Assessment of Rock Mass Quality and Deformation Modulus by Empirical Methods along Kandiah River, KPK, Pakistan

The pivotal aim of this study is to evaluate the rock mass characterization and deformation modulus. It is vital for rock mass classification to investigate important parameters of discontinuities. Therefore, Rock Mass Rating (RMR) and Tunneling quality index (Q) classification systems are applied to analyze 22 segments along proposed tunnel routes for hydropower in Kandiah valley, Khyber Pakhtunkhwa, Pakistan. RMR revealed the range of fair to good quality rocks, whereas Q yielded poor to fair quality rocks for investigated segments of the rock mass. Besides, Em values were acquired by empirical equations and computer-aided program RocLab, and both methods presented almost similar variation trend of their results. Hence, the correlations of Em with Q and RMR were carried out with higher values of the regression coefficient. This study has scientific significance to initially understand the rock mass conditions of Kandiah valley.

Performance analysis of empirical models for predicting rock mass deformation modulus using regression and Bayesian methods

Deformation modulus of rock mass is one of the input parameters to most rock engineering designs and constructions.The field tests for determination of deformation modulus are cumbersome,expensive and time-consuming.This has prompted the development of various regression equations to estimate deformation modulus from results of rock mass classifications,with rock mass rating(RMR)being one of the frequently used classifications.The regression equations are of different types ranging from linear to nonlinear functions like power and exponential.Bayesian method has recently been developed to incorporate regression equations into a Bayesian framework to provide better estimates of geotechnical properties.The question of whether Bayesian method improves the estimation of geotechnical properties in all circumstances remains open.Therefore,a comparative study was conducted to assess the performances of regression and Bayesian methods when they are used to characterize deformation modulus from the same set of RMR data obtained from two project sites.The study also investigated the performance of different types of regression equations in estimation of the deformation modulus.Statistics,probability distributions and prediction indicators were used to assess the performances of regression and Bayesian methods and different types of regression equations.It was found that power and exponential types of regression equations provide a better estimate than linear regression equations.In addition,it was discovered that the ability of the Bayesian method to provide better estimates of deformation modulus than regression method depends on the quality and quantity of input data as well as the type of the regression equation.

Application of numerical modeling and genetic programming to estimate rock mass modulus of deformation

Estimation of the rock mass modulus of deformation(Em)is one of the most important design parameters in designing many structures in and on rock.This parameter can be obtained by in situ tests,empirical relations between deformation modulus and rock mass classifcation,and estimating from laboratory tests results.In this paper,a back analysis calculation is performed to present an equation for estimation of the rock mass modulus of deformation using genetic programming(GP)and numerical modeling.A database of 40,960 datasets,including vertical stress(rz),horizontal to vertical stresses ratio(k),Poisson’s ratio(m),radius of circular tunnel(r)and wall displacement of circular tunnel on the horizontal diameter(d)for input parameters and modulus of deformation for output,was established.The selected parameters are easy to determine and rock mass modulus of deformation can be obtained from instrumentation data of any size circular galleries.The resulting RMSE of 0.86 and correlation coeffcient of97%of the proposed equation demonstrated the capability of the computer program(CP)generated by GP.

Development of a multivariate empirical model for predicting weak rock mass modulus

Estimating weak rock mass modulus has historically proven difficult although this mechanical property is an important input to many types of geotechnical analyses. An empirical database of weak rock mass modulus with associated detailed geotechnical parameters was assembled from plate loading tests performed at underground mines in Nevada, the Bakhtiary Dam project, and Portugues Dam project. The database was used to assess the accuracy of published single-variate models and to develop a multivariate model for predicting in-situ weak rock mass modulus when limited geotechnical data are available.Only two of the published models were adequate for predicting modulus of weak rock masses over limited ranges of alteration intensities, and none of the models provided good estimates of modulus over a range of geotechnical properties. In light of this shortcoming, a multivariate model was developed from the weak rock mass modulus dataset, and the new model is exponential in form and has the following independent variables:(1) average block size or joint spacing,(2) field estimated rock strength,(3) discontinuity roughness, and(4) discontinuity infilling hardness. The multivariate model provided better estimates of modulus for both hard-blocky rock masses and intensely-altered rock masses.

