高渗透压脆性岩石蠕变宏−细观力学模型研究

高渗透压对深部地下工程脆性岩石蠕变力学特性有着重要影响。然而,能够解释高渗透压作用脆性岩石完整减速、稳态及加速三级蠕变过程中,细观裂纹扩展与宏观变形关系的宏细观力学模型研究很少。基于考虑含有初始裂纹与新生成翼型裂纹影响的裂纹尖端应力强度模型,引入渗透水压与初始裂纹及新生成翼型裂纹之间的力学关系,建立了考虑渗透水压作用的裂纹尖端应力强度模型;然后结合亚临界裂纹扩展法则,与裂纹及应变损伤关系模型,推出了考虑渗透水压影响的脆性岩石蠕变裂纹扩展与宏观变形关系的宏细观力学模型。当施加轴向应力小于岩石裂纹启裂应力时,岩石近似表现为线弹性变形;当施加轴向应力大于裂纹启裂应力且小于岩石峰值强度,岩石表现为塑性蠕变变形。研究了不同渗透压作用下,分级轴向应力加载岩石蠕变应变时间演化曲线,并通过试验结果验证了模型的合理性。分别讨论了恒定渗透压与分级渗透压,对脆性岩石蠕变过程中裂纹长度、裂纹扩展速率、轴向应变及轴向应变率的影响。该模型为高渗透压深部地下工程围岩稳定性评价提供了重要理论依据。     

Microstructure and fabric development in ice: Lessons learned from in situ experiments and implications for understanding rock evolution

In this contribution we present a review of the evolution of microstructures and fabric in ice. Based on the review we show the potential use of ice as an analogue for rocks by considering selected examples that can be related to quartz-rich rocks. Advances in our understanding of the plasticity of ice have come from experimental investigations that clearly show that plastic deformation of polycrystalline ice is initially produced by basal slip. Interaction of dislocations play an essential role for dynamic recrystallization processes involving grain nucleation and grain-boundary migration during the steady-state flow of ice. To support this review we describe deformation in polycrystalline ‘standard’ water-ice and natural-ice samples, summarize other experiments involving bulk samples and use in situ plane-strain deformation experiments to illustrate the link between microstructure and fabric evolution, rheological response and dominant processes. Most terrestrial ice masses deform at low shear stresses by grain-size-insensitive creep with a stress exponent (n ≤ 3). However, from experimental observations it is shown that the distribution of plastic activity producing the microstructure and fabric is initially dominated by grain-boundary migration during hardening (primary creep), followed by dynamic recrystallization during transient creep (secondary creep) involving new grain nucleation, with further cycles of grain growth and nucleation resulting in near steady-state creep (tertiary creep). The microstructural transitions and inferred mechanism changes are a function of local and bulk variations in strain energy (i.e. dislocation densities) with surface grain-boundary energy being secondary, except in the case of static annealing. As there is a clear correspondence between the rheology of ice and the high-temperature deformation dislocation creep regime of polycrystalline quartz, we suggest that lessons learnt from ice deformation can be used to interpret polycrystalline quartz deformation. Different to quartz, ice allows experimental investigations at close to natural strain rate, and through in-situ experiments offers the opportunity to study the dynamic link between microstructural development, rheology and the identification of the dominant processes.     

Quartz microstructures developed during non-steady state plastic flow at rapidly decaying stress and strain rate

Synseismic loading to very high stresses (>0.5 GPa) and subsequent creep during stress relaxation in the uppermost plastosphere at temperatures of ca. 300–350 °C, near the lower tip of an inferred once seismically active crustal scale fault, was proposed based on peculiar microstructures identified in rocks exposed over >100 km² in the Sesia Zone, European Western Alps. Here we discuss the conspicuous and highly heterogeneous microstructural record of quartz in disseminated small-scale shear zones. Sub-basal deformation lamellae and arrays of elongate subgrains on the TEM-scale indicate an early stage of glide-controlled deformation at high stresses. Distributed brittle failure is indicated by healed microcracks. Very fine-grained recrystallised aggregates with a pronounced crystallographic preferred orientation reflect intense plastic flow by dislocation creep. Locally, a fine-grained foam microstructure indicates a final stage of static grain growth at low differential stress. For the previously inferred peak stresses of about 0.5 GPa and given temperatures, initial strain rates on the order of 10⁻¹⁰ s⁻¹ are predicted by available flow laws for dislocation creep of quartz. We emphasise the importance of short-term non-steady state deformation in the uppermost plastosphere underlying seismically active upper crust. The related heterogeneous record of quartz is governed by the local stress history at constant temperature.     

