Article(id=1149735927511172040, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149735925967663173, articleNumber=1003-3033(2024)10-0143-09, orderNo=null, doi=10.16265/j.cnki.issn1003-3033.2024.10.0636, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1718035200000, receivedDateStr=2024-06-11, revisedDate=1723996800000, revisedDateStr=2024-08-19, acceptedDate=null, acceptedDateStr=null, onlineDate=1752048006179, onlineDateStr=2025-07-09, pubDate=1730044800000, pubDateStr=2024-10-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1752048006179, onlineIssueDateStr=2025-07-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1752048006179, creator=13701087609, updateTime=1752048006179, updator=13701087609, issue=Issue{id=1149735925967663173, tenantId=1146029695717560320, journalId=1146031787341344770, year='2024', volume='34', issue='10', pageStart='1', pageEnd='252', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1752048005811, creator=13701087609, updateTime=1756361993174, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1167830100474082271, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149735925967663173, language=EN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1167830100478276576, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149735925967663173, language=CN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=143, endPage=151, ext={EN=ArticleExt(id=1149735927767024587, articleId=1149735927511172040, tenantId=1146029695717560320, journalId=1146031787341344770, language=EN, title=Experimental study on expansion and creep characteristics of high flow sealed grouting material, columnId=1149733269173878863, journalTitle=China Safety Science Journal, columnName=Safety engineering technology, runingTitle=null, highlight=null, articleAbstract=

In order to investigate the expansion law of high flow grouting material and the creep mechanical properties and pore structure of coal after grouting,a new nonlinear viscoplastic element was created and a creep mechanical model was constructed. Firstly,the high flow grouting material was prepared and injected into the coal body to simulate the coal body grouting around the borehole. Secondly,mercury injection experiment and uniaxial fractional loading creep test were used to test the pore structure of the coal after grouting and the creep performance of the coal under different stress levels,and the strain variation law of the coal at different creep stages was obtained. Finally,based on the creep test results,a new nonlinear viscoplastic element was constructed and introduced into the Boedin-Thomson model. Finally,the relevant parameters of the creep model were obtained by inversion,the reliability of the model was verified,and the creep instability failure law of the coal after grouting was obtained. The results show that the expansion rate of high flow grouting material is 92% higher than that of ordinary cement material,which effectively improves the shrinkage problem of cement-based grouting material after curing. After the high flow grouting material is injected into the coal body,the critical load of instability failure of the coal body is 15.3 MPa,which improves the stability of the coal body to some extent.

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为探究高流态注浆材料膨胀规律以及注浆后煤体蠕变力学特性和孔隙结构,设计新非线性黏塑性元件结构,并据此构建蠕变力学模型。首先,制备高流态注浆材料并将其注入至煤体中,以模拟钻孔周围煤体注浆情况;然后,采用压汞试验和单轴分级加载蠕变试验方法,测试注浆后煤体孔隙结构以及不同应力水平下注浆煤体蠕变性能,进而获取注浆煤体在不同蠕变阶段的应变变化规律。最后基于蠕变试验结果,设计新非线性黏塑性元件,并将其引入到鲍埃丁-汤姆逊模型,反演获得蠕变模型相关参数,揭示注浆后煤体的蠕变失稳破坏规律。研究结果表明:高流态注浆材料膨胀率相比普通水泥材料提高92%,能够有效解决水泥基注浆材料固化后收缩的问题;当高流态注浆材料注入煤体后,煤体失稳破坏临界荷载为15.3 MPa,在一定程度上提高了煤体稳定性。

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郭 鑫 (1994—),男,山东鄄城人,博士,讲师,主要从事矿井灾害防治等方面的研究。E-mail:

鲁义,教授;

施式亮,教授;

李贺,副教授

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郭 鑫 (1994—),男,山东鄄城人,博士,讲师,主要从事矿井灾害防治等方面的研究。E-mail:

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Chemical composition of raw materials

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类别 SiO2 Al2O3 Fe2O3 CaO MgO SO3 损失量
超细硅酸盐水泥 20.57 9.89 3.08 57.65 2 2.7 2.6
氧化钙-硫酸钙复合膨胀剂 4.96 8.52 0.99 64.18 2.67 16.97 1.19
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原材料化学组成

