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.

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.

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.

Empirical Development of the Rock Mass Deformation Modulus

Rock mass deformation modulus is a fundamental factor for a safe and economical design of rock structures like large underground openings, tunneling, and open pit mine as well as foundations in both the initial state of stresses act on rock mass and its strength characteristics. The rock mass deformation modulus recently has been measured by in-situ loading tests and has been estimated by use of empirical equation based on classification systems and data of laboratory tests. In-situ tests to measure modulus directly are so expensive, times consuming and the reliability of the results of these tests is sometimes doubtful; subsequently, many researches have been carried out to estimate this parameter based on classification systems. In this study, a new empirical equation was proposed by use of statistical analyses based on a database of more than 142 in-situ tests, like plate load tests, dilatometer tests, flat jack tests, and classification systems; in addition, properties of the intact rock.

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.

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.

Unsaturated expansive soil fissure characteristics combined with engineering behaviors

The relationship among the surface fissure ratio, moisture content, seepage coefficient and deformation modulus of field unsaturated expansive soil in Nanning, Guangxi Province, China, was obtained by a direct or indirect method. Digital images of expansive soil of the surface fissure with different moisture contents were analyzed with the binarization statistic method. In addition, the fissure fractal dimension was computed with a self-compiled program. Combined with in situ seepage and loading plate tests, the relationship among the surface fissure ratio, moisture content, seepage coefficient and deformation modulus was initially established. The surface fissure ratio and moisture content show a linear relation, ＂y=-0.019 1x＋1.028 5＂ for rufous expansive soil and ＂y=-0.07 1x＋2.610 5＂ for grey expansive soil. Soil initial seepage coefficient and surface fissure ratio show a power function relation, ＂y=1× 10^-9exp（15.472x）＂ for rufous expansive soil and ＂y=5× 10^-7exp（4.209 6x）＂ for grey expansive soil. Grey expansive soil deformation modulus and surface fissure ratio show a power fimction relation of ＂y=3.935 7exp（0.993 6x）＂. Based on the binarization and fractal dimension methods, the results show that the surface fissure statistics can depict the fissure distribution in the view of two dimensions. And the evolvement behaviors of permeability and the deformation modulus can indirectly describe the developing state of the fissure. The analysis reflects that the engineering behaviors of unsaturated expansive soil are objectively influenced by fissure.

Strength and elastic properties of sandstone under different testing conditions

A laboratory experimental program performed on Wuhan sandstones was presented under monotonic loading, partial cyclic loading during loading path and sine wave cyclic loading with different strain rates to compare uniaxial compression strength and elastic properties (elastic modulus and Poisson ratio) under different conditions and influence of pore fluid on them. When the loading strain rates are 10^(-5), 10^(-4) and 10^(-3)/s, uniaxial compression strengths of dry sandstones are 82.3, 126.6 and 141.6 MPa, respectively, and that of water saturated sandstones are 70.5, 108.3 and 124.1 MPa, respectively. The above results show that the uniaxial compression strength increases with the increase of strain rate, however, variation of softening coefficient is insignificant. Under monotonic loading condition, tangent modulus increases with an increment of stress (strain) to a maximum value at a certain stress level, beyond which it starts to decline. Under the partial cyclic loading during loading path condition, unloading or reloading modulus is larger than loading modulus, and unloading and reloading moduli are almost constants with respect to stress level, especially unloading modulus. Under the sine wave cyclic loading condition, tangent modulus and Poisson ratio display asymmetric 'X' shape with various strain, and the average unloading modulus is larger than the average loading modulus.

The Influence of Freeze-Thaw Cycles on Unconfined Compressive Strength of Lignin Fiber-Reinforced Loess

In the seasonal permafrost region with loess distribution,the influence of freeze-thaw cycles on the engineering performance of reinforced loess must be paid attention to.Many studies have shown that the use of fiber materials can improve the engineering performance of soil and its ability to resist freeze-thaw cycles.At the same time,as eco-environmental protection has become the focus,which has been paid more and more attention to,it has become a trend to find new environmentally friendly improved materials that can replace traditional chemical additives.The purpose of this paper uses new environmental-friendly improved materials to reinforce the engineering performance of loess,improve the ability of loess to resist freeze-thaw cycles,and reduce the negative impact on the ecological environment.To reinforce the engineering performance of loess and improve its ability to resist freeze-thaw cycles,lignin fiber is used as a reinforcing material.Through a series of laboratory tests,the unconfined compressive strength(UCS)of lignin fiber-reinforced loess under different freeze-thaw cycles was studied.The effects of lignin fiber content and freeze-thaw cycles on the strength and deformation modulus of loess were analyzed.Combined with the microstructure features,the change mechanism of lignin fiber-reinforced loess strength under freeze-thaw cycles was discussed.The results show that lignin fiber can improve the UCS of loess under freeze-thaw cycles,but the strengthening effect no longer increases with the increase of fiber content.When the fiber content is less than 1%,the UCS growth rate of loess is the fastest under freeze-thaw cycles.And the UCS of loess with 1%fiber content is the most stable under freeze-thaw cycles.The freeze-thaw cycles increase the deformation modulus of loess with 1%fiber content,and its ability to resist deformation is obviously better than loess with 1.5%,2%and 3%fiber content.The fiber content over 1%will weaken the strengthening effect of lignin fiber-reinforced loess,and the optimum fiber content of lignin fiber-reinforced loess under freeze-thaw cycles is 1%.