Influence of stress-induced microcracks on viscoplastic creep deformation in Marcellus shale

Time is one of the often-neglected factors in the assessment of the erratic failure of shale rock. Laboratory-creep experiments showed that constant stress induces time-dependent failure in brittle shale. However, the microscopic reason for time-dependent deformation in shale is still unknown. In the current study, triaxial creep and recovery experiments showed that the brittle shale specimens exhibit viscoelastic and viscoplastic creep deformation at constant stress state. In addition, the X-ray computed tomography scan of Marcellus shale showed that the shale specimens contained significant volume of preexisting microcracks. The statistical correlation among permanent strain during the triaxial experiment and stress-induced change in the three-dimensional geometry of microcracks showed that the microcracking is the microscopic reason for viscoplastic creep deformation in shale. In addition to the time and level of constant differential stress, factors such as orientation of bedding planes and specimen heterogeneity also influence the nature of creep deformation.

     

Micromechanics modelling for stress–strain behaviour of brittle rocks

A micromechanics model for stress–strain behaviour of brittle rocks has been developed. Microcracking is the mechanism of the non-linear deformation behaviour for brittle rocks in the pre-peak stage. The non-linear behaviour in this stage is simulated by considering the local axial splitting of microcracks. The relationships between the compressive stresses, the growth of microcracks, and the fracture-induced deformation are analytically established. In the post-peak stage the shear faulting predominates the process of deformation, which is simulated by a damage model. This micromechanics model is helpful in understanding the failure process in brittle rocks. The model can be used to simulate the complete stress–strain behaviour of rock. The model simulations are consistent with experimental results.     

Deformation Localization-A Review on the Maximum- Effective-Moment (MEM) Criterion

The essential difference in the formation of conjugate shear zones in brittle and ductile deformation is that the intersection angle between brittle conjugate faults in the contractional quadrants is acute(usually ~60°) whereas the angle between conjugate ductile shear zones is obtuse(usually 110°). The Mohr-Coulomb failure criterion, an experimentally validated empirical relationship, is commonly applied for interpreting the stress directions based on the orientation of the brittle shear fractures. However, the Mohr-Coulomb failure criterion fails to explain the formation of the low-angle normal fault, high-angle reverse fault, and the conjugate strike-slip fault with an obtuse angle in the σ1 direction. Although it is ten years since the Maximum-Effective-Moment(MEM) criterion was first proposed, and increasingly solid evidence in support of it has been obtained from both observed examples in nature and laboratory experiments, it is not yet a commonly accepted model to use to interpret these antiMohr-Coulomb features that are widely observed in the natural world. The deformational behavior of rock depends on its intrinsic mechanical properties and external factors such as applied stresses, strain rates, and temperature conditions related to crustal depths. The occurrence of conjugate shear features with obtuse angles of ~110° in the contractional direction on different scales and at different crustal levels are consistent with the prediction of the MEM criterion, therefore ~110° is a reliable indicator for deformation localization that occurred at medium-low strain rates at any crustal levels. Since the strain–rate is variable through time in nature, brittle, ductile, and plastic features may appear within the same rock.     

上部地壳岩石流动与显微构造演化--天然与实验岩石变形证据

岩石流动性和变形显微构造的发育直接受温度、压力、应变速率和流体相等制约 ,致使在不同地壳层次岩石的流动性表现出很大的差异。对上部地壳环境条件下天然和实验变形岩石的显微构造分析揭示出一系列具有不同特点以及由不同的成核、扩展和联合方式形成的破裂与微破裂型式的存在。讨论了在上部地壳环境中 ,温度与围压的变化对岩石破裂的影响 ,并阐述了高压破裂与低压破裂及其力学、流变学和显微构造特点 ,提出高压破裂对应于天然变形环境下出现的剪切 (挤压 )破裂 ,而碎裂岩带是典型的天然低压破裂 ,其低压环境的出现可以是浅部低围压或深部高流体压力所致。流体相的存在不仅可以引起石英 ,也可以引起方解石类碳酸盐岩矿物的水解弱化 ,并进而导致岩石流动机制的转变。岩石变形及流体等因素所致的岩石粒度变化 ,则从另一个方面影响着上部地壳岩石流动性的变化。从变形环境考虑 ,随着深度的加大 ,温度和压力升高 ,导致岩石由脆性向韧性转变 ;转变域内岩石的变形是一个复杂过程 ,是多种不同脆性和晶质塑性机制的综合。     

