则决定何时忽略历史状态以专注于当前输入。这种门控设计让GRU能够准确识别并响应混凝土生产过程中的关键影响因素，忽略不相关的变量，从而显著提升预测的准确性和可靠性，即便在多变的生产条件和环境因素下也能保持高性能。
式中：Zt和Rt分别为更新门和重置门；σ表示sigmoid激活函数；Xt表示模型的输入；W和U是权重矩阵；Ht和Ht−1分别为t和t−1时刻的隐藏激活状态；为候选隐藏激活状态；bz，br，bh分别为对应偏置项；tanh为激活函数。
1.3.3　基于差分进化的自适应粒子群优化算法(DP)
PSO是一种经典的群优化算法，该算法通过模仿鸟群的行为来定位最优解。在PSO中，每个问题的解被视为多维搜索空间中的一个粒子，PSO根据单个粒子得到的最优解和整个鸟群找到的最优解，不断调整粒子的位置和速度，最终得到问题的最优解。PSO算法具有搜索速度快、实现简单、精度高等特点。PSO公式如下：
式中：和表示粒子i在第t和t+1次迭代中的速度；和表示粒子i在第t和t+1次迭代中的位置；w，c1和c2分别是惯性参数、认知影响参数和社会影响参数；r1和r2是取值范围在0到1之间的随机值；和分别表示粒子i和整个群体在第t次迭代中的最佳位置。
惯性因子是PSO算法中的关键参数，表示上一代粒子速度对当前粒子速度的影响。传统静态惯性因子难以平衡局部和全局搜索。为提升PSO优化性能并减少陷入局部极值的风险，本研究采用非线性递减策略优化惯性因子。训练初期较大的惯性因子增强了全局搜索能力，随着迭代次数的增加，惯性因子逐渐减小，使粒子快速收敛至全局最优解，增强PSO算法的适应性和寻优能力。
为进一步增强PSO的全局搜索能力，本研究引入DE。DE是一种基于种群的全局优化算法，通过变异和选择机制，不断生成和筛选候选解，逐步逼近全局最优解。DE的变异和交叉操作增加了种群多样性，避免PSO陷入局部最优。在本研究中，粒子代表CNN的一组超参数，使用MSE作为适应度函数评估模型性能。PSO正常迭代更新时，每隔一定的代数利用DE的变异和交叉操作生成新位置，根据适应度选择更优的个体进入下一代，从而选出最优模型。
2　基于DP优化算法的CNN-GRU模型
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2.1　数据集
金尾矿数据集是从1 133个混凝土抗压强度数据集[22]中随机选取的50组配合比，用金尾矿替代20%、40%、60%的细骨料，按照《混凝土物理力学性能试验方法标准》（GB/T 50081—2019）进行试验，并记录每组配合比下混凝土的7 d、14 d、28 d抗压强度，并将记录到的数据组成金尾矿基混凝土抗压强度数据集，见表5。
为了方便观察金尾矿掺量对混凝土抗压强度的影响规律，根据表5中的混凝土抗压强度试验值绘制的柱状图如图4所示。从图4可以看出，金尾矿基混凝土抗压强度均低于普通混凝土，且随着金尾矿掺量的增大，混凝土强度的下降趋势明显。这主要是因为尾矿粒径较细，在掺量为20%时，此时细骨料的级配良好，金尾矿基混凝土的水泥水化相对较优，内部结构较为致密，且金尾矿中SiO2、Al2O3、Fe2O3和CaO等活性成分能够与水泥水化产物发生离子交换反应，形成坚固的凝聚体。当金尾矿的掺量逐渐提高时，高比例的金尾矿导致混凝土内部的颗粒不能形成良好的梯度分配，出现了较多的孔隙，影响了混凝土的整体性能。
2.2　CNN-GRU模型构建
本研究中CNN-GRU模型主要分为两个部分，第一部分是CNN层，主要由输入层、两个卷积层和一个全连接层构成，模型输入是由9个特征整合到一个3×3的矩阵中，矩阵包含非常重要的特征信息，因此，去掉池化层以避免在这个阶段丢失可能影响模型性能的特征。为了充分利用CNN的空间特征提取能力，结合空间注意力机制，对卷积输出结果进行注意力加权，进一步增强特征的表达。第二部分是GRU层，负责接收CNN层提取的特征，进一步处理输入特征的时间依赖性。通过有效结合CNN的空间特征提取能力、注意力机制的特征加权能力和GRU的时序列处理能力，形成一个综合性能优越的预测模型。CNN-GRU模型的结构如图5所示。
2.3　模型参数
2.3.1　待优化的超参数