A comparative assessment of rock mass deformation modulus

Deformation modulus of a rock mass(E_m) is one of the most important design parameters in construction of rock engineering projects such as underground excavations.However,difficulties are frequently encountered during in-situ tests which are also time-consuming and expensive for determining this parameter.Although E_m is often estimated indirectly from proposed equations by different researchers,many of these equations cannot be used in case of problematic rock conditions(thinly bedded,highly jointed rock masses,etc.) as high quality core samples are required.This study aims to explore more practical and useful equation for E_m estimation using Rock Quality Designation(RQD) and point load index values.Comparisons were made between available empirical equations and the proposed E_m equation in terms of the estimation capacity.Multiple comparison tests(ANOVA) showed that E_m can be reliably estimated using proposed equation especially at the preliminary stages of projects.

Prediction Research of Deformation Modulus of Weak Rock Zone under In-situ Conditions

Weak rock zone (soft interlayer, fault zone and soft rock) is the highlight of large-scale geological engineering research. It is an important boundary for analysis of rock mass stability. Weak rock zone has been formed in a long geological period, and in this period, various rocks have undergone long-term consolidation of geostatic stress and tectonic stress; therefore, under in-situ conditions, their density and modulus of deformation are relatively high. Due to its fragmentary nature, once being exposed to the earth's surface, the structure of weak rock zone will soon be loosened, its density will be reduced, and its modulus of deformation will also be reduced significantly. Generally, weak rock zone can be found in large construction projects, especially in the dam foundation rocks of hydropower stations. These rocks cannot be eliminated completely by excavation. Furthermore, all tests nowadays are carried out after the exposure of weak rock zone, modulus of deformation under in-situ conditions cannot be revealed. In this paper, a test method explored by the authors has been introduced. This method is a whole multilayered medium deformation method. It is unnecessary to eliminate the relatively complete rocks covering on weak rock zone. A theoretical formula to obtain the modulus of deformation in various mediums has also been introduced. On-site comparative trials and indoor deformation modulus tests under equivalent density conditions have been carried out. We adopted several methods for the prediction researches of the deformation modulus of weak rock zone under in-situ conditions, and revealed a fact that under in-situ conditions, the deformation modulus of weak rock zone are several times higher than the test results obtained after the exposure. In a perspective of geological engineering, the research findings have fundamentally changed peoples' concepts on the deformation modulus of weak rock zone, provided important theories and methods for precise definition of deformation modulus of deep weak rock zone under cap rock conditions, as well as for reasonable engineering applications.

Evolution of mechanical parameters of Shuangjiangkou granite under different loading cycles and stress paths

Surrounding rocks at different locations are generally subjected to different stress paths during the process of deep hard rock excavation.In this study,to reveal the mechanical parameters of deep surrounding rock under different stress paths,a new cyclic loading and unloading test method for controlled true triaxial loading and unloading and principal stress direction interchange was proposed,and the evolution of mechanical parameters of Shuangjiangkou granite under different stress paths was studied,including the deformation modulus,elastic deformation increment ratios,fracture degree,cohesion and internal friction angle.Additionally,stress path coefficient was defined to characterize different stress paths,and the functional relationships among the stress path coefficient,rock fracture degree difference coefficient,cohesion and internal friction angle were obtained.The results show that during the true triaxial cyclic loading and unloading process,the deformation modulus and cohesion gradually decrease,while the internal friction angle gradually increases with increasing equivalent crack strain.The stress path coefficient is exponentially related to the rock fracture degree difference coefficient.As the stress path coefficient increases,the degrees of cohesion weakening and internal friction angle strengthening decrease linearly.During cyclic loading and unloading under true triaxial principal stress direction interchange,the direction of crack development changes,and the deformation modulus increases,while the cohesion and internal friction angle decrease slightly,indicating that the principal stress direction interchange has a strengthening effect on the surrounding rocks.Finally,the influences of the principal stress interchange direction on the stabilities of deep engineering excavation projects are discussed.