, figureFileSmall=null, figureFileBig=null, tableContent=
类别 SiO2 Al2O3 Fe2O3 CaO MgO SO3 损失量
超细硅酸盐水泥 20.57 9.89 3.08 57.65 2 2.7 2.6
氧化钙-硫酸钙复合膨胀剂 4.96 8.52 0.99 64.18 2.67 16.97 1.19
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Axial loading parameters for creep test

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级别 σ0/MPa 恒载时间/min 加载时间/min
1 4.5 180 10
2 8.1 180 10
3 11.7 180 10
4 15.3 180 10
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蠕变试验轴向加载参数

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级别 σ0/MPa 恒载时间/min 加载时间/min
1 4.5 180 10
2 8.1 180 10
3 11.7 180 10
4 15.3 180 10
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Parametric inversion results under non-yield stress (σ0s) conditions

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σ0/MPa E1/GPa E2/GPa η1/(GPa·h) η3/(GPa·h)
4.5 206.04 7.048 0.87 347.65
8.1 22.83 9.87 0.61 3.07×103
11.7 17.15 11.66 0.63 4.16×103
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非屈服应力(σ0s)条件下参数反演结果

, figureFileSmall=null, figureFileBig=null, tableContent=
σ0/MPa E1/GPa E2/GPa η1/(GPa·h) η3/(GPa·h)
4.5 206.04 7.048 0.87 347.65
8.1 22.83 9.87 0.61 3.07×103
11.7 17.15 11.66 0.63 4.16×103
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Results of parametric inversion under yield stress (σ1σs)

, figureFileSmall=null, figureFileBig=null, tableContent=
σ0/
MPa
E1/
GPa
E2/
GPa
η1/
(GPa·h)
η2/
(GPa·h)
η3/
(GPa·h)
n
15.3 26.95 4.69 0.49 126.28 2.39×106 2.88
), ArticleFig(id=1167812286887506526, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149735927511172040, language=CN, label=表4, caption=

屈服应力(σ1σs)条件下参数反演结果

, figureFileSmall=null, figureFileBig=null, tableContent=
σ0/
MPa
E1/
GPa
E2/
GPa
η1/
(GPa·h)
η2/
(GPa·h)
η3/
(GPa·h)
n
15.3 26.95 4.69 0.49 126.28 2.39×106 2.88
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高流态注浆材料膨胀及蠕变特性试验研究
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郭鑫 1 , 鲁义 1, 2 , 施式亮 1 , 李贺 1 , 李大芳 1
中国安全科学学报 | 安全工程技术 2024,34(10): 143-151
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中国安全科学学报 | 安全工程技术 2024, 34(10): 143-151
高流态注浆材料膨胀及蠕变特性试验研究
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郭鑫1 , 鲁义1, 2, 施式亮1, 李贺1, 李大芳1
作者信息
  • 1 湖南科技大学 资源环境与安全工程学院,湖南 湘潭 411201
  • 2 湖南科技大学 南方煤矿瓦斯与顶板灾害预防控制安全生产重点实验室,湖南 湘潭 411201
  • 郭 鑫 (1994—),男,山东鄄城人,博士,讲师,主要从事矿井灾害防治等方面的研究。E-mail:

    鲁义,教授;

    施式亮,教授;

