A new testing method for investigating the loading rate dependency of peak and residual rock strength

One of the important methods for investigating viscoelasticity is to measure the loading-rate dependency of peak strength; however, no experimental method has been established for accurately measuring the loading-rate dependency of peak strength from a small number of samples. In this study we propose such a method. A single sample is loaded at alternating strain rates to obtain stress–strain curves for both strain rates. The loading-rate dependency of peak strength obtained via this method was compared with the findings of conventional methods. The loading-rate dependency indicated for Tage tuff, Sanjome andesite and Akiyoshi marble was nearly identical to previous results obtained using conventional methods, including results obtained under confining pressure. The loading-rate dependency of peak strength in these experiments shows a close relation with the creep stress-dependency of creep life. We also investigated the loading-rate dependency of the stress–strain curve for the post-failure region for which few results have been published. Under confining pressure, the corrected stress–strain curve, obtained by multiplying the stress of the complete stress–strain curve obtained at the fast strain rate by a constant determined by the ratio between the fast strain rate and slow strain rate, is nearly coincident with the stress–strain curve for the slow strain rate. This is an interesting result and represents new knowledge that may help elucidate failure mechanisms in the post-failure region. The loading-rate dependency of stress in the alternating strain rate experiment proposed here was most clearly observed when the stress–strain curve becomes flat, parallel to the strain axis. Some improvements to the proposed method are required to enable accurate investigations of loading-rate dependency during low stresses immediately after initiation of loading or during the abrupt decreases in stress that occur following peak strength.     

A Simple Pneumatic Loading System Controlling Stress and Strain Rates for One-Dimensional Compression of Clay

A simple but automated pneumatic loading system that can control the stress and strain rates for one-dimensional (1D) compression of clay was developed. The rate-dependency of stress-strain behaviour due to the viscous property of clay was investigated by 1D compression tests on standard-size specimens by various loading methods: 1) Standard Consolidation Tests (SCTs), stepwise increasing the axial stress two times every one day; 2) ordinary Constant-Rate-of-Strain (CRS) tests at different strain rates; 3) special CRS tests including unloading and reloading cycles with different stress amplitudes at strain rates of which the absolute value was either kept constant throughout respective tests or changed at the start of reloading; and 4) special CRS tests including a number of sustained loading (SL) during otherwise primary loading or unloading or reloading at constant strain rate. Sufficiently low strain rates were employed to ensure essentially fully drained condition. The followings were found. Despite that the newly developed pneumatic loading system is rather simple, 1D compression tests following such various loading histories as above can be performed on four types of clay rather accurately. The stress-strain behaviour of clay is significantly rate-dependent, exhibiting significant creep strains at SL stages. The creep strain rate is significantly different whether SL starts during otherwise primary loading or unloading or reloading, controlled by the magnitude and sign of the initial strain rate at the start of SL. The whole observed trends of rate-dependent stress-strain behaviour can be qualitatively explained by the non-linear three-component elasto-viscoplastic model extended to cyclic loading conditions.     

砂岩力学特性及其改进Duncan-Chang模型

 为了研究砂岩的力学特性,对砂岩试件开展了不同围压下的常规三轴压缩试验。试验结果显示,随围压增加,砂岩峰值应力、峰值点应变及残余强度均逐渐增大;当围压低于15 MPa时,砂岩弹性模量随围压增加也逐渐增大,但增大幅度逐渐降低;当围压在15 MPa以上时,其弹性模量则与围压无关。为了描述砂岩破坏过程的应力–应变响应,提出一种改进的Duncan-Chang模型,并根据岩石应力–应变曲线峰值点处斜率为0的特点给出模型参数的确定方法。利用砂岩三轴压缩试验结果对模型合理性进行验证。预测曲线和试验结果对比显示,该模型能够准确描述砂岩应变软化特性和不同围压下砂岩破坏过程中除初始压密阶段以外的其余4个阶段,特别是能够反映砂岩破坏后的残余强度。对模型特性的进一步分析表明,除应变软化特性外,该模型还可模拟岩石在高围压下的应变硬化行为,具有较强的适应性。     

