纤维聚合物锚杆的锚固机理及数值分析
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摘要
钢锚杆加固技术是岩土工程加固的一种重要手段，它能比较充分地调动和提高岩土体自身的强度和稳定，缩小结构物尺寸和减轻其自重，显著节约工程材料。随着锚固技术的发展和应用领域的拓宽，钢锚杆几乎应用于土木建筑领域的各个方面，如在边坡、基坑、矿井、隧道、地下工程、坝体、机场、港口、挡土墙、桥台锚固等工程建设与改造中都已得到广泛应用。
工程应用表明，钢锚杆在锚固工程中的应用也存在一些突出的问题，如钢锚的腐蚀和防腐处理、自重偏大、运输和安装困难等。这些不足在一定程度上制约了钢锚杆的应用，尤其是钢锚杆的腐蚀不仅影响结构的耐久性，严重时还会出现重大工程事故。纤维增强塑料(简称FRP)筋是以纤维为增强材料，以合成树脂为基体材料，掺入适量的辅助剂，经挤拉成型技术和必要的表面处理所形成的一种新型复合材料。它具有比强度高、耐腐蚀性能好、可设计性强、抗疲劳性能优良、耐电磁等独特优点。因此，用纤维增聚合物锚杆代替钢锚杆为锚固技术在岩土工程中的应用开辟了广阔的前景。
但是，目前对于纤维增强塑料锚杆的研究和应用相对较少。在我国，理论研究处于起步阶段，生产应用及设计理论方面几乎是空白。概括国内外的研究现状主要存在以下几方面的问题：(1)纤维增强塑料筋锚具受力性能研究较少；(2)纤维增强塑料锚杆与水泥浆、水泥砂浆的粘结性能研究不够；(3)考虑纤维增强塑料拉杆、粘结材料(如浆体)性能、岩体之间三者相互作用的受力模式还没有具体的粘结理论方程；(4)纤维增强塑料锚杆承载力计算方法以及数值模拟计算还没有引起应有的重视。
为了推动纤维增强塑料锚杆在锚固工程中的广泛应用，本文在国家自然科学基金(项目名称：纤维增强塑料锚杆锚固机理研究，编号：50079028)和河南杰出青年基金的资助下，进行理论分析和数值模拟。在考虑了锚杆、混凝土锚固体以及周围岩土体三者的相互作用下，选取合理的受力模式，推导出粘结—滑移理论微分方程；在FRP锚杆锚固在混凝土块体和野外岩土体的具体试验数据的基础上，对纤维增强塑料锚杆的受力性能进行了较为深入的分析研究；依托这些试验参数和数据，编制计算机程序进行数值模拟，为锚杆在实际中的应用提供了理论依据和分析计算方法。主要研究成果如下：
(1) 详细论述了纤维增强塑料筋与混凝土粘结试验方法、粘结机理以及影响因素。根据纤维增强塑料筋和混凝土锚固体粘结应力和滑移之间的关系，并在总结国内外已有的纤维增强塑料筋与混凝土之间的粘结—滑移本构模式的基础上，选取了合适的FRP锚固粘结—滑移模式。
郑州大学硕士学位论文
(2)把纤维增强塑料锚杆与锚固体之间的粘结层简化为粘结界面，把锚固体和
岩土体之间的粘结层也简化为界面，在考虑三者的共同作用下建立了粘结滑移理
论方程。
(3)以建立的粘结滑移力学模式为基础，采用纤维增强塑料锚杆与锚固体的非
线性的粘结一滑移本构关系以及混凝土锚固体和岩土体之间的折线粘结一滑移本
构关系，利用数值迭代方法和递推计算进行数值分析，对纤维增强塑料锚杆与锚
固体锚固性能进行了全过程分析。
(4)运用编制的数值模拟计算程序，计算并分析了室内和野外锚固拉拔试验。
将计算结果和与实验结果以及理论公式计算结果进行分析和对比，得到了纤维增
强塑料锚杆与混凝土的粘结力与滑移以及锚固长度和滑移之间的关系，以及应变
沿锚固长度的分布。
(5)探讨了纤维增强塑料粘结型锚杆锚固力的计算方法，建议了纤维增强塑料
锚杆与水泥浆体之间粘结强度值，提出了适合于纤维增强塑料粘结型锚杆特点的
计算方法。
Steel anchors are being used in a wide range of ground or rock conditions. They can improve the strength and reliability of ground, reduce the dimension of structures and lighten their weight. So they can save the materials in engineering. With increased experience and improved anchoring techniques, steel anchors have become a common practice in almost every aspect of civil engineering such as slopes, foundations, mines, tunnels, underground excavations, concrete dams, airports, aerodrome, ports, retaining wall, bridge abutments, rehabilitation of existing concrete structures, and so on.