岩石变形机制与流变学研究的近期发展--显微构造、变形机制与流变学国际会议简介

结合显微构造,变形机制与流学国际会议讨论的有关为形机制与流学的几个主要方面,阐述了目前在该学科领域与研究方向上的研究现状与进展;地壳岩石脆－韧性转变变形机制,强调脆性变形机制与韧性变形机制之间的反应及由此引起的岩石强度降低;应变局部化机理与主要影响因素,应变局部化可以由是软化或硬化机制引起的。     

韧性剪切带向剪破裂的转化与成岩成矿作用

岩石应力-应变实验表明,在中等载荷(等于或大于岩石蠕变极限)作用下,岩石蠕变最终可导致破裂;三轴差应力实验后的试件中,多见极小的韧性剪切带中存在剪破裂;研究发现,糜棱岩并不一定有利于后来断层的叠加,然而二者共存一处的现象却十分普遍;牵引褶皱和剪切断层的应变速率差别极大,只能先牵后断。由此可见,韧性剪切带在同一构造层次情况下,可在变形较强的部位产生剪破裂;此时温度较高和压力骤降,导致部分熔融和流体卸载,这一转化过程产生的温度、压力和流体浓度等梯度变化,促使流体(物质)运移与富集导致成岩成矿。这一认识对解释动力成岩成矿、断层双层结构模式等诸多问题有重要意义。      

The creep of potash salt rocks from Saskatchewan

Summary The results of creep tests on the Esterhazy-and the Patience-Lake-types of potash salt rocks from Saskatchewan, Canada are presented. The investigations involved over 6 years of time-dependent experiments in uniaxial compression using potash from the Rocanville and the Lanigan mines of the Potash Corporation of Saskatchewan. A creep test at a given load would last from 2 to 8 months, with most tests conducted over a 4-month period.Since the yield stress of both types of potash lies between 9 and 11 MPa, there is very little creep below 11 MPa. Between 11 and 13 MPa, creep strain production increases sharply through plastic deformation. Above about 13 MPa, however, plastic creep is dominated by brittle creep caused by microcracking. As a result, the lateral and volume creep strain curves may then display the transient and the steady-state, or all three stages of creep, while the axial strain, which is not affected by microcracking, usually attenuates for the whole duration.Two different interpretations of the results are offered. Identifying the last (the fourth) month of testing with the steady-state model, the stress dependence of the steady-state rate has been established for both rock types. A unimodal rate model for the axial strain and a bimodal model for the lateral strain are suggested. The alternate interpretation proceeds on the assumption that under 13 MPa, both the axial and the lateral strain can be modelled through the power function formulation of transient strain.     

Rock mechanics observations pertinent to the rheology of the continental lithosphere and the localization of strain along shear zones

Emphasized in this paper are the deformation processes and rheologies of rocks at high temperatures and high effective pressures, conditions that are presumably appropriate to the lower crust and upper mantle in continental collision zones. Much recent progress has been made in understanding the flexure of the oceanic lithosphere using rock-mechanics-based yield criteria for the inelastic deformations at the top and base. At mid-plate depths, stresses are likely to be supported elastically because bending strains and elastic stresses are low. The collisional tectonic regime, however, is far more complex because very large permanent strains are sustained at mid-plate depths and this requires us to include the broad transition between brittle and ductile flow. Moreover, important changes in the ductile flow mechanisms occur at the intermediate temperatures found at mid-plate depths.Two specific contributions of laboratory rock rheology research are considered in this paper. First, the high-temperature steady-state flow mechanisms and rheology of mafic and ultramafic rocks are reviewed with special emphasis on olivine and crystalline rocks. Rock strength decreases very markedly with increases in temperature and it is the onset of flow by high temperature ductile mechanisms that defines the base of the lithosphere. The thickness of the continental lithosphere can therefore be defined by the depth to a particular isotherm T_c above which (at geologic strain rates) the high-temperature ductile strength falls below some arbitrary strength isobar (e.g., 100 MPa). For olivine T_c is about 700°–800°C but for other crustal silicates, T_c may be as low as 400°–600°C, suggesting that substantial decoupling may take place within thick continental crust and that strength may increase with depth at the Moho, as suggested by a number of workers on independent grounds. Put another way, the Moho is a rheological discontinuity. A second class of laboratory observations pertains to the general phenomenon of ductile faulting in which ductile strains are localized into shear zones. Ductile faults have been produced in experiments of five different rock types and is generally expressed as strain softening in constant-strain-rate tests or as an accelerating-creep-rate stage at constant differential stress. A number of physical mechanisms have been identified that may be responsible for ductile faulting, including the onset of dynamic recrystallization, phase changes, hydrothermal alteration and hydrolytic weakening. Microscopic evidence for these processes as well as larger-scale geological and geophysical observations suggest that ductile faulting in the middle to lower crust and upper mantle may greatly influence the distribution and magnitudes of differential stresses and the style of deformation in the overlying upper continental lithosphere.     