Time-dependent tests on intact rocks in uniaxial compression

The influence of strain history on rock specimen deformation during multi-level loading and unloading cyclic uniaxial compression creep tests is studied with a creep testing machine. An experimental data processing method for such creep tests is suggested. The correction formulas to determine the rheological model parameters are derived for the case when load relaxation is considered. Creep and relaxation tests under uniaxial compression on four types of rocks are conducted using an electronic hydraulic servo-controlled stiff testing machine. The creep and relaxation laws of the different rocks are compared. The complete stress–strain curves for red sandstone specimens are obtained at nine strain rates from 2.43×10⁻⁶ to 4.38×10⁻³/s. The effects of strain rates on rock strength and limit strain are discussed. Empirical equations to evaluate the strain rate dependence of rock mechanical properties are presented.     

Effect of time on the stress–strain behaviour of a single rock joint

The time-dependent behaviour of discontinuities is important in many geotechnical applications. To investigate the stress–strain behaviour of jointed specimens tested at various rates of strain and at constant deformation in various stress conditions, three cases were examined: (a) increasing compressive load at different constant strain rates, (b) increasing compressive load at changing strain rates, (c) stress variations with a constant amount of displacement along the complete stress–strain curves for 5 min (stress relaxation). Triaxial tests were carried out on samples of the Penrith and Stainton Sandstones using a 5 MN servo-controlled stiff testing machine and confining pressures in the range of 0–30 MPa. Both intact and jointed specimens with saw cut and split joints were tested. The joints were produced with orientations of 30, 45 and 60° to the direction of the principal stress. Three different strain rates were applied.      

三维静载与循环冲击组合作用下砂岩动态力学特性研究

 利用动静组合加载试验装置,对具有不同轴压和围压的砂岩进行循环冲击试验,研究砂岩抵抗循环冲击载荷能力的变化特性,并重点讨论围压和轴压对砂岩动态疲劳力学特性的影响。围压分别设置为4,8,10和12 MPa四个系列,轴向静载荷分别设置为49,84,105和125 MPa四个系列,入射杆上的入射波大小相等,入射能大小为230 J。结果表明,相同围压下,总循环冲击次数随轴压的增大而减小;相同轴压下,随围压的增加,岩石承受的总循环冲击次数增加。随循环冲击次数的增加,岩石动态峰值应力、加载段的变形模量和弹性应变逐渐减小,动态峰值应变和残余应变逐渐增加。动态峰值应力和平均应变率具有良好的负线性关系;相同围压情况下,随轴压的递增,动态峰值应力和平均应变率拟合直线斜率的绝对值越来越大;相同轴压情况下,随着围压的增加,拟合直线斜率的绝对值越来越小。三维静应力情况下,减小轴压或增加围压有利于提高岩石抵抗外部循环冲击的能力。     

黏土蠕变量的试验研究

对黏土的原状和重塑土样在三轴排水剪切试验条件下的蠕变性进行研究,试验方法包括改变加载应变率的单向加载试验、单向加载试验过程中的蠕变试验、卸载和重复加载过程的蠕变试验等。试验结果表明:1)黏土蠕变量大小与黏土试样的状态有关;2)黏土蠕变量大小与蠕变之前的应变率有关,蠕变前应变率越大,蠕变量就越大;3)黏土蠕变量大小与蠕变时所处的应力水平有关,所处的应力水平越高,蠕变量就越大;4)在重复加载过程中,随着应力水平的提高,黏土的蠕变表现出由负蠕变、中性蠕变到正蠕变的逐渐转化。     