With the engineering applications, it has been shown that there exist some problems in steel anchors such as corrosion of steel tendon, requirements for corrosion protection, heavy weight, difficulty in transportation and installation. These disadvantages of steel restrict their applications to a certain extent. Above all, the corrosion of steel anchors not only affects the durability of steel anchors, but may result in serious accidents. Fiber reinforced plastic (FRP) rebar is a new composite material. It is composed of fiber filaments and a resin matrix. The fiber of high tensile strength and high modulus of elasticity is used as reinforcing material. The synthetic resin is used as matrix material and is mixed with adequate auxiliaries. The fiber reinforced plastic rebar is manufactured using a pul-trusion method and necessary surface process. It offers significant advantages over conventional reinforcing steel bars, namely, high tensile strength to weigh ratio, excellent chemical resistance, liable to des
ign, high fatigue strength and electro-magnetic neutrality. So the fiber reinforced plastic bar anchors can make the anchoring techniques have a more wide range of rock engineering applications.
However, few investigations and filed applications are available recently. In our country, theory analysis has just begun, no information is available for the field applications, and the design theories have already been formed. According to the available investigations at home and abroad, main problems should be attached importance to. namely, the study of the properties of FRP rebar and concrete/cement grout is scarcely investigated; The definite bond-slip theoretical differential functions have not been available, which takes into account the effect among FRP rebar members; the calculating method and the numerical analysis of applied tensile load about FRP anchor have not taken seriously, in according to
the three factors reminded in the front; and the properties of bond materials (such as cement grout) and rock, has not yet been attached importance to.
In order to make the FRP rebar anchors widely applied in anchoring engineering, with the help of the Physical Science Fund of our country (the title of the item: Research into the anchoring mechanism of FRP anchors, No. 0079028) and The Prominent Youth Fund of Henan province, proceeding the theory analysis and numerical simulator. In the case of the three mutual effects of the anchor, the concrete anchorage and the rock, selecting the reasonable loading model, the bond-slip differential equation is derived. Based on the about the practical anchoring experiments in the concrete block (in the laboratory) and in the rock (in the field), the study of the mechanical properties of FRP tendon anchors is made. According these experimental parameters and the data, the simulators are made up and displayed in the computer. These researches provide the basis and the methods for the application of FRP anchors. The main achievements of this dissertation are as follows:
1. The testing method of the behavior about the bond of FRP rebar to concrete, the bond mechanisms and influential factors are discussed. According to the mechanism of force transference between FRP rebar and concrete, this dissertation discusses the relationship among bond stress, the stress of FRP bar and embedment length. Based on the summary of the existence bond-slip relation models home and abroad, the continuous smooth
工程应用表明，钢锚杆在锚固工程中的应用也存在一些突出的问题，如钢锚的腐蚀和防腐处理、自重偏大、运输和安装困难等。这些不足在一定程度上制约了钢锚杆的应用，尤其是钢锚杆的腐蚀不仅影响结构的耐久性，严重时还会出现重大工程事故。纤维增强塑料(简称FRP)筋是以纤维为增强材料，以合成树脂为基体材料，掺入适量的辅助剂，经挤拉成型技术和必要的表面处理所形成的一种新型复合材料。它具有比强度高、耐腐蚀性能好、可设计性强、抗疲劳性能优良、耐电磁等独特优点。因此，用纤维增聚合物锚杆代替钢锚杆为锚固技术在岩土工程中的应用开辟了广阔的前景。