Settlement of composite foundation with discrete material pile considering modulus change

Based on deeply discussing the deformation mechanism of composite foundation with discrete material pile, firstly, the settlement of composite foundation in rigid foundation conditions was assumed to consist of two parts, an expanding part and an un-expanding part. Then, in view of the differences of deformation properties between the expanding part and the un-expanding part, the relationships between the pile modulus and the applied load in these two parts were respectively developed. Thirdly, by introducing the above relationships into settlement analysis, a new method to calculate displacement of composite foundation with discrete material pile was proposed by using the multi-stage loading theory and the layer-wise summation approach. This method is effective not only for accounting for the effect of variations of pores on deformation modulus of the pile body in different depths, but also for describing the characteristics of different deformation mechanisms of the pile body with varying depth. Finally, the proposed method was used to a practical composite foundation problem, whose theoretical results were presented and compared to those of other methods. The rationality and feasibility of this method are identified through comparative analysis.

A new estimation method and an anisotropy index for the deformation modulus of jointed rock masses

The deformation modulus of a rock mass is an important parameter to describe its mechanical behavior.In this study,an analytical method is developed to determine the deformation modulus of jointed rock masses,which considers the mechanical properties of intact rocks and joints based on the superposition principle.Due to incorporating the variations in the orientations and sizes of joint sets,the proposed method is applicable to the rock mass with persistent and parallel joints as well as that with nonpersistent and nonparallel joints.In addition,an anisotropy index AIdmfor the deformation modulus is defined to quantitatively describe the anisotropy of rock masses.The range of AIdmis from 0 to 1,and the more anisotropic the rock mass is,the larger the value of AIdmwill be.To evaluate the proposed method,20 groups of numerical experiments are conducted with the universal distinct element code(UDEC).For each experimental group,the deformation modulus in 24 directions are obtained by UDEC(numerical value)and the proposed method(predicted value),and then the mean error rates are calculated.Note that the mean error rate is the mean value of the error rates of the deformation modulus in 24 directions,where for each direction,the error rate is equal to the ratio of numerical value minus predicted value to the numerical value.The results show that(i)for different experimental groups,the mean error rates vary between 5.06%and 22.03%;(ii)the error rates for the discrete fracture networks(DFNs)with two sets of joints are at the same level as those with one set of joints;and(iii)therefore,the proposed method for estimating the deformation modulus of jointed rock masses is valid.

A new model to describe effect of plastic deformation on elastic modulus of aluminum alloy

In order to improve the prediction capability of spring-back in aluminum sheet metal forming, the influence of the plastic deformation on elastic modulus is considered when the material undergoes a large plastic deformation. The present work focused on establishing a new model to accurately describe the relation of elastic modulus and plastic deformation. The tensile tests were performed to investigate the influence of plastic deformation on elastic modulus at low strain rate. Two different aluminum sheets were used, AA2024-T3 and LY12-CZ, and the thickness of sheet metals was 1.3 mm and 2.0 mm, respectively. In order to overcome the drawback, which is directly measuring the slope of tension curve to obtain elastic modulus, an extrapolation method was adopted. The proposal macroscopic piecewise sinusoidal function can accurately model the elastic modulus variation.

Settlement predictions of footings on sands using probabilisticanalysis

The design of footings on sands is often controlled by settlement rather than bearing capacity.Therefore,settlement predictions are essential in the design of shallow foundations.However,predicted settlements of footings are highly dependent on the chosen elastic modulus and the used method.This paper presents the use of probabilistic analysis to evaluate the variability of predicted settlements of footings on sands,focusing on the load curve(predicted settlements)characterization.Three methodologies,the first-and second-order second-moment(FOSM and SOSM),and Monte Carlo simulation(MCS),for calculating the mean and variance of the estimated settlements through Schmertmann(1970)’s equation,are presented and discussed.The soil beneath the footing is treated as an uncorrelated layered material,so the total settlement and variance are found by adding up the increments of the layers.The deformability modulus(ESi)is considered as the only independent random variable.As an example of application,a hypothetical case of a typical subsoil in the state of Espirito Santo,southeast of Brazil,is evaluated.The results indicate that there is a significant similarity between the SOSM and MCS methods,while the FOSM method underestimates the results due to the non-consideration of the high-order terms in Taylor’s series.The contribution of the knowledge of the uncertainties in settlement prediction can provide a safer design.