岩石圈的流变性与大陆动力学的科学基础

地球是一动态系统,其各层圈的构造运动归根究底就是多矿物复合岩石及其中各主要造岩矿物在变化的物理条件(例如,温度、围压、差应力、应变速率、应变方式等)下和化学环境(例如,氧逸度和水含量)中的形变。岩石流变学是一门研究岩石力学性质和变形行为的科学,现已成为定量大陆动力学和构造地质学发展的一个瓶颈,超越这个瓶颈,学科才能大踏步前进。本文对过去四十年来岩石流变学的实验和韧性变形域内古应力研究成果做了简明扼要的总结,特别关注尚存的问题与急需克服的困难。强调运用现代材料学、地球物理学和地球化学的新理论和新方法,改进与完善高温高压实验设备,提高其力学测量的灵敏度和准确度。而且必须采用大应变的实验途径解决稳态蠕变与稳态显微构造的问题,保证实验所获流动律外延至自然界的合理性与稳定性。鼓励那些有坚实积累、开阔视野和科学思维的青年学者,开拓进取,在岩石圈流变学与大陆动力学领域做出经得起时间淘洗、实践检验的原创性成果来。     

Fluid-assisted fracturing,cataclasis, and resulting plastic flow in mylonites from the Moresby Seamount detachment,Woodlark Basin

The Moresby Seamount detachment (MSD) in the Woodlark Basin (offshore Papua New Guinea) is a large active low-angle detachment excellently exposed at the seafloor, and cutting through mafic metamorphic rocks. Hydrothermal infiltration of quartz followed by that of calcite occurred during cataclastic deformation. Subsequent deformation of these a priori softer minerals leads to mylonite formation in the MSD. This study aims at a better understanding of the deformation mechanism switch from cataclastic to plastic flow. Deformation fabrics of the fault rocks were analyzed by light-optical microscopy. Rheologically critical phases were mapped to determine distributions and area proportions, and EBSD was used to measure crystallographic preferred orientation (CPO). Strong calcite CPOs indicate dominant dislocation creep. Quartz CPOs, however, are weak and more difficult to interpret, suggesting at least some strain accommodation by diffusion creep mechanisms. When quartz aggregates are intermixed with the polymineralic mylonite matrix diffusion creep grain boundary sliding may be dominant. The syntectonic conversion from mafic cataclasites to more siliceous and carbonaceous mylonites induced by hydrothermal processes is a critical weakening mechanism enabling the MSD to at least intermittently plastic flow at low shear stresses. This is probably a crucial process for the operation of low-angle detachments in hydrated and dominantly mafic crust.     

Low-Temperature Plasticity of Naturally Deformed Calcite Rocks

Optical, cathodoluminescence and transmission electron microscope (TEM) analyses were conducted on four groups of calcite fault rocks, a cataclastic limestone, cataclastic coarse-grained marbles from two fault zones, and a fractured mylonite. These fault rocks show similar microstructural characteristics and give clues to similar processes of rock deformation. They are characterized by the structural contrast between macroscopic cataclastic (brittle) and microscopic mylonitic (ductile) microstructures. Intragranular deformation microstructures (i.e. deformation twins, kink bands and microfractures) are well preserved in the deformed grains in clasts or in primary rocks. The matrix materials are of extremely fine grains with diffusive features. Dislocation microstructures for co-existing brittle deformation and crystalline plasticity were revealed using TEM. Tangled dislocations are often preserved at the cores of highly deformed clasts, while dislocation walls form in the transitions to the fine-grained     