高应力强卸荷条件下大理岩损伤破裂的应变能转化过程机制研究

基于高应力条件下大理岩峰前卸围压试验和能量原理,研究岩样吸收应变能、塑性变形及裂纹扩展耗散应变能、环向变形消耗应变能和弹性应变能储存及释放的能量转化全过程特征,揭示其损伤破裂演化的应变能转化机制。峰前储存的弹性应变能较耗散应变能多,耗散应变能仅在临近峰值强度点附近才明显增加。峰后应力快速跌落伴随着弹性应变能的迅速释放和快速的塑性变形及裂隙扩展所耗散应变能。峰前、峰后应变能转化速率均随卸荷速率的增大而明显增大,特别是峰后转化速率增大得更为剧烈。而初始围压对应变能转化速率的影响与卸荷速率密切相关,快速卸荷时应变能转化速率随初始围压的升高而明显增大,而较慢速卸荷时随围压变化相对不明显,但初始围压增大明显加强峰前弹性应变能储存。峰后弹性应变能释放速率远大于环向变形消耗应变能速率,而吸收的应变能约与耗散应变能基本相等,故高应力强卸荷条件下硬性岩石常表现为近垂直于卸荷方向的张性破裂或劈裂特征,甚至出现岩爆现象。高应力强卸荷条件下大理岩具有峰前快速储存较多弹性应变能和相对较少的损伤耗能,而峰后弹性应变能快速大量释放和耗散,并伴有相对较快速地向卸荷方向的张裂变形消耗应变能的释放与耗散机制。     

基于应力归还控制的岩石荷载速率依存性研究

 采用应力归还伺服控制方法,对I和II类岩石荷载速率依存性进行研究。首先,运用变阻器技术,实现伺服试验机应力归还控制,能对岩石峰后进行稳定控制,完整地获得岩石的全应力–应变曲线。其次,对I(田下凝灰岩、荻野凝灰岩)和II类岩石(江持安山岩、井口砂岩)进行恒定荷载速率、交替荷载速率和加载–卸载–加载组合试验,组合试验对弹性和非弹性应变成功地进行了分离,得到非弹性应变和应力的对应关系。试验结果表明,破坏强度、破坏应变、杨氏模量和破坏寿命具有明显的荷载速率特性。最后,对峰前区域的荷载速率依存性常数n提出了3种求解方法,为研究岩石的速率效应奠定了基础。     

高围压卸荷条件下大理岩破碎块度分形特征及其与能量相关性研究

 高应力条件下,岩石卸荷的力学响应特征及发生机制是高地应力地区岩体工程开挖稳定性评价及控制的关键问题。基于不同卸荷速率和初始围压条件下三轴高应力大理岩卸围压试验,结合分形理论和能量原理,研究高应力卸荷条件下岩石破裂块度分布规律及其与能量耗散和释放的相关性。高应力条件下三轴卸围压大理岩试样碎块分形性质具有较强的局部性,仅在小于某一特征尺度(分形特征尺寸阈值)范围内表现出较好的分形性质,其碎块分维数均大于2,分维数随卸荷速率增大而单调减小,但初始围压对分维数的影响与卸荷速率密切相关。相对常规三轴压缩岩样,高围压下卸荷岩样虽然峰值点附近耗散和储存应变相对少得多,但其峰值前、后应变能转化速率相对大得多,特别是峰后的弹性应变能释放速率和环向膨胀消耗应变能速率。高应力卸荷条件下卸荷速率越快、初始围压越高,峰前损伤和峰后破裂贯通历时越短,峰值点处耗散应变能和储存弹性应变能越大,峰前、峰后应变能转化速率越快,破碎岩样的分形特征尺寸阈值越大,分维数越小,张性破裂程度和性质越强。     

Stress–strain relations of cement-mixed gravelly soil from multiple-step triaxial compression test results

The peak compressive strengths at different confining pressures of cement-mixed gravel (CMG) that are very similar to those obtained by single-step loading (SL) drained triaxial compression (TC) tests using multiple specimens can be obtained by a multiple-step loading (ML) test using a single specimen. However, only the unload/reload stress–strain relations at different confining pressures (except for the primary loading pressure at the first step) can be obtained from an ML test, and the reloading relations become softer with the increases in negative irreversible axial strain increments that have taken place during the respective immediately preceding unloading regimes. This phenomenon is formulated by a unique empirical equation for the CMG tests. Undamaged reloading stress–strain curves (URCs) were inferred by removing the damage effects from measured reloading curves (MRCs) in the ML TC test based on this correlation. A method was developed within the framework of the proportional rule to infer primary loading curves (PLCs) at different confining pressures from the URCs and the PLC at the first step obtained from a given ML TC test. A procedure was formulated to modify the PLCs obtained by this procedure based on the PLCs measured at stresses exceeding the yield stress for large-scale yielding during reloading at different confining pressures in the ML test. This method was validated by comparing the PLCs obtained from the results of a pair of ML tests, increasing and decreasing the confining pressure, with those obtained from a set of SL TC tests at different confining pressures.     

