Numerical evaluation of strength and deformability of fractured rocks

Knowledge of the strength and deformability of fractured rocks is important for design, construction and stability evaluation of slopes, foundations and underground excavations in civil and mining engineering. However, laboratory tests of intact rock samples cannot provide information about the strength and deformation behaviors of fractured rock masses that include many fractures of varying sizes, orientations and locations. On the other hand, large-scale in situ tests of fractured rock masses are economically costly and often not practical in reality at present. Therefore, numerical modeling becomes necessary. Numerical predicting using discrete element methods(DEM) is a suitable approach for such modeling because of their advantages of explicit representations of both fractures system geometry and their constitutive behaviors of fractures, besides that of intact rock matrix. In this study, to generically determine the compressive strength of fractured rock masses, a series of numerical experiments were performed on two-dimensional discrete fracture network models based on the realistic geometrical and mechanical data of fracture systems from feld mapping. We used the UDEC code and a numerical servo-controlled program for controlling the progressive compressive loading process to avoid sudden violent failure of the models. The two loading conditions applied are similar to the standard laboratory testing for intact rock samples in order to check possible differences caused by such loading conditions. Numerical results show that the strength of fractured rocks increases with the increasing confning pressure, and that deformation behavior of fractured rocks follows elasto-plastic model with a trend of strain hardening. The stresses and strains obtained from these numerical experiments were used to ft the well-known Mohr-Coulomb(MC) and Hoek-Brown(H-B) failure criteria, represented by equivalent material properties defning these two criteria. The results show that both criteria can provide fair estimates of the co     

A modified Hoek–Brown failure criterion for anisotropic intact rock

The Hoek–Brown criterion parameters (σ_ci, m_i and s) are significantly influenced by the strength anisotropy of intact rock. In the present study, the criterion was modified by incorporating a new parameter (k_β) to account for the effect of strength anisotropy, thus being able to determine the strength of intact anisotropic rock under loading in different orientations of the plane of anisotropy. The range of the parameter (k_β) for the rocks tested has been analytically investigated by carrying out triaxial tests, in different orientations of the foliation plane. The proposed modification was studied for metamorphic rocks (gneiss, schist, marble), but could also be applied to other rock types exhibiting “inherent” anisotropy, e.g. sedimentary as well as igneous rocks. The proposed modified criterion is intended for use for prediction of strength of intact rock, but can also be extended to rock masses.     

Anisotropy of strength and deformability of fractured rocks

Anisotropy of the strength and deformation behaviors of fractured rock masses is a crucial issue for design and stability assessments of rock engineering structures, due mainly to the non-uniform and non- regular geometries of the fracture systems. However, no adequate efforts have been made to study this issue due to the current practical impossibility of laboratory tests with samples of large volumes con- taining many fractures, and the difficulty for controlling reliable initial and boundary conditions for large-scale in situ tests. Therefore, a reliable numerical predicting approach for evaluating anisotropy of fractured rock masses is needed. The objective of this study is to systematically investigate anisotropy of strength and deformability of fractured rocks, which has not been conducted in the past, using a nu- merical modeling method. A series of realistic two-dimensional （2D） discrete fracture network （DFN） models were established based on site investigation data, which were then loaded in different directions, using the code UDEC of discrete element method （DEM）, with changing confining pressures. Numerical results show that strength envelopes and elastic deformability parameters of tested numerical models are significantly anisotropic, and vary with changing axial loading and confining pressures. The results indicate that for design and safety assessments of rock engineering projects, the directional variations of strength and deformability of the fractured rock mass concerned must be treated properly with respect to the directions of in situ stresses. Traditional practice for simply positioning axial orientation of tunnels in association with principal stress directions only may not be adequate for safety requirements. Outstanding issues of the present study and su~zestions for future study are also oresented.     

Influence of geometrical distribution of rock joints on deformational behavior of underground opening

Mechanisms of deformation and failure of underground opening in jointed rock masses are governed by the characteristics of the geometrical distribution of discontinuities. In this paper, the extracting method of geometrical distribution of discontinuities in rock masses by image processing is presented and used to make networks of rock joints from the construction field. Next, using those networks, fractal characteristics of the discontinuities are described by using the box-counting method for quantitatively evaluating the state of the discontinuous distribution. Finally, numerical analysis based a case of the excavation of underground power plant is carried out to find the relation between geometrical distribution of rock joints and deformational behavior of underground opening by using distinct element method.     

