Experimental investigation on the relevance of mechanical properties and porosity of sandstone after hydrochemical erosion

Under the effect of chemical etching, the macroscopic mechanical properties, mesoscopic structure, mineral content, and porosity of rocks undergo significant changes, which can lead to the geological disasters; thus, an understanding of changes in the microscopic and macroscopic structure of rocks after chemical etching is crucial. In this study, uniaxial mechanical tests and nuclear magnetic resonance (NMR) spectroscopy were carried out on sandstone samples that had been previously subjected to chemical erosion under different pH values. The aim was to study changes in properties and mechanical characteristics, including deformation and strength characteristics, of the rock, and microscopic pore variation characteristics, and to perform preliminary studies of the chemical corrosion mechanism. Results show that different chemical solutions have a significant influence on the uniaxial compressive strength, the axial strain corresponding to the peak axial stress, elastic modulus, etc. With the passage of time, porosity increases gradually with exposure to different chemical solutions, and exposure to chemical solutions results in large changes in the NMR T2 curve and T2 spectrum area. Sandstone exposed to different chemical solutions exhibits different corrosion mechanisms; the root cause is the change of mineral.     

浸泡作用下碎石土剪切强度衰减规律及机理

水库蓄水后,滑坡体碎石土经受长时期的浸泡,力学性质发生改变,从而影响滑坡整体稳定性。为探究浸泡对碎石土力学性质的影响规律,选取三峡库区马家沟滑坡后缘未经受长期浸泡作用的碎石土进行大型直剪试验,分析了不同浸泡天数下碎石土的剪切力学性质。试验结果表明：浸泡40 d后,碎石土黏聚力下降幅度达39%,内摩擦角下降幅度为8.3%;碎石土黏聚力在浸泡前期快速下降,下降速率随浸泡天数增加而降低,浸泡20 d后,黏聚力基本达到稳定。为探究碎石土抗剪强度降低的原因和机理,对粉质黏土(碎石土细粒成分)进行了三轴剪切试验、激光粒度分析及浸出液阳离子分析等试验,揭示了碎石土抗剪强度的衰减机理为：浸泡作用下,碎石土中的粉质黏土发生矿物溶解、离子交换与吸附作用,土体中大颗粒细化,胶结作用减弱,进而导致碎石土整体抗剪强度降低。研究结果对库区碎石土滑坡评价与治理具有一定的指导意义。     

Grain size distribution of soils within the Cordillera Blanca,Peru: An indicator of basic mechanical properties for slope stability evaluation

This paper presents results of a study on the mechanical properties of sandy and gravely soils within the Cordillera Blanca, Peru. The soils were divided into groups according to their origin （glacial, fluvial, or debris flow）. The grain size distribution of forty three soil samples was used to classify the soils according to the scheme of the Unified Soil Classification System （USCS）. These distributions have then been used to estimate shear strength and hydraulic properties of the soils. There are clear differences between the soils which reflect their divergent origins. The glacial soils normally fit within one of two distinctive groups according to the proportion of fines （Group A, 7%-21.5%; Group B, 21%-65%）. The estimation of shear strength at constant volume friction angle and peak shear strength of the glacial sediments with low content of fines was made using published data relating to the measured shear strength characteristics of soils with similar origins and grain size distributions. The estimated values were supported by measurements of the angle of repose taken from fourteen samples from two moraines and by shear tests on samples from one locality. The results of the grain size distribution werealso used to estimate the average hydraulic conductivity using the empirical Hazen formula which results were verified by field infiltration tests at two localities.     

基于CT扫描的黄土孔隙结构特征研究

孔隙特征作为反映黄土微观结构的重要特征之一,直接影响黄土的水敏性、渗透性和强度等物理力学性质。为了研究水力耦合作用下黄土微观孔隙结构特征,使用CT技术对天然原状、原状饱和与重塑黄土的初始结构以及不固结不排水剪切试验后的土体结构进行了扫描,通过建立黄土三维结构模型,分析了剪切试验前后孔隙结构的演变特征。结果表明：饱和与重塑作用使天然原状黄土的大孔隙减少,剪切作用使天然原状黄土和重塑黄土发生剪切破坏,原状饱和黄土发生压缩破坏,局部孔隙率增加。天然原状黄土与原状饱和黄土在剪切前后均表现为微孔和小孔数量较多,其孔隙倾角主要分布在50°～90°之间,解释了黄土亚稳态结构形成的主要原因。扰动作用使重塑黄土的孔隙尺寸分布均匀,且重塑黄土与原状饱和黄土在水力作用下更易失稳屈服。揭示了黄土剪切变形破坏的微观结构主要表现为粒间胶结物的溶解、孔隙的坍塌与填充以及颗粒旋转、破碎和滑移。试验结果可为黄土剪切强度降低和湿陷机理研究提供依据。     