    李贺,副教授

Experimental study on expansion and creep characteristics of high flow sealed grouting material
Xin GUO1 , Yi LU1, 2, Shiliang SHI1, He LI1, Dafang LI1
Affiliations
  • 1 School of Resource,Environment and Safety Engineering,Hunan University of Science and Technology,Xiangtan Hunan 411201,China
  • 2 Work Safety Key Lab on Prevention and Control of Gas and Roof Disasters for Southern Coal Mines,Hunan University of Science and Technology,Xiangtan Hunan 411201,China
出版时间: 2024-10-28 doi: 10.16265/j.cnki.issn1003-3033.2024.10.0636
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为探究高流态注浆材料膨胀规律以及注浆后煤体蠕变力学特性和孔隙结构,设计新非线性黏塑性元件结构,并据此构建蠕变力学模型。首先,制备高流态注浆材料并将其注入至煤体中,以模拟钻孔周围煤体注浆情况;然后,采用压汞试验和单轴分级加载蠕变试验方法,测试注浆后煤体孔隙结构以及不同应力水平下注浆煤体蠕变性能,进而获取注浆煤体在不同蠕变阶段的应变变化规律。最后基于蠕变试验结果,设计新非线性黏塑性元件,并将其引入到鲍埃丁-汤姆逊模型,反演获得蠕变模型相关参数,揭示注浆后煤体的蠕变失稳破坏规律。研究结果表明:高流态注浆材料膨胀率相比普通水泥材料提高92%,能够有效解决水泥基注浆材料固化后收缩的问题;当高流态注浆材料注入煤体后,煤体失稳破坏临界荷载为15.3 MPa,在一定程度上提高了煤体稳定性。

高流态  /  注浆材料  /  材料膨胀  /  蠕变特性  /  分级加载  /  孔隙结构

In order to investigate the expansion law of high flow grouting material and the creep mechanical properties and pore structure of coal after grouting,a new nonlinear viscoplastic element was created and a creep mechanical model was constructed. Firstly,the high flow grouting material was prepared and injected into the coal body to simulate the coal body grouting around the borehole. Secondly,mercury injection experiment and uniaxial fractional loading creep test were used to test the pore structure of the coal after grouting and the creep performance of the coal under different stress levels,and the strain variation law of the coal at different creep stages was obtained. Finally,based on the creep test results,a new nonlinear viscoplastic element was constructed and introduced into the Boedin-Thomson model. Finally,the relevant parameters of the creep model were obtained by inversion,the reliability of the model was verified,and the creep instability failure law of the coal after grouting was obtained. The results show that the expansion rate of high flow grouting material is 92% higher than that of ordinary cement material,which effectively improves the shrinkage problem of cement-based grouting material after curing. After the high flow grouting material is injected into the coal body,the critical load of instability failure of the coal body is 15.3 MPa,which improves the stability of the coal body to some extent.