Strain-based strength model for direct punching shear of interior slab-column connections

A strength model was developed to predict the direct punching shear strength of interior slab-column connections without shear reinforcement. At slab-column connections damaged by flexural cracking, it was assumed that the punching shear force was resisted mainly by the compression zone of the critical section. The punching shear strength at the critical section was determined at the intersection between the shear capacity curve and the demand curve. The shear capacity was defined by the material failure criteria of concrete, addressing the effect of the slab flexural stresses on the shear stress capacity of concrete. The shear demand was defined as a shear force required to develop the flexural moment of the slab. For the application of the proposed model to design practice, a simplified strength model was also developed, introducing two modification factors involving in the size effect and non-uniform shear stress distribution. For verification, the proposed strength model was applied to existing test specimens tested by other researchers.     

The elastic deformability and strength of a high porosity, anisotropic chalk

The submission explores the mechanical behavior of a very porous chalk formation, in which a system of ancient caverns was excavated. Incidents of general and localized failure of these ancient caverns initiated a comprehensive laboratory testing program aimed at investigating the anisotropic nature of the stress–strain response and strength of the material. It was felt that these aspects could be of profound importance in the stability of the cavern systems. The effect of water content over a broad range from 1.5% to saturation, on the compressive and tensile strength was also studied. Testing was based on the hollow cylinder methodology and was supplemented with uniaxial compression of solid cylinders and diametric compression of Brazilian disks. Use of the hollow cylinder methodology was extended to failure conditions.Test results illustrate the anisotropic nature of the stress–strain response of the chalk. The material clearly displays transverse isotropy, with horizontal bedding planes corresponding to the plane of material symmetry. The modulus of deformation within the plane of material symmetry is significantly higher than that perpendicular to bedding planes. Torsional shear of hollow cylinder specimens was employed to measure the shear modulus of the chalk.The testing carried out up to failure illustrated the anisotropy of the chalk strength. The compressive strength was found to be 50% higher in compression parallel to bedding than perpendicular to bedding. Increasing water content was found to have a consistent detrimental effect on compressive strength, tensile strength and material stiffness. The most drastic effect was found due to relatively small increases in water content, at initial water contents of less than 5%. Anisotropy of the chalk strength was found to persist over the entire range of water contents considered.     

Plasticity role in strength behavior of cement-phosphogypsum stabilized soils

Dredged soil and phosphogypsum are frequently regarded as wasted materials, which require further treatment to control their environmental impact. Hence, phosphogypsum is proposed as a binder to stabilize dredged soil, aiming at efficiently reducing and reusing these waste materials. In this study, the engineering properties of cement-phosphogypsum stabilized dredged soils were investigated through a series of unconfined compression tests, and the effects of plasticity index of original soils on the strength improvement were identified. Then, the microstructure test and mineralogical test were performed to understand the mechanism of physical role of original soils in strength improvement. The results revealed that the unconfined compressive strength significantly decreased with the increase in plasticity index at the same binder content. The essential factor for strength improvement was found to be the formation of cementitious materials identified as calcium silicate hydrate (CSH), calcium aluminate hydrate (CAH), and ettringite (Aft). The normalized integrated intensity of cementitious materials (CSH + CAH + Aft) by pore volume decreased with the increase in plasticity index. Consequently, the density of cementitious materials filling the soil pores controlled the effectiveness of strength improvement. More cementitious materials per pore volume were observed for the original soils with lower values of plasticity index. That is, the higher strength of stabilized soils with lower values of plasticity index was attributed to a packed structure forming by integrated fabric through denser cementitious components. It can be anticipated from the above findings that the effectiveness of stabilization treatment will significantly reduce with the increase in plasticity of origin soil.     

扭矩和轴压共同作用下各向异性薄壁和中厚壁圆筒的屈曲性能

采用基于考虑了各向异性和横向剪切刚度影响的厚壳理论的分析模型,研究各向异性、横向剪切刚度、长度和它们的相互作用对纯扭或者扭矩与轴压共同作用下圆筒屈曲性能的影响。由于该模型仅轴压下的屈曲性能得到验证,故将轴压下分析结果与扭转作用下作对比。结果表明,该模型对扭矩作用下屈曲性能亦有较好的适用性。研究表明,各向异性、横向剪切刚度及壳体长度均影响柱壳的临界力大小。这说明空心壳理论(Donnell理论)并不准确,应该采用考虑了各向异性和横向剪切刚度影响的厚壳理论。     

Arranging the plastic hinges and improving the strength of steel tubes with tapered ends: Analysis and tests

A new form of space structure, polyhedron frames, was developed recently. In polyhedron frame structures, most structural members are under multi-loads of compression, bending and torsion. A new type of tapered member that is obtained by axially connecting a constant-section tube to two tapered and relatively short tubes was proposed to be the structural member of polyhedron frame structures. We named this kind of tapered member a tapered-end tube. This paper has analytically and experimentally proved that tapered-end tubes can restrict the plastic hinge to the interface of the constant-section part and the tapered part, and the location of the plastic hinge can be arranged by correctly choosing the ratio of slope of the tapered ends. Corresponding tests and simulations are done to verify the analytical prediction, and these also reveal that the strength of the tubes is significantly improved by the tapered ends.     

