Three-dimensional(3D)parametric measurements of individual gravels in the Gobi region using point cloud technique

Gobi spans a large area of China,surpassing the combined expanse of mobile dunes and semi-fixed dunes.Its presence significantly influences the movement of sand and dust.However,the complex origins and diverse materials constituting the Gobi result in notable differences in saltation processes across various Gobi surfaces.It is challenging to describe these processes according to a uniform morphology.Therefore,it becomes imperative to articulate surface characteristics through parameters such as the three-dimensional(3D)size and shape of gravel.Collecting morphology information for Gobi gravels is essential for studying its genesis and sand saltation.To enhance the efficiency and information yield of gravel parameter measurements,this study conducted field experiments in the Gobi region across Dunhuang City,Guazhou County,and Yumen City(administrated by Jiuquan City),Gansu Province,China in March 2023.A research framework and methodology for measuring 3D parameters of gravel using point cloud were developed,alongside improved calculation formulas for 3D parameters including gravel grain size,volume,flatness,roundness,sphericity,and equivalent grain size.Leveraging multi-view geometry technology for 3D reconstruction allowed for establishing an optimal data acquisition scheme characterized by high point cloud reconstruction efficiency and clear quality.Additionally,the proposed methodology incorporated point cloud clustering,segmentation,and filtering techniques to isolate individual gravel point clouds.Advanced point cloud algorithms,including the Oriented Bounding Box(OBB),point cloud slicing method,and point cloud triangulation,were then deployed to calculate the 3D parameters of individual gravels.These systematic processes allow precise and detailed characterization of individual gravels.For gravel grain size and volume,the correlation coefficients between point cloud and manual measurements all exceeded 0.9000,confirming the feasibility of the proposed methodology for measuring 3D parameters of individual gravels.The proposed workflow yields accurate calculations of relevant parameters for Gobi gravels,providing essential data support for subsequent studies on Gobi environments.

Three-dimensional numerical analysis of plant-soil hydraulic interactions on pore water pressure of vegetated slope under different rainfall patterns

Understanding the pore water pressure distribution in unsaturated soil is crucial in predicting shallow landslides triggered by rainfall,mainly when dealing with different temporal patterns of rainfall intensity.However,the hydrological response of vegetated slopes,especially three-dimensional(3D)slopes covered with shrubs,under different rainfall patterns remains unclear and requires further investigation.To address this issue,this study adopts a novel 3D numerical model for simulating hydraulic interactions between the root system of the shrub and the surrounding soil.Three series of numerical parametric studies are conducted to investigate the influences of slope inclination,rainfall pattern and rainfall duration.Four rainfall patterns(advanced,bimodal,delayed,and uniform)and two rainfall durations(4-h intense and 168-h mild rainfall)are considered to study the hydrological response of the slope.The computed results show that 17%higher transpiration-induced suction is found for a steeper slope,which remains even after a short,intense rainfall with a 100-year return period.The extreme rainfalls with advanced(PA),bimodal(PB)and uniform(PU)rainfall patterns need to be considered for the short rainfall duration(4 h),while the delayed(PD)and uniform(PU)rainfall patterns are highly recommended for long rainfall durations(168 h).The presence of plants can improve slope stability markedly under extreme rainfall with a short duration(4 h).For the long duration(168 h),the benefit of the plant in preserving pore-water pressure(PWP)and slope stability may not be sufficient.

Three-dimensional stability calculation method for high and large composite slopes formed by mining stope and inner dump in adjacent open pits