high flow state  /  grouting material  /  material expansion  /  creep characteristics  /  graded loading  /  pore structure
郭鑫, 鲁义, 施式亮, 李贺, 李大芳. 高流态注浆材料膨胀及蠕变特性试验研究. 中国安全科学学报, 2024 , 34 (10) : 143 -151 . DOI: 10.16265/j.cnki.issn1003-3033.2024.10.0636
Xin GUO, Yi LU, Shiliang SHI, He LI, Dafang LI. Experimental study on expansion and creep characteristics of high flow sealed grouting material[J]. China Safety Science Journal, 2024 , 34 (10) : 143 -151 . DOI: 10.16265/j.cnki.issn1003-3033.2024.10.0636
钻孔密封性能是保障煤矿井下瓦斯有效抽采利用的关键因素。煤体开采越深,钻孔周围煤体越易出现非线性变形特征[1-2],产生更多裂隙,进而形成新的漏气通道,导致瓦斯抽采钻孔失稳破坏,降低抽采效率,影响煤矿井下安全生产[3]。因此,构建非线性蠕变模型,获得注浆煤体的孔隙结构与蠕变失稳破坏规律,对于预防瓦斯灾害事故的发生,减少钻孔变形破坏,具有重要实用意义。
当前,学者们大多针对瓦斯抽采钻孔围岩力学特性展开研究。例如:王旭锋等[4]研究软岩巷道蠕变变形破坏机理,提出针对深部软岩巷道蠕变加固方法。张钧祥等[5]研究穿层钻孔围岩蠕变效应,优化了封孔参数。张天军等[6]制备不同配比的CF材料试样,通过单轴蠕变试验分析CF材料蠕变特性,确定最优配比以满足井下钻孔封孔需求。张起等[7]研究顺层钻孔围岩蠕变特性,提出预置筛管的钻孔支护策略。郝富昌等[8]研究瓦斯抽采钻孔围岩蠕变-渗流耦合作用对瓦斯运移的影响,精准确定瓦斯抽采钻孔的布置位置。王猛等[9]研究深部钻孔卸压蠕变变形规律,提出钻孔二次支护技术。陈昌富等[10]改进锚-土注浆蠕变力学模型,研究不同注浆压力对锚固结构的影响。上述工作主要研究了瓦斯抽采钻孔变形以及围岩稳定性,而对于注浆后钻孔周围煤体的蠕变规律及其模型研究还相对较少。
鉴于此,笔者拟采用单轴蠕变试验系统和压汞试验系统,研究高流态封孔材料膨胀特性以及注浆后煤体试块的蠕变特征,通过引入非线性黏塑性元件,最终构建注浆煤体蠕变力学模型,以期为煤矿工程瓦斯抽采钻孔加固和注浆材料设计提供参考。
新型封孔材料基料为超细硅酸盐水泥,其外观为灰色粉末,各项技术参数和指标均符合规范要求[11]。试验所用膨胀剂为氧化钙-硫酸钙复合膨胀剂的化学组分见表1;聚羧酸减水剂(PCE)的外观为白色粉末状,易溶于水,减水率为20% ~ 35%;缓凝剂为海菜粉,其外观为白色粉末,易溶于水,溶液为无色透明的黏稠液体。考虑添加到高流态注浆材料的黏度和稳定性,控制溶液中海菜粉和水质量比为1:130。
在试样制备过程中,控制膨胀剂、减水剂、缓凝剂的质量分数分别为8% ~ 10%、0.3% ~ 0.5%、0.03 %~ 0.05%,确定膨胀剂掺量8%、减水剂掺量0.5%、缓凝剂掺量0.04%。将超细水泥与外加剂混合制备注浆材料,按水灰比1:1混合后用搅拌器匀速搅拌3 min。将煤样置于50 mm × 100 mm刚性模具内,采用注浆泵将高流态封孔注浆材料注入煤样,待煤样内的注浆材料完全凝固后养护,如图1所示。
按照水泥胶砂流动度测定法[12]以及《水泥胶砂强度测试标准》(GB/T 17671—2021),对制备后的材料进行流动性测试和抗压强度测试。