原状及重塑黄土双轴试验微观力学特征离散元模拟

黄土作为一种特殊的颗粒材料,微观上颗粒组成的结构决定了其力学特性。原状及重塑黄土因结构的差异而具有不同的力学特性。针对黄土结构性如何影响其力学特征这一基本问题,开展基于电镜扫描获取细观颗粒信息,同时考虑颗粒形状、颗粒破碎可能性进行建模的离散单元法进行原状黄土和饱和重塑土在恒定应变速率双轴试验下的宏观力学和细观力学性能研究。研究结果显示:试样微观结构的差异对变形破坏过程产生显著影响。当轴向应力较低时原状黄土及重塑黄土力链多分布于大型骨架颗粒附近,随着轴向应力增加,原状黄土力链形成网状图案但仍具备主要传导区域,重塑黄土无明显主要传导区,呈现均匀网状。原状土及重塑土骨架颗粒簇周围多形成张拉裂隙,剪切裂隙多数形成于骨架颗粒簇内部,又以颗粒簇相互挤压接触时最为明显。使用该建模方法,可以有效反映原状及重塑黄土由于内部结构组成差异导致相同应力条件下产生的不同内部应力状态。基于以上研究结论,给出了黄土结构性对宏观强度影响的微观解释。研究成果可为黄土地区地质灾害防治提供一定依据。使用该建模方法,可以有效反映原状及重塑黄土由于内部结构组成差异导致相同应力条件下产生的不同内部应力状态。基于以上研究结论,给出了黄土结构性对宏观强度影响的微观解释。      

龙马溪组层状页岩微观非均质性及力学各向异性特征

层状页岩的微观非均质性及力学各向异性对研究井壁稳定以及水力裂缝扩展形态具有重要意义。为了向页岩优化钻井、压裂工艺参数提供一定的理论和试验依据,对沿不同角度取心的页岩试样开展单轴压缩实验,配合场发射扫描电镜、原子力显微镜观测实验和波速测试等,研究龙马溪组层状页岩微观非均质性及力学各向异性特征,并讨论这些物理力学特征对水力裂缝形态的影响规律。结果表明:受层理面的影响,龙马溪组页岩呈现出较强的微观非均质性和宏观力学各向异性特征。具体的,微观孔隙结构特征方面,随着观测方向与层理方向之间夹角β的增大,微观孔隙结构的发育程度逐渐增加,说明气体的储集和空间呈增加趋势;宏观力学特征方面,单轴压缩条件下,随着加载方向与层理方向间夹角θ的增加,页岩试样的破坏模式从贯穿层理面的张拉破坏,先转变为剪切破坏,再变为劈裂-剪切混合破坏;龙马溪组层状页岩的单轴抗压强度、泊松比随着θ的增加呈现出先减小后增大的"U"形各向异性模式,弹性模量、横纵波速则逐渐减小,胶结程度较弱的页岩层理面会先于基质体发生破坏,进而显著影响岩石整体的力学性质;页岩微观非均质性及力学各向异性特征在一定程度上影响压裂过程中水力裂缝的扩展行为,以及停泵后压裂液的渗流路径。研究结果可为页岩压裂工艺参数优选提供一定依据。      

长期静水浸泡对三峡库区滑带土物理-化学-力学性质的影响

三峡水库蓄水使得库岸大量土体长期处于浸泡状态,导致土体软化从而诱发滑坡失稳。为研究长期浸泡对滑坡土体物理-化学-力学性质的影响,以马家沟滑坡原状滑带土为对象开展了浸泡软化试验,通过比较不同浸泡时间滑带土的粒度分布、界限含水率、化学与矿物成分、剪切特性等特征,探讨了滑带土浸泡软化机理。研究结果表明:浸泡过程中滑带土中Ca2+、Mg2+等离子流失较多,但矿物成分无变化;浸泡后滑带土出现阶段性粒度细化现象,液塑限和塑性指数均随黏粒含量增加而增大;随着浸泡时间增加,滑带土应力应变关系在低法向应力下由强软化型变为弱软化型,在高法向应力下由软化型变为硬化型;滑带土抗剪强度参数随着浸泡时间增加呈指数形式降低,黏聚力c降低程度大于内摩擦角φ。研究成果可以为水库滑坡稳定性评价提供理论依据。      