The 2D limit equilibrium method is widely used for slope stability analysis.However,with the advancement of dump engineering,composite slopes often exhibit significant 3D mechanical effects.Consequently,it is of significant importance to develop an effective 3D stability calculation method for composite slopes to enhance the design and stability control of open-pit slope engineering.Using the composite slope formed by the mining stope and inner dump in Baiyinhua No.1 and No.2 open-pit coal mine as a case study,this research investigates the failure mode of composite slopes and establishes spatial shape equations for the sliding mass.By integrating the shear resistance and sliding force of each row of microstrip columns onto the bottom surface of the strip corresponding to the main sliding surface,a novel 2D equivalent physical and mechanical parameters analysis method for the strips on the main sliding surface of 3D sliding masses is proposed.Subsequently,a comprehensive 3D stability calculation method for composite slopes is developed,and the quantitative relationship between the coordinated development distance and its 3D stability coefficients is examined.The analysis reveals that the failure mode of the composite slope is characterized by cutting-bedding sliding,with the arc serving as the side interface and the weak layer as the bottom interface,while the destabilization mechanism primarily involves shear failure.The spatial form equation of the sliding mass comprises an ellipsoid and weak plane equation.The analysis revealed that when the coordinated development distance is 1500 m,the error rate between the 3D stability calculation result and the 2D stability calculation result of the composite slope is less than 8%,thereby verifying the proposed analytical method of equivalent physical and mechanical parameters and the 3D stability calculation method for composite slopes.Furthermore,the3D stability coefficient of the composite slope exhibits an exponential correlation with the coordinated development distance,with the coefficient gradually decreasing as the coordinated development distance increases.These findings provide a theoretical guideline for designing similar slope shape parameters and conducting stability analysis.

Phase II Clinical Study of Three-Dimensional Printed Coplanar Template Combined with CT-Guided Percutaneous Core Needle Biopsy of Pulmonary Nodules in Elderly Patients

Background: As the population age structure gradually ages, more and more elderly people were found to have pulmonary nodules during physical examinations. Most elderly people had underlying diseases such as heart, lung, brain and blood vessels and cannot tolerate surgery. Computed tomography (CT)-guided percutaneous core needle biopsy (CNB) was the first choice for pathological diagnosis and subsequent targeted drugs, immune drugs or ablation treatment. CT-guided percutaneous CNB requires clinicians with rich CNB experience to ensure high CNB accuracy, but it was easy to cause complications such as pneumothorax and hemorrhage. Three-dimensional (3D) printing coplanar template (PCT) combined with CT-guided percutaneous pulmonary CNB biopsy has been used in clinical practice, but there was no prospective, randomized controlled study. Methods: Elderly patients with lung nodules admitted to the Department of Oncology of our hospital from January 2019 to January 2023 were selected. A total of 225 elderly patients were screened, and 30 patients were included after screening. They were randomly divided into experimental group (Group A: 30 cases) and control group (Group B: 30 cases). Group A was given 3D-PCT combined with CT-guided percutaneous pulmonary CNB biopsy, Group B underwent CT-guided percutaneous pulmonary CNB. The primary outcome measure of this study was the accuracy of diagnostic CNB, and the secondary outcome measures were CNB time, number of CNB needles, number of pathological tissues and complications. Results: The diagnostic accuracy of group A and group B was 96.67% and 76.67%, respectively (P = 0.026). There were statistical differences between group A and group B in average CNB time (P = 0.001), number of CNB (1 vs more than 1, P = 0.029), and pathological tissue obtained by CNB (3 vs 1, P = 0.040). There was no statistical difference in the incidence of pneumothorax and hemorrhage between the two groups (P > 0.05). Conclusions: 3D-PCT combined with CT-guided percutaneous CNB can improve the puncture accuracy of elderly patients, shorten the puncture time, reduce the number of punctures, and increase the amount of puncture pathological tissue, without increasing pneumothorax and hemorrhage complications. We look forward to verifying this in a phase III randomized controlled clinical study. .

3D bioprinting of complex biological structures with tunable elastic modulus and porosity using freeform reversible embedding of suspended hydrogels

Three-dimensional(3D)bioprinting has been used widely for the construction of hard tissues such as bone and cartilage.However,constructing soft tissues with complex structures remains a challenge.In this study,complex structures characterized by both tunable elastic modulus and porosity were printed using freeform reversible embedding of suspended hydrogels(FRESHs)printing methods.A mixture of alginate and gelatin was used as the main functional component of the bioink.Rheological analysis showed that this bioink possesses shear thinning and shear recovery properties,supporting both cryogenic and FRESH printing methods.Potential printing capabilities and limitations of cryogenic and FRESH printing were then analyzed by printability tests.A series of complex structures were printed by FRESH printing methods which could not be realized using conventional approaches.Mechanical tests and scanning electron microscopy analysis showed that the printed structure is of excellent flexibility and could be applied in various conditions by adjusting its mechanical modulus and porosity.L929 fibroblast cells maintained cell viability in cell-laden-printed structures,and the addition of collagen further improved the hydrogels’biocompatibility.Overall,all results provided useful insight into the building of human soft tissue organ blocks.

Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses

In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.

Reflection of three-dimensional plane waves at the free surface of a rotating triclinic half-space under the context of generalized thermoelasticity

The reflection of three-dimensional(3D) plane waves in a highly anisotropic(triclinic) medium under the context of generalized thermoelasticity is studied. The thermoelastic nature of the 3D plane waves in an anisotropic medium is investigated in the perspective of the three-phase-lag(TPL), dual-phase-lag(DPL), Green-Naghdi-III(GNIII), Lord-Shulman(LS), and classical coupled(CL) theories. The reflection coefficients and energy ratios for all the reflected waves are obtained in a mathematical form. The rotational effects on the reflection characteristics of the 3D waves are discussed under the context of generalized thermoelasticity. Comparative analyses for the reflection coefficients of the waves among these generalized thermoelastic theories are performed. The energy ratios for each of the reflected waves establish the energy conservation law in the reflection phenomena of the plane waves. The highly anisotropic materials along with the rotation may have a significant role in the phenomenon of the reflection behavior of the 3D waves. Numerical computations are performed for the graphical representation of the study.

Computation of elastic properties of 3D digital cores from the Longmaxi shale

The dependence of elastic moduli of shales on the mineralogy and microstructure of shales is important for the prediction of sweet spots and shale gas production. Based on 3D digital images of the microstructure of Longmaxi black shale samples using X-ray CT, we built detailed 3D digital images of cores with porosity properties and mineral contents. Next, we used finite-element （FE） methods to derive the elastic properties of the samples. The FE method can accurately model the shale mineralogy. Particular attention is paid to the derived elastic properties and their dependence on porosity and kerogen. The elastic moduli generally decrease with increasing porosity and kerogen, and there is a critical porosity （0.75） and kerogen content （ca. ≤3%） over which the elastic moduli decrease rapidly and slowly, respectively. The derived elastic moduli of gas- and oil-saturated digital cores differ little probably because of the low porosity （4.5%） of the Longmaxi black shale. Clearly, the numerical experiments demonstrated the feasibility of combining microstructure images of shale samples with elastic moduli calculations to predict shale properties.

Modeling time-dependent mechanical behavior of hard rock considering excavation-induced damage and complex 3D stress states

To investigate the long-term stability of deep rocks,a three-dimensional(3D)time-dependent model that accounts for excavation-induced damage and complex stress state is developed.This model comprises three main components:a 3D viscoplastic isotropic constitutive relation that considers excavation damage and complex stress state,a quantitative relationship between critical irreversible deformation and complex stress state,and evolution characteristics of strength parameters.The proposed model is implemented in a self-developed numerical code,i.e.CASRock.The reliability of the model is validated through experiments.It is indicated that the time-dependent fracturing potential index(xTFPI)at a given time during the attenuation creep stage shows a negative correlation with the extent of excavationinduced damage.The time-dependent fracturing process of rock demonstrates a distinct interval effect of the intermediate principal stress,thereby highlighting the 3D stress-dependent characteristic of the model.Finally,the influence of excavation-induced damage and intermediate principal stress on the time-dependent fracturing characteristics of the surrounding rocks around the tunnel is discussed.

SAR regional all-azimuth observation orbit design for target 3D reconstruction

Three-dimensional(3D) synthetic aperture radar(SAR)extends the conventional 2D images into 3D features by several acquisitions in different aspects. Compared with 3D techniques via multiple observations in elevation, e.g. SAR interferometry(InSAR) and SAR tomography(TomoSAR), holographic SAR can retrieve 3D structure by observations in azimuth. This paper focuses on designing a novel type of orbit to achieve SAR regional all-azimuth observation(AAO) for embedded targets detection and holographic 3D reconstruction. The ground tracks of the AAO orbit separate the earth surface into grids. Target in these grids can be accessed with an azimuth angle span of360°, which is similar to the flight path of airborne circular SAR(CSAR). Inspired from the successive coverage orbits of optical sensors, several optimizations are made in the proposed method to ensure favorable grazing angles, the performance of 3D reconstruction, and long-term supervision for SAR sensors. Simulation experiments show the regional AAO can be completed within five hours. In addition, a second AAO of the same area can be duplicated in two days. Finally, an airborne SAR data process result is presented to illustrate the significance of AAO in 3D reconstruction.