但是，目前对于纤维增强塑料锚杆的研究和应用相对较少。在我国，理论研究处于起步阶段，生产应用及设计理论方面几乎是空白。概括国内外的研究现状主要存在以下几方面的问题：(1)纤维增强塑料筋锚具受力性能研究较少；(2)纤维增强塑料锚杆与水泥浆、水泥砂浆的粘结性能研究不够；(3)考虑纤维增强塑料拉杆、粘结材料(如浆体)性能、岩体之间三者相互作用的受力模式还没有具体的粘结理论方程；(4)纤维增强塑料锚杆承载力计算方法以及数值模拟计算还没有引起应有的重视。
为了推动纤维增强塑料锚杆在锚固工程中的广泛应用，本文在国家自然科学基金(项目名称：纤维增强塑料锚杆锚固机理研究，编号：50079028)和河南杰出青年基金的资助下，进行理论分析和数值模拟。在考虑了锚杆、混凝土锚固体以及周围岩土体三者的相互作用下，选取合理的受力模式，推导出粘结—滑移理论微分方程；在FRP锚杆锚固在混凝土块体和野外岩土体的具体试验数据的基础上，对纤维增强塑料锚杆的受力性能进行了较为深入的分析研究；依托这些试验参数和数据，编制计算机程序进行数值模拟，为锚杆在实际中的应用提供了理论依据和分析计算方法。主要研究成果如下：
(1) 详细论述了纤维增强塑料筋与混凝土粘结试验方法、粘结机理以及影响因素。根据纤维增强塑料筋和混凝土锚固体粘结应力和滑移之间的关系，并在总结国内外已有的纤维增强塑料筋与混凝土之间的粘结—滑移本构模式的基础上，选取了合适的FRP锚固粘结—滑移模式。
郑州大学硕士学位论文
(2)把纤维增强塑料锚杆与锚固体之间的粘结层简化为粘结界面，把锚固体和
岩土体之间的粘结层也简化为界面，在考虑三者的共同作用下建立了粘结滑移理
论方程。
(3)以建立的粘结滑移力学模式为基础，采用纤维增强塑料锚杆与锚固体的非
线性的粘结一滑移本构关系以及混凝土锚固体和岩土体之间的折线粘结一滑移本
构关系，利用数值迭代方法和递推计算进行数值分析，对纤维增强塑料锚杆与锚
固体锚固性能进行了全过程分析。
(4)运用编制的数值模拟计算程序，计算并分析了室内和野外锚固拉拔试验。
将计算结果和与实验结果以及理论公式计算结果进行分析和对比，得到了纤维增
强塑料锚杆与混凝土的粘结力与滑移以及锚固长度和滑移之间的关系，以及应变
沿锚固长度的分布。
(5)探讨了纤维增强塑料粘结型锚杆锚固力的计算方法，建议了纤维增强塑料
锚杆与水泥浆体之间粘结强度值，提出了适合于纤维增强塑料粘结型锚杆特点的
计算方法。
Steel anchors are being used in a wide range of ground or rock conditions. They can improve the strength and reliability of ground, reduce the dimension of structures and lighten their weight. So they can save the materials in engineering. With increased experience and improved anchoring techniques, steel anchors have become a common practice in almost every aspect of civil engineering such as slopes, foundations, mines, tunnels, underground excavations, concrete dams, airports, aerodrome, ports, retaining wall, bridge abutments, rehabilitation of existing concrete structures, and so on.
With the engineering applications, it has been shown that there exist some problems in steel anchors such as corrosion of steel tendon, requirements for corrosion protection, heavy weight, difficulty in transportation and installation. These disadvantages of steel restrict their applications to a certain extent. Above all, the corrosion of steel anchors not only affects the durability of steel anchors, but may result in serious accidents. Fiber reinforced plastic (FRP) rebar is a new composite material. It is composed of fiber filaments and a resin matrix. The fiber of high tensile strength and high modulus of elasticity is used as reinforcing material. The synthetic resin is used as matrix material and is mixed with adequate auxiliaries. The fiber reinforced plastic rebar is manufactured using a pul-trusion method and necessary surface process. It offers significant advantages over conventional reinforcing steel bars, namely, high tensile strength to weigh ratio, excellent chemical resistance, liable to des
ign, high fatigue strength and electro-magnetic neutrality. So the fiber reinforced plastic bar anchors can make the anchoring techniques have a more wide range of rock engineering applications.
However, few investigations and filed applications are available recently. In our country, theory analysis has just begun, no information is available for the field applications, and the design theories have already been formed. According to the available investigations at home and abroad, main problems should be attached importance to. namely, the study of the properties of FRP rebar and concrete/cement grout is scarcely investigated; The definite bond-slip theoretical differential functions have not been available, which takes into account the effect among FRP rebar members; the calculating method and the numerical analysis of applied tensile load about FRP anchor have not taken seriously, in according to
the three factors reminded in the front; and the properties of bond materials (such as cement grout) and rock, has not yet been attached importance to.