水泥固化剂提高风积沙承载性能试验

沙漠风积沙稳定性差,采用水泥作为固化剂进行风积沙固化,是改善风积沙性质和实现风积沙资源化利用的有效手段。以取自内蒙古库布齐沙漠的风积沙为材料,制备3%含水量的重塑风积沙,掺入水泥固化剂并充分拌匀而形成固化风积沙,开展水泥固化风积沙的抗剪、抗压和抗拔承载性能试验。结果表明,水泥掺量对固化风积沙黏聚强度的提高程度要大于内摩擦角。含水量3%的风积沙掺入6%的水泥经28 d常温养护的固化风积沙无侧限抗压强度平均值为0.156 MPa。固化风积沙扩展基础抗拔荷载-位移曲线呈现初始弹性段至峰值荷载以及峰值荷载后破坏的两阶段脆性破坏特征。水泥固化提高风积沙抗拔承载性能效果显著,且与基础底板尺寸、抗拔埋深及基础深宽比等因素有关。     

Influences of soil moisture and salt content on loess shear strength in the Xining Basin,northeastern Qinghai-Tibet Plateau

Moisture and salt content of soil are the two predominant factors influencing its shear strength. This study aims to investigate the effects of these two factors on shear strength behavior of loess in the Xining Basin of Northeast Qinghai-Tibet Plateau, where such geological hazards as soil erosion, landslides collapse and debris flows are widespread due to the highly erodible loess. Salinized loess soil collected from the test site was desalinized through salt-leaching in the laboratory. The desalinized and oven-dried loess samples were also artificially moisturized and salinized in order to examine how soil salinity affects its shear strength at different moisture levels. Soil samples prepared in different ways(moisturizing, salt-leaching, and salinized) were measured to determine soil cohesion and internal friction angle. The results show that salt-leaching up to 18 rounds almost completely removed the salt content and considerably changed the physical components of loess, but the soil type remained unchanged. As salt content increases from 0.00% to 12.00%, both the cohesion and internal friction angle exhibit an initial decrease and then increase with salt content. As moisture content is 12.00%, the salt content threshold value for both cohesion and internal friction angle is identified as 3.00%. As the moisture content rises to 16.0% and 20.00%, the salt content threshold value for cohesion is still 6.00%, but 3.00% for internal friction angle. At these thresholds soil shear strength is the lowest, below which it is inversely related to soil salinity. Beyond the thresholds, however, the relationship is positive. Dissimilar to salinity, soil moisture content exerts an adverse effect on shear strength of loess. The findings of this study can provide a valuable guidance on stabilizing the engineering properties of salinized loess to prevent slope failures during heavy rainfall events.     

Quantification of 3D macropore networks in forest soils in Touzhai valley (Yunnan,China) using X-ray computed tomography and image analysis

The three dimensional(3D) geometry of soil macropores largely controls preferential flow, which is a significant infiltrating mechanism for rainfall in forest soils and affects slope stability. However, detailed studies on the 3D geometry of macropore networks in forest soils are rare. The intense rainfall-triggered potentially unstable slopes were threatening the villages at the downstream of Touzhai valley(Yunnan, China). We visualized and quantified the 3D macropore networks in undisturbed soil columns(Histosols) taken from a forest hillslope in Touzhai valley, and compared them with those in agricultural soils(corn and soybean in USA; barley, fodder beet and red fescue in Denmark) and grassland soils in USA. We took two large undisturbed soil columns(250 mm×250 mm×500 mm), and scanned the soil columns at in-situ soil water content conditions using X-ray computed tomography at a voxel resolution of 0.945 × 0.945 × 1.500 mm~3. After reconstruction and visualization, we quantified the characteristics of macropore networks. In the studiedforest soils, the main types of macropores were root channels, inter-aggregate voids, macropores without knowing origin, root-soil interface and stone-soil interface. While macropore networks tend to be more complex, larger, deeper and longer. The forest soils have high macroporosity, total macropore wall area density, node density, and large macropore volume, hydraulic radius, mean macropore length, angle, and low tortuosity. The findings suggest that macropore networks in the forest soils have high interconnectivity, vertical continuity, linearity and less vertically oriented.     