在本研究中，粒子群中的每个粒子代表一个模型配置，每个粒子包含6个维度，代表不同的超参数：卷积核数量、大小、GRU隐藏层数量、激活函数类型、学习率和dropout率。6个维度包含8个变量，表6给出了各变量的含义及其范围。
2.3.2　DP优化算法超参数
在基于差分进化的自适应粒子群算法中有6个参数需要确定：惯性因子(ω)、粒子特征数、最大迭代次数、自身认知学习因子(c2)、群体认知学习因子(c1)、差分权重(f)、交叉率(cr)。参数的设置见表7。
2.4　DP-CNN-GRU的训练及评价指标
本试验通过Pytorch平台构建DP-CNN-GRU预测模型。首先，将数据集按8:2的比例划分为训练集和测试集。引入DP优化算法对6个超参数（卷积核数量、大小、激活函数、学习率、dropout率）进行寻优，MSE作为适应度函数，进行20次迭代，每个迭代训练2 000次。对具有最优超参数的模型进行十折交叉验证训练，并使用MSE、RMSE、R2，MAE、MAPE等指标评估模型在训练集和测试集上的性能，取10折交叉验证的平均值。最后，将综合性能最优的模型与其他优秀的模型进行比较。MSE、RMSE、R2，MAE、MAPE的计算公式如下：决定系数(R2)：
均方误差(MSE)：
均方根误差(RMSE)：
平均绝对百分比误差(MAPE)：
平均绝对误差（MAE）：
式中：yi和ȳi分别为检验值和预测值；yave为所有检验数据的平均值；N为检验（或预测）数据的总数。
3　结果与讨论
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3.1　DP优化结果
图6和表8分别展示了迭代过程中模型适应度及参数分布的变化。前4次迭代适应度呈显著下降趋势，随后趋于稳定，表明初期较大的惯性因子增强了全局搜索能力，帮助粒子跳出局部最优解，而随着迭代进行，局部搜索能力提高，全局最优位置逐渐稳定。第16次迭代后适应度达到最低值9.39，对应最优超参数配置为X[128, 16, 3，3, 64, tanh，0.006 6, 0]。同时通过图5能够观察到全局最优适应度存在多段水平阶段，呈阶段式下降。这表明PSO在寻优期间陷入了局部最优，通过引入的DE算法进行变异和交叉操作，增加了粒子多样性，避免了早熟收敛，证明了所提出的优化算法具有较高的有效性和鲁棒性。
3.2　模型10折交叉验证结果
图7展示了模型的10折交叉验证结果及迭代过程中损失值L和R2的变化趋势。随着迭代次数的增加，损失值迅速下降，R2值迅速上升并接近1，迭代约1 000次后，损失值和R2趋于平稳，表明模型在早期迭代阶段迅速学习并优化参数，接近全局最优状态。最终，模型的评价指标为：。在测试集上，RMSE平均值为2.806 MPa，相对于数据集中抗压强度平均值35.82 MPa降低了92%。其他评价指标（见表9）进一步显示了模型在数据集上的优异性能，能够有效地捕捉混凝土的实际抗压强度与预测抗压强度之间的线性关系，具有较高的可靠性和稳定性。
CNN-GRU模型预测值与真实值的对比如图8所示。由图8可以看出，模型在训练集和测试集的实际拟合线与理想拟合线几乎重合，大部分数据点集中在理想拟合线附近，少量偏离的数据点可能源于数据集中的异常样本或特征。图9进一步分析了模型的相对误差，训练集和测试集的相对误差主要集中在−0.25 MPa到0.25 MPa之间，平均误差分别为−0.01 MPa和−0.04 MPa，模型误差分布对称性较好，显示出模型具有优异的预测性能和良好的泛化能力。
综上所述，本研究所提出的模型在训练和测试阶段均展现出高精度和低误差，这归功于DP优化算法对CNN-GRU模型的有效组合和优化，CNN在提取输入数据的局部特征方面表现出色，通过多层卷积层的操作，能够捕捉到变量之间复杂的局部依赖关系；GRU进一步处理了这些提取的特征，保留时间依赖信息并通过其门控机制传递重要信息，增强模型的时序依赖建模能力。注意力机制的引入使模型能够有选择地关注输入特征的关键部分，提高了预测的精度和模型的解释能力。
4　工程案例试验验证
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为了进一步验证改进后的CNN-GRU模型在实际工程中的预测能力，本研究选择了一段道路铺设作为验证试验对象，将掺加金尾矿制备的混凝土应用于道路面层，结合模型预测，评估金尾矿基混凝土在实际工程中的力学性能，进而探讨用尾矿替代混凝土细骨料的可行性，并验证模型的预测准确性。