Axial load behavior and strength of tubed steel reinforced-concrete (SRC) stub columns

This paper presents experimental and analytical studies on the behavior of tubed SRC stub columns subjected to axial compressive load. Fourteen circular tubed SRC (CTSRC) and fifteen square tubed SRC (STSRC) stub columns were tested to investigate the failure mode and axial loaded behavior of tubed SRC columns. The effect of diameter/width to thickness ratio of the tubes was studied. The effect of height to diameter/width ratio of the separated tubes in tubed SRC columns was studied to investigate the effect of bond and friction between tube and concrete on the behavior of tubed SRC columns. The test results indicated that tubed SRC stub columns exhibited higher axial load capacity than common SRC columns with the same volumetric steel ratio. Elastic–plastic analysis on the steel tube was employed to study the mechanism of tubed SRC stub columns subjected to axial compression. Equations for the prediction of the axial load strength of tubed SRC stub columns were also proposed based on the proposed experimental results.     

节理的剪切力学性质与含三维形貌参数的剪切强度准则比较研究

利用水泥砂浆材料浇注3组不同表面形貌的节理试件,由常法向应力下的直剪试验研究节理的剪切力学性质,并分析法向应力、三维形貌特征对抗剪强度的影响。直剪试验结果表明：峰值剪胀角与法向应力成反变化关系,与粗糙程度呈正变化关系;峰值抗剪强度与法向应力、粗糙程度均呈正变化关系。分析了JRC-JCS准则计算值偏低于试验值的原因,根据试验现象建议采用三维形貌参数、抗拉强度描述节理的剪切强度。对比分析了含三维形貌参数的峰值抗剪强度准则,建议低法向应力水平下采用双曲线形式的峰值剪切强度准则估算岩石节理的峰值抗剪强度。     

A review of floc strength and breakage

The main focus of the paper is to review current understanding of floc structure and strength. This has been done by reviewing current theoretical understanding of floc growth and breakage and an analysis of different techniques used for measuring floc strength. An overview has also been made of the general trends seen in floc strength analysis. The rate of floc formation is a balance between breakage and aggregation with flocs eventually reaching a steady-state size for a given shear rate. The steady-state floc size for a particular shear rate can, therefore, be a good indicator of floc strength. This has resulted in the development of a range of techniques to measure floc size at different applied shear levels using a combination of one or more of the following tools: light scattering and transmission; microscopy; photography; video and image analysis software. Floc strength may be simply quantified using the initial floc size for a given shear rate and the floc strength factor. More complex techniques have used theoretical modelling to determine whether flocs break by large-scale fragmentation or smaller-scale surface erosion effects, although this interpretation is open to debate. Impeller-based mixing, ultrasound and vibrating columns have all been used to provide a uniform, accurate and controllable dissipation of energy onto a floc suspension to determine floc strength. Other more recent techniques have used sensitive micromanipulators to measure the force required to break or compress individual flocs, although these techniques have been limited to the measurement of only a few hundred flocs. General trends emerge showing that smaller flocs tend to have greater strength than larger flocs, whilst the use of polymer seems to give increased strength to only some types of floc. Finally, a comparison of the strength of different types of floc (activated sludge flocs, organic matter flocs, sweep flocs and charge neutralised flocs) has been made highlighting differences in relative floc strength.     

Numerical analysis of tensile behavior of geogrids with rectangular and triangular apertures

Geogrids, made of polymeric materials, have been used as a construction material for many applications, such as walls, slopes, roads, building foundations, etc. In the past, geogrids were manufactured with apertures in a rectangular or square shape. Recently, geogrids with a triangular aperture shape have been introduced into the market. The new geogrids are manufactured with ribs oriented in three equilateral directions and expected to have a more stable grid structure, which can provide more uniform resistance in all directions. In this study, the numerical software - FLAC was adopted to investigate the responses of geogrids with rectangular and triangular apertures when subjected to a uniaxial tensile load at different directions relative to the orientations of ribs in air. The geogrid ribs were modeled using beam elements jointed rigidly at nodes (i.e., the angle between two adjacent ribs did not change) and subjected to tension in one direction. The numerical results showed that the stress-strain responses of the geogrids were different at different loading directions relative to the orientations of ribs. The effects of aperture shape of geogrid, and elastic modulus and cross-section area of geogrid ribs on the tensile stiffness of the geogrid were also evaluated. The geogrid with triangular apertures had more uniform tensile stiffness and strength distributions than the geogrid with rectangular apertures. An increase of the elastic modulus and cross-section area of the geogrid ribs could increase the stiffness of the geogrid with triangular apertures. The numerical results were verified by experimental data for geogrids with rectangular and triangular apertures.     