川西凹陷地区中更新统冰水沉积滑坡稳定性分析

为了研究川西凹陷地区中更新统冰水沉积滑坡的变形破坏机制和稳定性, 以G5京昆高速成雅段K1887+350滑坡为例, 通过工程地质勘察和物理力学试验, 运用综合监测技术, 以滑坡的实际变形量为基础, 分析了滑坡变形破坏机制, 研究加固处治前后的滑坡稳定性。结果表明: 不利的地质结构、前缘临空及降水诱发是K1887+350滑坡变形破坏失稳的主要原因, 中更新统冰水沉积层细粒土的膨胀性进一步降低了土体抗剪性质, 地表水长期渗润最终导致冰水沉积物浅表发生蠕动-拉裂变形; 地表裂缝监测是判断山体变形趋势、分析滑坡稳定性的有效途径。      

Shear strength features of soils developed from purple clay rock and containing less than two-millimeter rock fragments

Soil shear strength is an important indicator of engineering design and an essential parameter of soil precision tillage and agricultural machinery and equipment design. Although numerous studies have investigated the characteristics of different soil shear strengths, only a few of these works have paid attention to soils containing considerable quantities of rock fragments. To date, most studies on the effects of rock fragments on the shear strength have paid attention to the role of rock fragments with sizes >2 mm. The effects of rock fragments <2 mm in soil are generally ignored. Similar to rock fragments >2 mm, the presence of rock fragments <2 mm could also change the mechanical properties of soils. Thus, in the present study we evaluated the potential influence of <2 mm rock fragments on soil shear strength via an unconsolidated undrained (UU) triaxial compression test. Our results were as follows: (1) A certain quantity of <2 mm rock fragments presented in purple soils developed from clay rocks; and an appropriate quantity of <2 mm rock fragments could improve the shear strength of soils. (2) The different PSDs of soils containing <2 mm rock fragments mainly caused variations in the internal friction angle of soils. (3) The shear strengths of the two mudstone-developed red-brown and gray-brown purple soils was more sensitive to water than that of the shale-developed coarse-dark purple soil. As the soil water content increased from 9% to 23%, the changes in the cohesion, internal friction angle, shear strength, and the maximum principal stress difference were smaller in the coarse dark purple soil than in the two other soils. We therefore concluded that <2 mm rock fragments in purple soils exerted important effects on soil shear strength. A better understanding of the differences among the shear strength features of purple soils could help improve the design of agricultural machinery and equipment.     

Effect of drying environment on engineering properties of an expansive soil and its microstructure

This paper investigates the effect of drying environment, i.e. temperature and relative humidity, on the engineering properties and microscopic pore size distribution of an expansive soil. The shrinkage tests under different drying temperatures and relative humidity are carried out in a constant climate chamber. Then, the undisturbed samples, prepared in different drying environment, are used for the triaxial tests and mercury intrusion tests. It is found that the drying environment has noticeable influence on the engineering properties of expansive soils and it can be characterized by the drying rate. The linear shrinkage and strength increase with the decrease of the drying rate. The non-uniform deformation tends to happen in the high drying rate, which subsequently furthers the development of cracks. In addition, during the drying process, the variation of pores mainly focuses on the inter-aggregate pores and inter-particle pores. The lower drying rate leads to larger variation of pore size distribution.     

The measure of friction angles for different types of granular material

The aim of this research is to deepen the knowledge of the role of friction on the dynamics of granular media; in particular the friction angle is taken into consideration as the physical parameter that drives stability, motion and deposition of a set of grains of any nature and size. The idea behind this work is a question: is the friction angle really that fundamental and obvious physical parameter which rules stability and motion of granular media as it seems from most works which deal with particle dynamics? The experimental study tries to answer this question with a series of laboratory tests, in which different natural and artificial granular materials have been investigated in dry condition by means of a tilting flume. The characteristic friction angles, both in deposition(repose) and stability limit(critical) conditions, were measured and checked against size, shape, density and roughness of the considered granular material. The flume tests have been preferred to "classical" geotechnical apparatuses(e.g. shear box) since the flume experimental conditions appear closer to the natural ones of many situations of slope stability interest(e.g. a scree slope). The results reveal that characteristic friction angles depend on size and shape of grains while mixtures of granules of different size show some sorting mechanism with less clear behaviour.     