（1）道路铺设试验设计。试验场地为源鑫矿业有限公司的矿区，选取了一段长度为55 m、宽度为4.5 m的道路，使用掺加不同比例金尾矿的混凝土铺设路面。
（2）模型预测。在道路铺设之前，使用改进的CNN-GRU模型对掺入20%、30%、40%金尾矿的混凝土的抗压强度进行预测。模型输入包括水泥、高炉矿渣、粉煤灰、金尾矿等变量。
（3）试验施工与数据采集。根据尾矿掺量将试验道路划分为3段，每段道路的路面混凝土配合比见表10。施工过程中严格按照配合比进行材料的混合与浇筑，以确保模型预测条件与实际施工保持一致。在浇筑过程中，对三段路面进行现场取样、装模成型、现场养护，并测试路面混凝土的7 d、14 d、28 d抗压强度。
（4）模型验证。3段试验道路路面的抗压强度实际值和预测值见表11。通过对比表11中的数据可知，改进的CNN-GRU模型的预测精度较高，误差在−4.1%至5.7%之间，特别是在28 d龄期强度的预测中，模型的稳定性和准确性较为突出。试验结果表明，改进的CNN-GRU模型能够有效预测金尾矿基混凝土的抗压强度，具有显著的工程应用价值。
5　结论
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（1）抗压强度试验表明：随着金尾矿掺量的增加，混凝土抗压强度逐渐降低。当金尾砂的掺量为20%时，混凝土的7 d、14 d、28 d抗压强度相比普通混凝土的抗压强度有小幅的下降；当金尾砂的掺量提高至40%及以上时，抗压强度显著下降。
（2）通过模型性能测试发现，金尾矿基混凝土强度DP-CNN-GRU预测模型的预测精度显著优于传统方法。在10折交叉验证中，模型在测试集上的决定系数R2达到0.968，均方根误差（RMSE）为2.806 MPa，模型的相对误差主要集中在±2.5 MPa以内，说明预测模型具有较高的稳定性与可靠性。
（3）实际工程案例验证表明，采用DP-CNN-GRU预测模型预测金尾矿基混凝土7 d、28 d抗压强度的相对误差为−4.1%~5.7%，可满足实际工程的需求，证明了该模型的工程适用性和推广价值。
综上所述，本研究所提出的模型能够有效捕捉金尾矿基混凝土的非线性特性，显著提高预测精度，为工业固废的高效资源化利用和混凝土抗压强度预测提供了技术支持。未来的研究可以进一步探索模型在不同类型的混凝土和更广泛的工程应用中的适用性，以及进一步改进模型结构，如引入更多的环境因素和材料特性参数，以增强模型的泛化能力和适应性。
基金
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  • 国家重点研发计划项目(2019YFC1904103)
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2025年第45卷第10期
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  • 接收时间：2024-11-12
  • 首发时间：2026-02-06
  • 出版时间：2025-10-25
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  • 收稿日期：2024-11-12
基金
国家重点研发计划项目(2019YFC1904103)
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    福建理工大学生态环境与城市建设学院，福建　福州　350118
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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
species (%)
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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