Strain rate dependent strength and stress–strain characteristics of a welded tuff

Results of 61 uniaxial compression tests on the welded Topopah Spring tuff are presented. The tests were carried out under constant strain rates at room temperature. Stress–strain analysis indicates that dilatancy and compaction start at about 50% of ultimate strength. A sudden stress drop occurs at about 90% of the ultimate strength, which indicates the onset of specimen failure. Both strength and peak axial strain decrease with strain rate as power functions. Based on the strain rate dependence of strength and peak axial strain, it is inferred that the elastic modulus is strain rate dependent. A relationship between stress, axial strain, and axial strain rate is developed. The parameters in this relation are estimated using multivariate regression to fit stress–axial strain–strain rate data.     

盐岩应力松弛效应的研究

系统介绍了单轴及三轴应力松弛试验研究装置及试验结果。研究结果表明：盐岩在整个应力松弛试验过程中,其横向应变近乎是常数,也即体应变保持不变。盐岩预蠕变对应力松弛具有较大的影响;盐岩的最低蠕变极限是存在的。     

单轴试验条件下粘土的粘塑性与模拟计算

利用饱和、湿润、风干以及烘干的藤森粘土的单轴排水固结试验进行了粘土粘塑性研究。试验过程中采用计算机应变控制的控制式三轴仪来实现加载速率，可在不同加载阶段实现不同的恒应变率加载试验。试验结果表明：各种不同饱和度藤森粘土的粘塑性都表现为等时特性；经过一定时间的蠕变后，粘土弹性模量会有较大的提高，且藤森粘土所表现出的粘塑性与粘土含水量的大小无关。研究结果表明，粘土的粘塑性应力-应变特性可以采用非线性三要素模型进行较好的描述。     

Effects of inelastic volume increase on fractured rock behaviour

This study investigated the correlation between inelastic volumetric deformation and the bearing capacity of fractured rock. Triaxial compression tests on marble specimens have been performed under constant and controlled deformation rates using a servocontrolled loading machine supported by an electro-hydraulic volume-measuring unit connected to a data acquisition system. The triaxial compression tests were carried out on two different marble samples under constant confining pressures ranging from 1–12.5 MPa. The results indicate that stress–inelastic volumetric strain curves are generally linear through the initial part of the post-failure curve where fractured rock behaviour is dominant. It was found that brittle rock loses its strength in the post-failure region depending on volumetric deformation; the slopes of post-failure curves change with an increase in confining pressure. As a result it is concluded that there is a relationship between strength and volumetric strain of fissured rock. Electronic Publication     

盐岩三轴蠕变与损伤恢复变形特征研究

地下盐岩储气库建设在我国能源储备战略中具有重要的地位,盐岩蠕变特性对地下盐岩储气库长期安全运行具有重要意义。为研究长期荷载作用下盐岩蠕变变形与损伤恢复特征,进行了不同围压、定偏应力的三轴蠕变及损伤恢复试验,损伤恢复时长超过150 d。研究结果表明:(1)高偏应力作用下,盐岩试样出现了明显的蠕变变形,轴向变形在30~40 d达到7%,体积变形先压缩后发生扩容;(2)低偏应力作用下,盐岩轴向蠕变变形量较小,体积变形持续压缩并趋于稳定;盐岩体积应变增幅随围压增大而逐渐增大,损伤恢复阶段试验达到150 d时,围压10、15、20、25 MPa对应体积应变分别相对增大1.06%、1.31%、1.30%及1.42%,盐岩体积应变增幅与围压之间呈正线性相关;(3)根据盐岩损伤恢复过程中体积变化特征及盐岩体积变形速率曲线,将盐岩损伤恢复划分为损伤快速恢复与损伤缓慢恢复两个阶段;盐岩损伤恢复主要发生在损伤快速恢复阶段,该阶段的体积增幅均达到全恢复过程的80%以上。     