图2为普通水泥与高流态封孔材料膨胀率变化情况。其中,普通水泥材料由于在水化反应完成后会干裂收缩,膨胀率为负值,因此,在涉及普通水泥材料膨胀率时,采用收缩率表述。可以发现,膨胀率变化过程主要分为3个阶段:在第1阶段(1~ 14天),2种材料膨胀率变化较快,其中,高流态封孔材料膨胀率从0.21%迅速增长至1.24%,而普通水泥收缩率从-0.23%迅速下降至-0.62%;第2阶段(14~28天)2种材料膨胀率变化逐渐变缓,高流态封孔材料膨胀率从1.24%增长至1.53%,而普通水泥收缩率从-0.62%下降至-0.79%;第3阶段(28~60天)2种材料膨胀率基本达到稳定,高流态封孔材料膨胀率从1.53%增长至1.56%,普通水泥收缩率从-0.79%下降至-0.81%。这主要是由于普通水泥水化过程中消耗内部水分,产生的收缩力将导致试样体积缩小。其中,普通水泥材料在水化反应前期,内部水化反应充分,收缩率降幅较快,随着水化反应的结束,材料内部收缩率降幅较缓,直至保持稳定;由于高流态封孔材料含有一定膨胀剂,在水灰比较大时,其与水泥在水化早期具有相互促进作用,能生成大量钙矾石,该材料的吸水肿胀效应[13-14]是导致高流态封孔材料膨胀的主要驱动力,随着水化反应结束,膨胀率增加幅度逐渐变低,直至平衡。
孔隙率反映材料内部不同孔隙体积占比。通过压汞试验可以准确地测量出材料的总孔隙率以及不同孔径内的孔隙分布情况,得到孔径尺寸的相关信息,获得注浆前后煤体内部孔隙的连通性及形态变化规律。因此,采用压汞法测定不同注浆材料在注浆后,煤体内部孔隙结构的变化。
1) 孔径分布曲线。依据霍多特孔隙分类法划分孔径类别[15]:微孔直径小于0.01 μm;过渡孔直径为0. 01 ~ 0.1 μm;中孔直径为0.1 ~ 1.0 μm;大孔直径为1.0 ~ 100 μm。通过分析不同材料注浆后煤体孔径分布曲线,能够获得普通水泥封孔材料、高流态封孔材料注浆后试样孔径与进汞量(即不同外压下进入孔中汞的量)的对应关系[16],如图3所示。可以发现,高流态封孔材料注浆后,煤体孔隙分布更集中,并且大部分集中在微孔。在0.005 ~ 0.050 μm范围内,孔体积进汞量较高,这在一定程度上反映高流态封孔材料注浆后,煤体内部空间主要为微孔和过渡孔;而普通水泥材料注浆后,煤体内部孔径在0.050 ~ 0.100 μm范围内孔体积进汞量较高;当孔径在1 μm左右时,孔体积进汞量出现第2个峰值。此外,当孔径小于0.02 μm时,孔径对材料强度影响较小;而孔径大于0.02 μm时,孔径对强度影响较大,因此降低材料孔径有利于提升材料力学强度。
2) 进-退汞曲线。进-退汞曲线可直观反映出不同材料试样孔隙结构差异[17-18]。进汞曲线表示随压力增加,汞逐渐进入煤体内部孔隙的过程,曲线中快速上升部分对应着大孔径被汞填充过程,而缓慢上升部分则对应小孔径被汞填充过程;退汞曲线则反映了汞从孔隙中退出过程,与进汞曲线结合可以进一步验证孔径分布的准确性。图4为不同材料进退汞体积与孔径关系情况。可以看出,普通水泥材料注浆后,煤体进汞量高于高流态封孔材料注浆后煤体的进汞量。其中,普通水泥材料注浆后,煤体孔隙率为41.91%,平均孔径为40.44 nm,总进汞量0.33 mL/g;经过高流态注浆材料注浆后,煤体孔隙率下降至36.53%,平均孔径下降至23.08 nm,总进汞量下降至0.29 mL/g。此外,高流态注浆材料注浆后,煤体在微孔内孔体积进汞量较高,而普通水泥材料注浆后,煤体在微孔、过渡孔和中孔内孔体积进汞量较高,由于进汞量实质上反映了孔隙体积,所以普通水泥材料注浆后不能有效封堵煤体裂隙孔隙。
在蠕变试验前,需要开展注浆煤体单轴抗压试验,主要原因包括2方面:①注浆煤体单轴压缩应力-应变曲线能够反映固结体受压破坏的基本力学特性;②单轴压缩试验结果可为蠕变试验中分级加载的应力设置提供依据[19-20],具体步骤如下:将相似模拟试验中钻取的注浆煤体运回室内切割打磨,加工成直径50 mm、高度100 mm的标准圆柱体。利用单轴抗压试验机对注浆后的煤体进行单轴抗压试验,最终获取含孔充填试样的单轴抗压强度。
试样蠕变机制会随着应力水平变化而存在差异,为此,采用分级加载方式,以全面掌握试样在整个应力范围内的蠕变特性。煤体蠕变行为通常可在3 ~ 5次分级加载试验后较为全面地掌握,其中,加载次数和加载时间可根据应力范围和试样特性来确定。此外,煤体对蠕变响应速度较快,几小时内可以产生蠕变变形[21]。因此,共设定4级应力σ0,见表2
图5为含孔注浆试样的分级加载蠕变曲线。可发现,随压力等级提升,试样蠕变曲线整体呈阶梯状上升变化:
1) 在加载初期(0 ~ 0.3 h),不同应力条件下的蠕变位移均较大,由于注浆后煤样内部依旧存在一些小的孔隙,试样压密过程中,煤体内部孔隙结构不断闭合[20],蠕变位移也随之增加。
2) 在加载中期(0.3 ~ 2.5 h),试样开始进入稳定蠕变阶段,此加载应力条件下的煤样内部孔隙已被压实,当轴向应力较小时,注浆试样会发生减速蠕变和稳定蠕变过程。