Parametric modeling on spatial effect of excavation-damaged zone of underground cavern

Regarding excavation-damaged zone （EDZ） around underground opening as non-homogeneous rockmass with spatial deterioration effect on stuffiness and strength, a parametric model of EDZ using radius-displacement-dependent deformation modulus （RDDM） was proposed. Considering the nonlinearity characteristic of deformation and locality otherness of surrounding rock, deterioration parameter field of deformation modulus of rockmass around opening was quantitatively calculated through a given function. Applicability for multi-cavern condition and parameter sensibility of the model was analyzed by numerical experiments using synthetic data. Furthermore, the model was applied to identify EDZ of underground caverns of Pubugou hydropower station by calculating deterioration parameter field. Based on the parametric analysis of spatial effect and geological investigation, it is recognized that large radial deformation of deep fractured rock at the spandrel position and insufficient supporting bolts mainly result in great deformation pressure to act on the shotcrete and cause partial crack and spalling. It is shown that deterioration parameter field along the longitudinal axis of main powerhouse is evidently non-homogeneous in space and distributes exponentially along the radius from the opening. The model provides a simple and convenient way to identify the EDZ in the working state for rapid construction feedback analysis and support optimization of underground cavem from quantitative point of view and also aids in interpreting monitoring displacements and estimating support requirements.

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.

The critical pressure for driving a red blood cell through a contracting microfluidic channel

When a red blood cell （RBC） is driven by a pressure gradient through a microfluidic channel, its passage or blockage provides a measure of the rigidity of the cell. This has been developed as a means to separate RBCs according to their mechanical properties, which are known to change with pathological conditions such as malaria infection. In this study, we use numerical simulations to establish a quantitative connection between the minimum pressure needed to drive an RBC through a contracting microfluidic channel and the rigidity of the cell membrane. This provides the basis for designing such devices and interpreting the experimental data.

Effect of formulation of alginate beads on their mechanical behavior and stiffness

The aim of this work was to determine the effect of formulation of alginate beads on their mechanical behavior and stiffness when compressed at high speed. The alginate beads were formulated using different types and concentrations of alginate and gelling cations and were produced using an extrusiondripping method, Single wet beads were compressed at a speed of 40 mm/min, and their elastic limits were investigated, and the corresponding force versus displacement data were obtained. The Young＇s moduli of the beads were determined from the force versus displacement data using the Hertz＇s contact mechanics theory. The alginate beads were found to exhibit plastic behavior when they were compressed beyond 50% with the exception of copper-alginate beads for which yield occured at lower deformation, Alginate beads made of higher guluronic acid contents and gelling cations of higher chemical affinity were found to have greater stiffness. Increasing the concentration of alginate and gelling ions also generated a similar effect. At such a compression speed, the values of Young＇s modulus of the beads were found to be in the range between 250 and 900 kPa depending on the bead formulation.

Gement improved highly weathered phyllite for highway subgrades:A case study in Shaanxi province

In a cost-saving move, the soft rocks composed of highly-weathered phyllites available on- site were used to fill the subgrade in the eastern Ankang section of the expressway of Shiyan to Tianshui, China. Cement admixture was used to improve the performance of the weathered phyllites. In order to determine the best mix ratio, values corresponding to compaction performance, unconfined compressive strength, and the California bearing ratio （CBR） were analyzed for variable cement content weight percentages （3%, 4%, 5%, and 6%） using test subgrade plots in the field. Field measurements of resilience modulus and deflection confirmed that the strength of the subgrade increased as the cement ratio increased. In order to further evaluate the cement/phyllite mixture, the performance of the 3% cement ratio sample was evaluated under saturated conditions （with various levels of moisture addition and soaking time） using both the wetting deformation and resilient modulus values. Results suggest that moisture added and soaking time are key factors that affect the seepage depth, water content, and resilient modulus. The recommend values for the cement addition and for the water content are given out. This study can aid in pre- vention of highway damage by improving the foundation capacity and lengthening the lifecycle of the highway in phyllite distributed region at home and abroad.