地壳不同构造层次岩石变形机制及其构造岩类型

构造岩记录地壳构造变形演化重要信息,其成因、分类与命名一直没有统一认识。本文对构造岩变形机制、控制因素和构造岩分类进行系统总结。认为构造岩形成受物质成分、变形机制、应变速率、流体、温度、压力等因素控制,是物质成分与物理化学条件、变形机制等众多变量的函数。变形机制包括破裂作用、碎裂流动、晶质塑性、物质扩散、重结晶作用和超塑性流动,不同变形机制出现在不同地壳构造层次中,形成不同的显微组构。依据成因机制、物质组成和组构等标志对构造岩分类与命名进行重新修订,将构造岩划分为碎裂岩系列和变质构造岩系列,前者发育在地壳浅构造层次上,以破裂作用和碎裂流动变形机制为主;后者发育在中深部构造层次上,以晶质塑性、重结晶作用、物质扩散作用和超塑性流动作用为主。碎裂岩系列划分碎裂岩、角砾岩、微角砾岩、超碎裂岩、断层泥和假玄武玻璃;变质构造岩系列划分为构造片岩、糜棱岩和构造片麻岩。依据岩石流变性质、变形机制和构造岩分布,地壳构造层次划分为：脆性域,变形机制以碎裂作用和碎裂流动为主,发育碎裂岩系列;脆-韧性转换域,以晶质塑性、物质扩散和重结晶作用为主,并伴随有碎裂作用,形成糜棱岩、千糜岩和构造片岩;低温韧性域,以晶质塑性、物质扩散和重结晶作为主,发育糜棱岩与构造片岩;高温韧性域,以超塑性蠕变和重结晶作用为主,形成构造片麻岩。

     

The transition between deformation regimes dominated by intercrystalline diffusion and intracrystalline creep evaluated by oxygen isotope thermometry

The dominant flow mechanism in tectonic processes depends on the rheological properties of geological materials and the physical conditions prevailing during deformation. We have evaluated the relative importance of intercrystalline diffusion and intracrystalline creep in crustal deformation in terms of temperature and grain size.Oxygen isotope thermometry has been used to elucidate the thermal environment obtaining during deformation and contemporaneous metamorphism of Dalradian rocks from Southwest Scotland. The temperature and grain size data, applied in conjunction with microstructural criteria for evaluating independent mechanisms of steady-state flow, allow recognition of a low-temperature deformation regime dominated by intercrystalline diffusion, and a high-temperature regime dominated by dislocation processes.The transition between the fields of intercrystalline diffusion and dislocation creep for quartz and calcite of 100 Mm grain size occurs at about 450° C and about 300° C, respectively. These empirically derived results are consistent with the temperature intervals over which intercrystalline diffusion and dislocation creep, respectively, are predicted to be dominant at geologically reasonable strain rates, as derived from theoretically formulated deformation mechanism maps for quartz and calcite.Grain growth may play an important role in delimiting the higher-temperature boundary of the intercrystalline diffusion field. Intercrystalline diffusion is the only deformation mechanism that involves mass transfer over distances that are large in relation to the grain size. This result has important consequences for geochemical transport phenomena.     

Deformation mechanism maps for feldspar rocks

Deformation mechanism maps for feldspar rocks were constructed based on recently published constitutive laws for dislocation and grain boundary diffusion creep of wet and dry plagioclase aggregates. The maps display constant temperature contours in stress-grain size space for strain rates ranging from 10⁻¹⁶ to 10⁻¹² s⁻¹.Two fields of dominance of grain boundary diffusion-controlled creep and dislocation creep are separated by a strongly grain size-sensitive transition zone. For wet rocks, diffusion-controlled creep dominates below a grain size of about 0.1–1 mm, depending on temperature, stress, strain rate and feldspar composition. Plagioclase aggregates containing up to 0.3 wt.% water as often found in natural feldspars are more than 2 orders of magnitude weaker than dry rocks. The strength of water-bearing feldspar rocks is moderately dependent on composition and water fugacity.For a grain size range of about 10–50 μm commonly observed in natural ultramylonites, the deformation maps predict that diffusion-controlled creep is dominant at greenschist to granulite facies conditions. Low viscosity estimates of 10¹⁸–10¹⁹ Pa·s from modeling postseismic stress relaxation and channel flow of the continental lower crust can only be reconciled with laboratory experiments assuming dislocation creep at high temperatures >900 °C or, at lower temperatures, diffusion creep of fine-grained rocks possibly localized in abundant high strain shear zones. For similar thermodynamic conditions and grain size, lower crustal rocks are predicted to be less than order of magnitude weaker than upper mantle rocks.     