Effect of curing, capillary action, and groundwater level increment on geotechnical properties of lime concrete: Experimental and prediction studies

Lime concrete and lime treatment are two attractive techniques for geotechnical engineers.However,researches have rarely been carried out to study the effects of moisture and capillary action due to increasing groundwater level on geotechnical properties of lime concrete.The aim of this study is to investigate the effects of curing time and degree of saturation on some of geotechnical properties of lime concrete such as unconfined compressive strength(UCS),secant modulus(ES),failure strain,brittleness index(IB),and deformability index(ID) using unconfined compression tests.First of all,geotechnical and chemical properties of used materials were determined.After curing times of 14 d,28 d,45 d,and 60 d in laboratory condition,the specimens were exposed to saturation levels ranging from 0 to 100%.The results showed that the moisture and curing time have significant effects on the properties of lime concrete.Based on the results of scanning electron micrograph(SEM) test,it was observed that the specimen was characterized by a rather well-structured matrix since both the filling of a large proportion of the coarse-grained soil voids by clay and the pozzolanic activity of lime led to retaining less pore water in the specimen,increasing the UCS and ES,and consequently resisting against swelling and shrinkage of the clay soil.Moreover,due to the pozzolanic reactions and reduction of water,by increasing the curing time and decreasing the degrees of saturation,UCS,ES,and IBincreased,and IDdecreased.Based on the experimental results,a phenomenological model was used to develop equations for predicting the properties in relation to the ratio of degree of saturation/curing time.The results showed that there was a good correlation(almost R2> 90%) between the measured parameters and the estimated ones given by the predicted equations.

Three-dimensional numerical simulation on the coseismic deformation of the 2008 M_S8.0 Wenchuan earthquake in China

Based on the finite element numerical algorithm, the coseismic displacements of the Wenchuan Ms8.0 earthquake are calculated with the rupture slip vectors derived by Ji and Hayes as well as Nishimura and Yaji. Except in a narrow strip around the rupture zone, the coseismic displacements are consistent with those from GPS observation and InSAR interpretation. Numerical results show that rupture slip vectors and elastic properties have profound influences on the surface coseismic deformation, Results from models with different elastic parameters indicate that： （1） in homogeneous elastic medium, the surface displacements are weakly dependent on Poisson＇s ratio and independent of the elastic modulus; （2） in horizontally homogeneous medium with a weak zone at its middle, the thickness of the weak zone plays a significant role on calculating the surface displacements; （3） in horizontally and vertically heterogeneous medium, the surface displacements depend on both Poisson＇s ratio and elastic modulus. Calculations of eoseismic deformation should take account of the spatial variation of the elastic properties. The misfit of the numerical results with that from the GPS observations in the narrow strip around the rupture zone suggests that a much more complicated rupture model of the Wenchuan earthquake needs to be established in future study.

Effect of vertical stress rest period on deformation behaviour of unbound granular materials:Experimental and numerical investigations

Repeated load triaxial test is used to assess the deformation behaviour of unbound granular materials(UGMs) in flexible road pavements. Repeated load pulse characteristics(i.e. shape, loading period and rest period) are the stress configurations used in the experimental set-up to simulate the passing axle loads. Some researchers and standard testing protocols suggest a rest period of varying durations after a loading phase. A thorough review of existing literature and practises has revealed that there is no agreement about the effect of the rest period of vertical stress pulse on the deformation behaviour of the UGMs. Therefore,the main objective of this study is to investigate the effect of repeated stress rest period on the deformation behaviour of UGMs experimentally. Experiments are conducted, both with and without rest period, using basalt and granite crushed rocks from Victoria, Australia. Furthermore, in order to gain insight into the effect of the rest period, finite element modelling is also developed. Both the experimental and modelling results show that the rest period has a noticeable effect on both resilient and permanent deformation behaviours of UGMs. It is, therefore, recommended to take extra precautions while adopting a particular standard testing protocol and to supplement the results by additional tests with different loading configurations.