饱和软粘土的流变和循环流变试验研究

分别对上海淤泥质饱和软粘土进行了长期流变和循环流变试验,得出其在不同围压、不同偏压和不同动应力作用下的变形规律。结果显示,围压相同时,偏压比大,试样的流变变形大,而偏压比相同时,围压大,流变变形也大;循环流变试验总体规律和流变试验相同,但经过一个循环加载阶段之后,随后的流变变形则很小。这些结论对今后软土地区高速公路、铁路和地铁建设提供一些帮助。     

脆性岩石渐进及蠕变失效特性宏细观力学模型研究

压应力作用脆性岩石渐进及蠕变失效特性是其力学性质研究的两个主要研究方向。其对于深部地下开挖围岩稳定性的判断有着重要的指导意义。岩石内部微裂纹扩展对脆性岩石的渐进及蠕变特性有着重要的影响。因此,基于岩石的应力与裂纹扩展关系及裂纹扩张演化法则,并结合宏细观损伤定义之间的关系,提出了一个新的宏细观力学模型,推出了岩石完整的应力–应变关系与蠕变理论表达式。分析了围压对岩石的应力–应变关系的影响。研究了岩石内部初始微裂纹尺寸及裂纹间摩擦系数对应力应变关系及岩石强度的影响。并给出了不同围压下岩石裂纹初始应力与峰值应力,其对蠕变实验中的施加应力初始值选取提供了一定参考。然后,研究了恒定围压、轴压分级加载应力路径下的岩石蠕变应变及应变率变化趋势。通过试验结果验证了理论模型的合理性。进而,对压应力作用下细观裂纹扩展对岩石力学特性影响的理解提供了一定的理论参考。     

三轴应力下塑性混凝土应力应变关系试验研究

通过4组塑性混凝土的单轴和常规三轴压缩应力应变全曲线试验,研究了三轴应力下塑性混凝土应力应变关系.结果表明：在围压作用下,塑性混凝土轴向应力应变曲线与单轴压缩下的曲线差别明显,主要表现为直线上升段很短,曲线上升段较长,无明显峰值点,下降段较平缓.利用割线模量表征塑性混凝土三轴应力下应力应变曲线上升段的主要变形特征,分析了影响割线模量的主要因素,建立了割线模量与围压、单轴抗压强度和弹性模量之间的关系式.研究了塑性混凝土三轴应力下峰值应变随围压、单轴应力下抗压强度及峰值应变的变化规律,并建立了相应的关系式.全面分析了塑性混凝土单轴及三轴作用下应力应变曲线特征,通过归一化处理后,拟合出常规三轴应力下塑性混凝土轴向应力应变关系式.     

Oscillation elimination in the Hopkinson bar apparatus and resultant complete dynamic stress–strain curves for rocks

This paper highlights an improved experimental approach for eliminating oscillation that exists in the dynamic stress–strain response of rocks and other brittle materials obtained from tests using a split Hopkinson pressure bar (SHPB). Both analytical and experimental results for a number of rock types are presented to verify the idea. Results from the investigation indicate that oscillation in the dynamic stress–strain response of these materials originates from the Pochhammer–Chree dispersion of the loading incident wave, and more evidently from the relatively low strength and elastic modulus of the samples compared with metallic materials. In order to control the oscillation effectively, it is proposed that a half-sine loading waveform should be used instead of the conventional rectangular loading waveform in SHPB tests. Experimental results obtained from both the conventional and the improved methods are presented, including dynamic complete stress–strain curves for granite, sandstone and limestone. The improved method eliminates oscillation in the tests, provides better stability of strain rate and more representative results than those obtained from the conventional rectangular loading waveform shape.