超高压变质岩的塑性流变：显微构造和变形机制

超高压变质岩是大陆深俯冲作用的产物。超高压变质岩在深俯,中和快速折返过程中,经历了长距离地构造搬运和构造力的作用。其构造变形主要集中在韧性剪切带中,并发生强烈地塑性流变。研究超高压变质构造岩的显微构造及其变形机制对于深入了解大陆壳岩石在深俯;中过程中的流变学行为有十分重要的意义。山东仰口的超高压韧性剪切带中榴辉岩质和花岗质糜棱岩记录了超高压变形的历史。在超高压条件下的稳定矿物绿辉石、多硅白云母、兰晶石和钾长石具有不规则波状消光、亚晶界、核幔构造和动态重结晶等显微构造特征,TEM研究揭示了大量的位错构造,表明位错蠕变是其主要的变形机制。在花岗质糜棱岩中,金红石在刚性矿物的压力影中沉积,细粒的石榴石条带平行片理延伸,都说明超高压变形过程中有流体存在,流体助力的物质扩散迁移是又一个重要的变形机制、依据现有的流变学定律估算的流变应力应该在几十兆帕以上。     

奠基岩石封闭应力假说的气体包裹体和膨胀能力

陈宗基先生在1979年提出了封闭应力假说,认为它是岩石工程灾害的原因。近年来,钱七虎院士和王思敬院士分别对封闭应力假说作了肯定的定性讨论。30多年过去了,这个封闭应力假说仅得到极其少的定量研究和发展。在本文中,我提出和试图论证流体包裹体是一种具体、实在、可测量和计算的应力包裹体。它在地质岩石与矿物中普遍存在。它有压强和体积膨胀能。它是一种封闭应力和内应变能的具体存在和作用形式。我给出了这个压强、体积膨胀能和封闭应力包裹体对围岩作用的计算公式和算例。这个包裹流体压强值与深部岩石高地应力场值相当。我进一步分析和讨论了,岩石微小、密封、压紧的流体包裹体应该是深部工程岩石开挖洞室或巷道出现的岩爆、冲击地压、矿震、洞壁劈裂、围岩分区破裂和巷道大变形的一个共同张性体积力源。我认为,这个地质岩石与矿物内紧压膨胀的流体包裹体封闭应力能够完整逻辑一致地、符合自然规律地解释人们所见到的、报道的、与这些深部工程灾害相关的所有事实。并且,它能将这些事实和现象合理地、随时间演变地联系和重塑起来。这种实在、可测试、可定量的封闭应力源和能源的提出和研究能为岩石力学工作者,更好地沿着老一辈岩石力学专家们指引的途径和思路,来建立新的地质岩石力学理论、方法和技术,以更加符合自然规律地解决岩石力学领域世界性难题的深部工程灾害问题。     

Crystallographic preferred orientation development by dissolution–precipitation creep

Crystallographic preferred orientations (CPOs) in deformed rocks are commonly interpreted as resulting from crystal plastic deformation mechanisms, where deformation is achieved by the movement of dislocations. In this paper we investigate the possibility of CPO-development by dissolution–precipitation creep or pressure solution. A numerical model is presented, which simulates the development of a grain aggregate that deforms by reaction-controlled dissolution–precipitation creep. Grains are simulated as rectangular boxes that change their shape by growth, or dissolution of their surfaces, depending on the normal stresses acting on the individual surfaces. Grains can also rotate due to an applied vorticity (for non-coaxial deformation) and if they have a non-equidimensional shape. For each strain increment, stress that is applied to the grains is the same for all grains, while individual grains deform and rotate by different amounts. A variety of CPOs develop at moderate strains, depending on the reaction rates of the different crystal-surfaces and type of deformation (uni-axial shortening, plane strain pure shear and simple shear). The modelling results confirm that dissolution–precipitation creep may play a role in CPO-development in rocks.