High-Speed Ring Shear Tests to Study the Motion and Acceleration Processes of the Yingong Landslide

In this paper, the motion and acceleration process, as well as the mechanism of a high speed and long run landslide are investigated by adopting high speed ring shear test and taking the landslide occurred at Yigong River in Bomi, Tibet on April 9, 2000 as the background. According to the motion characteristics of high-speed and long distance motion landside, the mechanism is studied under different conditions such as shear speed, consolidated drained and consolidated undrained status. Results show that high speed shearing process hinders and delays the dissipation of pore pressure, and drives pore water migrating to shear zone slowly. Both of water content and fine particle content at shear zone are obviously higher than those in other layers; and soil liquefaction occurs at shear zone in the saturated consolidated undrained ring shear tests. The effective internal friction angle of the consolidated undrained soil is much lower than that of the consolidated drained soil under ring shearing. The results also indicate that the shearing speed affecting the strength of soil to some extent. The higher the ring shearing speed is, the lower the strength of soil is. This investigation provides a preliminary interpretation of the mechanism of the motion and acceleration process of the Yigong landslide, occurred in Tibet in 2000.     

Particle breakage and the mobilized drained shear strengths of sand

This paper presents particle breakage and the mobilized drained shear strengths of sand with the purpose of clarifying the influence of particle breakage on the mobilized shear strengths of sand. Several drained triaxial tests were carried out on Silica sand No.5 under 3 MPa confining pressure to produce the pre-crushed sands in simulating the high-pressure shear process on soil to result in particle breakage, and then the pre-crushed sands were re-sheared in series of drained triaxial tests to investigate the mobilized strengths of the pre-crushed sands in detecting the influence of particle breakage. It was found that, by deteriorating strain-stress behavior, particle breakage resulted in change of stress-dilatancy behavior in translation and rotation of the relation of the dilatancy factor and the effective principal stress ratio. For a given initial void ratio, particle breakage resulted in impairment of dilatancy behavior of soil to be more contractive in deterioration of the mobilized friction angle and the mobilized dilatancy angle and reduction of void ratio. However, particle breakage resulted in increase of the mobilized basic friction angle especially before failure. In addition, the influence of particle breakage on the mobilized strengths was revealed to be influenced by the shear stress-strain state.     

Cohesion variation during instability evolution of disaster medium in mud inrush of mountain tunnel

Mud inrush in mountain tunnel is an independent geological hazard type different from water inrush, landslide and debris flow. The intrinsic factor of mud inrush is the instability failure of disaster medium. Its essence is that when the cohesion decreases gradually with the increase of void ratio to the point where the movement of soil particles cannot be restricted, soil particles and groundwater form slurry and gush out. Thus, accurate calculation of cohesion with variable void ratios is crucial for analyzing the reliability of disaster medium. In this study, the disaster medium was regarded as graded soil and a structural model was established wherein soil particles were simplified as cubes and the interparticle pores were represented by the clearance between cubes. On the basis of the structure model of disaster medium, a function between the soil particle distance and void ratio was derived. Cohesion is equivalent to the resultant force between soil particles per unit area; thus, a cohesion function was derived in which the void ratio is the main variable. This function considers the influence of gradationcharacteristics on cohesion variation and is generally applicable to various types of disaster medium. A series of direct shear tests were carried out to determine the cohesion variation for different types of disaster medium with variable void ratios. By comparing the variation of cohesion obtained through direct shear tests with those deduced by the proposed cohesion function, we verified the validity and general applicability of the cohesion function. It is of great significance because the cohesion function can accurately predict the variation of cohesion by using the void ratio, and effectively evaluate the possibility of mud inrush according to the initial mechanical properties of disaster medium.     