3) 在加载末期(2.5 h以后),当轴向应力达到15.3 MPa后,注浆试样会加速蠕变,这反映注浆试样失稳破坏,因此可以得出含孔试样临界载荷为15.3 MPa。随应力等级进一步升高,由于煤样已经历压密过程,煤体应变增加逐渐放缓,进入屈服阶段后煤样内开始产生大量裂隙,并逐渐扩展、贯通,煤体产生不可恢复的塑性变形,此时煤样由压缩变形转变为膨胀变形,其内部裂隙不断汇合形成宏观裂纹,应变量进一步变大,最终产生加速蠕变。
图5中加载蠕变曲线求导,可得到不同应力下注浆煤体蠕变速率随时间变化特性[22],如图6所示。可以看出,随轴向加载应力增加,蠕变速率逐渐增大。而且随轴向应力增加,蠕变速率减速阶段时间也随之延长,随后注浆煤体试样进入稳定阶段。当蠕变试验进入第4次加载阶段(σ0= 15.3 MPa)时,蠕变速率明显增大,最大蠕变速率为0.023%/h,表明试样达到临界载荷,发生破坏。
由注浆煤体蠕变试验结果可知:注浆煤体受载后会产生瞬时弹性变形,说明注浆煤体中含有弹性体[23],因此具有典型弹性特性。随加载时间增加,注浆煤体应变速率逐渐减小;在低应力加载过程中,注浆煤体应变随时间增加逐渐趋于恒定值,在高应力加载过程中,注浆煤体应变会随时间增加而持续增加;当加载应力超过煤岩体的极限强度时,试样应变会急剧增大,最终发生破坏[24-25]
由注浆煤体蠕变特征可进一步得出,煤体注浆后表现出典型的非线性黏弹塑性特征。因此,可将注浆煤体假设为黏-弹-塑性介质,进而构建钻孔周围注浆煤体黏-弹-塑性蠕变模型,其中黏弹性区采用鲍埃丁-汤姆逊模型。通过引入黏塑性体元件η(t),可描述煤岩体塑性变形,该元件是将塑性元件和非线性黏性元件并联起来的非线性黏塑性元件[26-27],如图7所示。该元件可描述煤岩体在不同应力状态下的加速蠕变特征,具体如下:
ε = 0 σ 0 σ s σ 0 - σ s η 2 [ e x p ( t n ) - 1 ]   σ 0 σ s
式中:ε为应变,t为蠕变时间,min;σ0为材料所受载荷,MPa;σs为材料屈服极限,MPa;η2为模型黏性参数,n为时间系数。
将新建立的非线性黏塑性元件与鲍埃丁-汤姆逊体、弹性元件和塑性元件进行串联,可进一步得到能合理描述注浆煤岩体蠕变全程的非线性黏弹塑性力学模型,模型中的参量包括胡克体、黏弹性体、黏塑性体和黏性元件,上述参量对应的应变分别为ε1ε2ε3ε4,对应的应力分别为σ1σ2σ3σ4E1E2E3分别为胡克体、黏弹性体和黏塑性体的弹性参数,如图8所示。当模型所受的应力小于σs时,模型中非线性黏塑体不发挥作用,当模型所受应力大于σs时,非线性黏塑体开始触发。
根据元件串联和并联方式差异,非线性黏弹塑性流变模型总应变可表示如下:
ε = ε 1 + ε 2 + ε 3 + ε 4
σ = σ 1 + σ 2 + σ 3 + σ 4
各部分参数间的本构关系如下:
σ 0 = E 1 ε 1 σ 0 = η 1 E 2 ( E 2 + E 3 ) ε 2 + E 3 ε - η 1 E 2 σ 0 σ 0 = σ 1 + η 2 ε 3 σ 1 σ s σ 0 = σ s + η 2 ε 3 σ 1 σ s σ 0 = η 3 ε 4
对式(4)进行求解,可得模型中各参量蠕变方程。
ε 1 = σ 0 E 1 ε 2 = σ 0 E 2 1 - E 3 E 2 + E 3 e x p - E 2 E 3 ( E 2 + E 3 ) η 1 t ε 3 = 0 σ 1 σ s ε 3 = σ 0 - σ s η 2 [ e x p ( t n ) - 1 ] σ 1 σ s ε 4 = σ 0 t η 3
ε = σ 0 E 1 + σ 0 E 2 1 - E 1 E 1 + E 2 e x p - E 1 E 2 ( E 1 + E 2 ) η 1 t +   σ 0 t η 3 σ 1 σ s ε = σ 0 E 1 + σ 0 E 2 1 - E 1 E 1 + E 2 e x p - E 1 E 2 ( E 1 + E 2 ) η 1 t +   σ 0 - σ s η 2 [ e x p ( t n ) - 1 ] + σ 0 t η 3 σ 1 σ s
式中η1η2η3分别为模型中黏弹性体、黏塑性体和黏性元件的黏性参数。