Effect of Axial Deformation on Elastic Properties of Irregular Honeycomb Structure

Irregular honeycomb structures occur abundantly in nature and in man-made products,and are an active area of research.In this paper,according to the optimization of regular honeycomb structures,two types of irregular honeycomb structures with both positive and negative Poisson’s ratios are presented.The elastic properties of irregular honeycombs with varying structure angles were investigated through a combination of material mechanics and structural mechanics methods,in which the axial deformation of the rods was considered.The numerical results show that axial deformation has a significant influence on the elastic properties of irregular honeycomb structures.The elastic properties of the structure can be considered by the enclosed area of the unit structure,the shape of the unit structure,and the elastic properties of the original materials.The elastic properties considering the axial deformation of rods studied in this study can provide a reference for other scholars.

Effect of loading rate and time delay on the tangent modulus method(TMM)in coal and coal measured rocks

Non-destructive techniques of in-situ stress measurement from oriented cored rocks have great potential to be developed as a cost cost-effective and reliable alternative to the conventional overcoring and hydraulic fracturing methods.The tangent modulus method(TMM)is one such technique that can be applied to oriented cored rocks to measure in-situ stresses.Like the deformation rate analysis(DRA),the rock specimen is subjected to two cycles of uniaxial compression and the stress-tangent modulus curve for the two cycles is obtained from the stress-strain curve.A bending point in the tangent modulus curve of the first cycle is observed,separating it from the tangent modulus curve of the second cycle.The point of separation between the two curves is assumed to be the previously applied maximum stress.A number of experiments were conducted on coal and coal measured rocks(sandstone and limestone)to understand the effect of loading conditions and the time delay.The specimens were preloaded,and cyclic compressions were applied under three different modes of loading,four different strain rates,and time delays of up to one week.The bending point in the stress-tangent modulus curves occurred approximately at the applied pre-stress levels under all three loading modes,and no effect of loading rate was observed on the bending points in TMM.However,a clear effect of time delay was observed on the TMM,contradicting the DRA results.This could be due to the sensitivity of TMM and the range of its applicability,all of which need further investigation for the in-situ stress measurement.

A System for Road Pavement Composite Material Deformation

For a comprehensive experimental evaluation of the material quality, forecast of the properties and parameter change of the bituminous material was made at the time under the impact of external factors, they are subjected to the necessary tests. In the article the automated set “Tomsk-Asphalt-Test” for determining the elastic modulus of the specimens made of bituminous materials was used in road pavements, maximally close to natural conditions of operation of highways of the Siberian region inRussiaare described. The automated set contains: electromechanical, climate, electronic, PC and software subsystem. The operation principle is a short-time deformation of the asphalt specimens;measurement of physical values: the stress, strain, variation of the size line and temperature of the asphalt pavement material test specimen, converting the measured values into electrical signals, their program processing and visualization. The control of testing and viewing results of measurements is carried out in accordance with the menu software subsystem. The results of calculations: the maximum values of vertical load the difference between the maximum horizontal deformation value and the value measured last after specimen of asphalt material loading for each test cycle, the sum of the differences of the horizontal deformation values of the two sensors and modulus of elasticity.

EM算法在变形监测数据处理中的应用

针对测量数据在隐含的未观测变量或者观测数据不完整的情况下难以处理等一系列问题,引入EM算法,对不完全沉降数据进行建模分析,并对后期沉降数据进行较为精确的预测。建模结果表明,在缺失数据情况下,EM算法可以有效提高变形监测数据分析的精度和可靠性,提高变形监测数据处理质量。

不同含水状态砂岩裂纹稳定扩展阶段损伤特征

为深入揭示裂纹稳定扩展阶段的岩石损伤状态,以干燥、自然和饱水状态砂岩为研究对象,采用体积应变法测定起裂应力和损伤应力值,进一步通过增量循环加卸载试验,综合分析了裂纹稳定扩展阶段的残余应变、变形模量和能量演化规律。结果表明:轴向残余应变随轴向应力水平增加而增加,其增幅表现为先减小、后稳定、再增大,且增幅稳定阶段对应于裂纹稳定扩展阶段;在裂纹稳定扩展阶段,加载过程和卸载过程变形模量均呈线性减少趋势,而耗散能密度呈线性增加趋势。上述演化规律适用于不同含水状态砂岩,但其具体数值与含水率有关。对于裂纹稳定扩展阶段,加载过程变形模量可有效表征砂岩损伤状态,基于含水率和轴向应力水平的线性数学模型可用于评价工程岩体的实际损伤状态。