Characteristics of rock fragments in different forest stony soil and its relationship with macropore characteristics in mountain area,northern China

Rock fragments have major effect on soil macropores and water movement. However, the characteristics of rock fragments and their relationship with macropore characteristics remain elusive in forest stony soils in northern mountainous area of China. The objectives of this study are to (1) use Industrial Computed Tomography (CT) scanning to quantitatively analyze rock fragment characteristics in intact soil columns in different forest lands and (2) identify the relationship between characteristics of rock fragments and that of the macropores. Intact soil columns that were 100 mm in diameter and 300 mm long were randomly taken from six local forest stony soils in Wuzuolou Forest Station in Miyun, Beijing. Industrial CT was used to scan all soil column samples, and then the scanned images were utilized to obtain the three-dimensional (3D) images of rock fragments and macropore structures. Next, the parameters of the rock fragments and macropore structure were measured, including the volume, diameter, surface area, and number of rock fragments, as well as the volume, diameter, surface area, length, angle, tortuosity and number of macropores. The results showed that no significant difference was found in soil rock fragments content in the 10-30 cm layer between mixed forest and pure forest, but in the 0-10 cm soil layer, the rock fragments in mixed forest were significantly less than in pure forest. The number density of macropores has significant negative correlation with the number of rock fragments in the 0-10 cm soil layer, whereas this correlation is not significant in 10-20 cm and 20-30 cm soil layers. The volume density of macropore was not correlated with the volume density of rock fragments, and there is no correlation between the density of macropore surface area and the density of rock fragment surface area. Industrial CT scanning combined with image processing technology can provide a better way to explore 3D distribution of rock fragments in soil. The content of rock fragments in soil is mainly determined by parent rocks. The surface soil (0-10 cm) of forest contains fewer rock fragments and more macropores, which may be caused by bioturbation, root systems, gravitational settling and faunal undermining.     

Landslides & debris flows formation from gravelly soil surface erosion and particle losses in Jiangjia Ravine

Gravelly soils are made up of gravel, sand, silt and clay. They are widely used in engineering applications such as rock-fill dams with clay cores, which are the main researches at present. The strength and mechanical properties of the gravelly soils are affected by the content of coarse grain, fine particles, and their adhesive states. These Properties can be verified by laboratory unconsolidated undrained triaxial tests with grain size less than 5 mm and by large scale direct-shear tests with original grain content. Fine particles of the loose gravelly slopes are released under rainfalls, alternated the structures and mechanical properties, even affected the slope stability. There are a series of large scale direct-shear tests with different coarse grain contents to study the influence of fine particles releasing and migration, results showed the strength behavior of the gravelly soils were affected by the coarse grain content （5） and the inflection coarse grain contents. In order to study the erosion features of the gravelly soil slopes on rainfall conditions and the slopes stability alteration, we had carried out one sort of artificial rainfall local and model experiments, the runoff sediment contents were monitored during the experiments. Result showed that the shapes of the slopes surface transformed periodically, runoff sediment contents were divided into five phases according to the experiment phenomena, runoff sediment contents maintained downtrend during the rain time and the downtrend was obviouslyinterpreted by one descend belt no matter the rainfall intensity and the slope angels. Particle size analysis released the deposit on the slope surface lost almost all of the clay, most of the silt and sand after the experiments, this meant the fine particles releasing, migration and accumulation process on condition of rainfall resulted in the instability factor of the slopes even induced landslide or debris flow.     

Effect of Freeze-Thaw Cycles on Mechanical Properties and Permeability of Red Sandstone under Triaxial Compression

Geological disasters will happen in cold regions because of the effects of freeze-thaw cycles on rocks or soils, so studying the effects of these cycles on the mechanical characteristics and permeability properties of rocks is very important. In this study,red sandstone samples were frozen and thawed with 0,4, 8 and 12 cycles, each cycle including 12 h of freezing and 12 h of thawing. The P-wave velocities of these samples were measured, and the mechanical properties and evolution of the steady-state permeabilities were investigated in a series of uniaxial and triaxial compression tests. Experimental results show that, with the increasing of cyclic freeze-thaw times, the P-wave velocity of the red sandstone decreases. The number of freeze-thaw cycles has a significant influence on the uniaxial compressive strength, elastic modulus, cohesion, and angle of internal friction. The evolution of permeability of the rock samples after cycles of freeze-thaw in a complete stress-strain process under triaxial compression is closely related to the variation of the microstructure in the rock. There is a highly corresponding relationship between volumetric strain and permeability with axial strain in all stages of the stress-strain behaviour.