为验证所建立非线性黏弹塑性模型的准确性,对非线性黏弹塑性模型参数进行反演,得到相关参数与拟合曲线,如图9所示。通过计算非线性黏弹塑性模型相关系数可验证参数反演结果额准确性,非屈服应力(σ0<σs)及屈服应力(σ0σs)条件下模型参数的反演结果分别见表3表4
将所得到的参数代入非线性黏弹塑性模型中,得到注浆煤体在不同应力水平下的蠕变本构方程:
σ0= 4.5 MPa时,注浆煤体蠕变本构方程为:
ε ( t )   =   0.66 - 0.617 e x p ( - 7.8 t ) + 0.012   9 t  
σ0=8.1 MPa时,注浆煤体蠕变本构方程为:
ε ( t )   =   1.175 - 0.573 e x p ( - 11.35 t ) + 0.002   6 t
σ0=11.7 MPa时,注浆煤体蠕变本构方程为:
ε ( t )   =   1.686 - 0.597 e x p ( - 11 t ) +   0.002   8 t
σ0= 15.3 MPa时,注浆煤体蠕变本构方程为
ε ( t )   =   3.823 - 2.777 e - 8.17 t + 6.4 × 10 - 6 t +   0.005   6 e 2.88 t
通过图9中试验数据与本构方程的对比情况,可以发现,式(7)—式(10)的拟合效果较好,这反映浆煤体蠕变本构方程可用于研究高流态封孔注浆材料膨胀及蠕变特性。
1) 不同注浆材料膨胀率变化速率可分为加速阶段,减速阶段与稳定阶段3个阶段;随着水化反应的进行,高流态封孔材料膨胀率不断升高,最后增加到1.562%,普通水泥持续收缩,膨胀率不断减小,最后下降到-0.813%。高流态注浆材料可在一定程度上解决因材料收缩而导致的钻孔漏气问题。
2) 高流态注浆材料注浆后,煤体内部孔隙分布更集中,多为微孔,平均孔径23.08 nm,结构更致密;而普通水泥材料注浆后,煤体孔隙空间主要由微孔、过渡孔和中孔组成,平均孔径为40.44 nm。高流态浆体材料可较好改善煤体孔隙结构。
3) 当注浆煤体所受应力水平小于临界值时,注浆煤体单轴蠕变过程分为减速蠕变和稳定蠕变,当注浆煤体所受应力水平达到临界值时,注浆煤体失稳破坏,其破坏临界荷载为15.3 MPa;随加载应力的增加,试样蠕变速率逐步增大,而且施加应力越大,蠕变速率减速阶段时间也越大。
  • 国家自然科学基金面上项目资助(52274196)
  • 湖南省杰出青年基金资助(2022JJ10026)
  • 煤炭安全精准开采国家地方联合工程研究中心项目(EC2023019)
  • 湖南省青年基金资助(2023JJ40284)
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2024年第34卷第10期
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doi: 10.16265/j.cnki.issn1003-3033.2024.10.0636
  • 接收时间:2024-06-11
  • 首发时间:2025-07-09
  • 出版时间:2024-10-28
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  • 收稿日期:2024-06-11
  • 修回日期:2024-08-19
基金
国家自然科学基金面上项目资助(52274196)
湖南省杰出青年基金资助(2022JJ10026)
煤炭安全精准开采国家地方联合工程研究中心项目(EC2023019)
湖南省青年基金资助(2023JJ40284)
作者信息
    1 湖南科技大学 资源环境与安全工程学院,湖南 湘潭 411201
    2 湖南科技大学 南方煤矿瓦斯与顶板灾害预防控制安全生产重点实验室,湖南 湘潭 411201
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2种不同金属材料的力学参数

Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)

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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