Dynamic strength of rocks and physical nature of rock strength

Time-dependence of rock deformation and fracturing is often ignored.However,the consideration of the time-dependence is essential to the study of the deformation and fracturing processes of materials,especially for those subject to strong dynamic loadings.In this paper,we investigate the deformation and fracturing of rocks,its physical origin at the microscopic scale,as well as the mechanisms of the time-dependence of rock strength.Using the thermo-activated and macro-viscous mechanisms,we explained the sensitivity of rock strength to strain rate.These mechanisms dominate the rock strength in different ranges of strain rates.It is also shown that a strain-rate dependent Mohr-Coulomb-type constitutive relationship can be used to describe the influence of strain rate on dynamic rock fragmentation.A relationship between the particle sizes of fractured rocks and the strain rate is also proposed.Several time-dependent fracture criteria are discussed,and their intrinsic relations are discussed.Finally,the application of dynamic strength theories is discussed.     

Numerical analysis of anisotropic stiffness and strength for geomaterials

In numerical modelling, selection of the constitutive model is a critical factor in predicting the actual response of a geomaterial. The use of oversimplified or inadequate models may not be sufficient to reproduce the actual geomaterial behaviour. That selection is especially relevant in the case of anisotropic rocks, and particularly for shales and slates, whose behaviour may be affected, e.g. well stability in geothermal or oil and gas production operations. In this paper, an alternative anisotropic constitutive model has been implemented in the finite element method software CODE_BRIGHT, which is able to account for the anisotropy of shales and slates in terms of both deformability and strength. For this purpose, a transversely isotropic version of the generalised Hooke's law is adopted to represent the stiffness anisotropy, while a nonuniform scaling of the stress tensor is introduced in the plastic model to represent the strength anisotropy. Furthermore, a detailed approach has been proposed to determine the model parameters based on the stress–strain results of laboratory tests. Moreover, numerical analyses are performed to model uniaxial and triaxial tests on Vaca Muerta shale, Bossier shale and slate from the northwest of Spain (NW Spain slate). The experimental data have been recovered from the literature in the case of the shale and, in the case of the slate, performed by the authors in terms of stress-strain curves and strengths. A good agreement can be generally observed between numerical and experimental results, hence showing the potential applicability of the approach to actual case studies. Therefore, the presented constitutive model may be a promising approach for analysing the anisotropic behaviour of rocks and its impact on well stability or other relevant geomechanical problems in anisotropic rocks.     

矿渣粉对混凝土和易性及强度影响的研究

试验研究和分析了矿渣粉掺量对低水胶比混凝土的和易性及强度的影响。结果表明,除了减水剂掺量对新拌混凝土和易性有显著影响外,矿渣粉掺量对混凝土拌合物的和易性有明显改善。水胶比是影响混凝土强度的主要因素,而矿渣粉掺量对混凝土强度的影响也较为明显。矿渣粉的细度小于水泥的细度,可作为细集料用于混凝土中,以改善混凝土拌合物的和易性,降低施工成本。     

水泥土搅拌桩应力应变特征分析及单桩承载力的确定

在载荷试验条件下,水泥土单桩与复合地基下的单桩及钢筋混凝土单桩应力传递,桩周应力分配,桩土相互作用形式及形成桩顶沉降的原因,均有很大差异。本文通过分析这些差异产生的原因,结合现场试验资料,对单桩荷载试验与复合地基试验条件下单桩进行了对比,表明不同试验方法对质量检测与评价的影响。同时,结合现场单桩载荷试验资料,说明水泥土桩单桩载荷试验的Ｐ－Ｓ曲线近似为一条双曲线,通过对双曲线的特征分析,得出一种简单实用的确定水泥土单桩承载力的方法     

由重型圆锥动力触探与深层载荷试验确定圆砾层承载力与变形

对规范中重型动力触探与深层载荷试验确定地基承载力与变形模量方法进行研究,结合实际工程数据进行比较分析,对如何利用原位试验确定地基承载力提出一些建议,以便在岩土工程勘察中更好、更准确的应用更为方便经济的重型动力触探试验。