In order to make the FRP rebar anchors widely applied in anchoring engineering, with the help of the Physical Science Fund of our country (the title of the item: Research into the anchoring mechanism of FRP anchors, No. 0079028) and The Prominent Youth Fund of Henan province, proceeding the theory analysis and numerical simulator. In the case of the three mutual effects of the anchor, the concrete anchorage and the rock, selecting the reasonable loading model, the bond-slip differential equation is derived. Based on the about the practical anchoring experiments in the concrete block (in the laboratory) and in the rock (in the field), the study of the mechanical properties of FRP tendon anchors is made. According these experimental parameters and the data, the simulators are made up and displayed in the computer. These researches provide the basis and the methods for the application of FRP anchors. The main achievements of this dissertation are as follows:
1. The testing method of the behavior about the bond of FRP rebar to concrete, the bond mechanisms and influential factors are discussed. According to the mechanism of force transference between FRP rebar and concrete, this dissertation discusses the relationship among bond stress, the stress of FRP bar and embedment length. Based on the summary of the existence bond-slip relation models home and abroad, the continuous smooth
引文
[1]．谢晶晶．纤维增强塑料筋锚杆锚固机理[D]．郑州：郑州大学工学院硕士学位论文，2002年5月．
[2]．王焕文．王继良等．锚喷支护[M]．煤矿工业出版社，1989年1月．
[3]．朱浮生．郑雨天．全长粘结式锚杆加固作用分析[J]．岩石力学与工程学报．1996年12月，15(4)，333—337．
[4]．侯朝迥．郭宏亮．我国煤巷锚杆支护技术的发展方向[J]，煤炭学报．1996，No-2．114～118。
[5]．范世平．丁全录．玻璃钢锚杆的应用研究[J]．煤炭科学技术．996年9月，24(9)，4—5．
[6]．侯朝迥．江利．等．高强度锚杆[J]．矿山压力与顶板管理．1997年，No3-4，176—179．
[7]．程良奎．我国沿途锚固技术的现状与发展[A]．见：中国岩土锚固工程协会．岩土工程中的锚固技术[C]．北京：地震出版社，1992，1—5．
[8]. Suart Little John. "Rock Anchorages" [J]. News Journal, ISRM, 1995, 2(384), 23—30.
[9]. Peter Setphan," Extending the scope of application of rock bolting, and new developments", Gluckauf. Translation [M], 123 (1987)No. 9
[10]. Brahim Benmokrane, Ph. D., P.Eng. and Michael H. Xu, Ph. D, "Design and Applications of Aramid and Carbon Fiber-Reinforced Plastic (FRP) Ground Anehor"[J]. 1996.
[11]. Brahim Benmokrane, Burong Zhang, Adil Chennouf, "Tensile properities and pullout behavior of AFRP and CFRP rods for grouted anchor applieations"[J]. Construction and Building Materials, January, 2000. 14(2000), 157—170.
[12]. M.TOKUMARU and T.NARUSE, J.MIZUTANI and M.ASAI. "Development and construction of durable aramid anchors"[A]. Proceedings of Second International RILEM Symposium: FRPR-2 [C]. 1995, 696—703.
[2]．王焕文．王继良等．锚喷支护[M]．煤矿工业出版社，1989年1月．
[3]．朱浮生．郑雨天．全长粘结式锚杆加固作用分析[J]．岩石力学与工程学报．1996年12月，15(4)，333—337．
[4]．侯朝迥．郭宏亮．我国煤巷锚杆支护技术的发展方向[J]，煤炭学报．1996，No-2．114～118。
[5]．范世平．丁全录．玻璃钢锚杆的应用研究[J]．煤炭科学技术．996年9月，24(9)，4—5．
[6]．侯朝迥．江利．等．高强度锚杆[J]．矿山压力与顶板管理．1997年，No3-4，176—179．
[7]．程良奎．我国沿途锚固技术的现状与发展[A]．见：中国岩土锚固工程协会．岩土工程中的锚固技术[C]．北京：地震出版社，1992，1—5．
[8]. Suart Little John. "Rock Anchorages" [J]. News Journal, ISRM, 1995, 2(384), 23—30.
[9]. Peter Setphan," Extending the scope of application of rock bolting, and new developments", Gluckauf. Translation [M], 123 (1987)No. 9
[10]. Brahim Benmokrane, Ph. D., P.Eng. and Michael H. Xu, Ph. D, "Design and Applications of Aramid and Carbon Fiber-Reinforced Plastic (FRP) Ground Anehor"[J]. 1996.
[11]. Brahim Benmokrane, Burong Zhang, Adil Chennouf, "Tensile properities and pullout behavior of AFRP and CFRP rods for grouted anchor applieations"[J]. Construction and Building Materials, January, 2000. 14(2000), 157—170.
[12]. M.TOKUMARU and T.NARUSE, J.MIZUTANI and M.ASAI. "Development and construction of durable aramid anchors"[A]. Proceedings of Second International RILEM Symposium: FRPR-2 [C]. 1995, 696—703.