3D DEM simulation of hard rock fracture in deep tunnel excavation induced by changes in principal stress magnitude and orientation

To achieve the loading of the stress path of hard rock,the spherical discrete element model(DEM)and the new flexible membrane technology were utilized to realize the transient loading of three principal stresses with arbitrary magnitudes and orientations.Furthermore,based on the deep tunnel of China Jinping Underground Laboratory II(CJPL-II),the deformation and fracture evolution characteristics of deep hard rock induced by excavation stress path were analyzed,and the mechanisms of transient loading-unloading and stress rotation-induced fractures were revealed from a mesoscopic perspective.The results indicated that the stressestrain curve exhibits different trends and degrees of sudden changes when subjected to transient changes in principal stress,accompanied by sudden changes in strain rate.Stress rotation induces spatially directional deformation,resulting in fractures of different degrees and orientations,and increasing the degree of deformation anisotropy.The correlation between the degree of induced fracture and the unloading magnitude of minimum principal stress,as well as its initial level is significant and positive.The process of mechanical response during transient unloading exhibits clear nonlinearity and directivity.After transient unloading,both the minimum principal stress and minimum principal strain rate decrease sharply and then tend to stabilize.This occurs from the edge to the interior and from the direction of the minimum principal stress to the direction of the maximum principal stress on theε1-ε3 plane.Transient unloading will induce a tensile stress wave.The ability to induce fractures due to changes in principal stress magnitude,orientation and rotation paths gradually increases.The analysis indicates a positive correlation between the abrupt change amplitude of strain rate and the maximum unloading magnitude,which is determined by the magnitude and rotation of principal stress.A high tensile strain rate is more likely to induce fractures under low minimum principal stress.

Shear behavior of intact granite under thermo-mechanical coupling and three-dimensional morphology of shear-formed fractures

The shear failure of intact rock under thermo-mechanical(TM)coupling conditions is common,such as in enhanced geothermal mining and deep mine construction.Under the effect of a continuous engineering disturbance,shear-formed fractures are prone to secondary instability,posing a severe threat to deep engineering.Although numerous studies regarding three-dimensional(3D)morphologies of fracture surfaces have been conducted,the understanding of shear-formed fractures under TM coupling conditions is limited.In this study,direct shear tests of intact granite under various TM coupling conditions were conducted,followed by 3D laser scanning tests of shear-formed fractures.Test results demonstrated that the peak shear strength of intact granite is positively correlated with the normal stress,whereas it is negatively correlated with the temperature.The internal friction angle and cohesion of intact granite significantly decrease with an increase in the temperature.The anisotropy,roughness value,and height of the asperities on the fracture surfaces are reduced as the normal stress increases,whereas their variation trends are the opposite as the temperature increases.The macroscopic failure mode of intact granite under TM coupling conditions is dominated by mixed tensileeshear and shear failures.As the normal stress increases,intragranular fractures are developed ranging from a local to a global distribution,and the macroscopic failure mode of intact granite changes from mixed tensileeshear to shear failure.Finally,3D morphological characteristics of the asperities on the shear-formed fracture surfaces were analyzed,and a quadrangular pyramid conceptual model representing these asperities was proposed and sufficiently verified.

Investigation of long-wavelength elastic wave propagation through wet bentonite-filled rock joints

The saturation of the compacted bentonite buffer in the deep geological repository can cause bentonite swelling,intrusion into rock fractures,and erosion.Inevitably,erosion and subsequent bentonite mass loss due to groundwater inflow can aggravate the overall integrity of the engineered barrier system.Therefore,the coupled hydro-mechanical interaction between the buffer and rock during groundwater inflow and bentonite intrusion should be evaluated to guarantee the long-term safety of deep geological disposal.This study investigated the effect of bentonite erosion and intrusion on the elastic wave propagation characteristics in jointed rocks using a quasi-static resonant column test.Jointed rock specimens with different joint conditions(i.e.joint surface saturation and bentonite filling)were prepared using granite rock discs sampled from the Korea Underground Research Tunnel(KURT)and Gyeongju bentonite.The long-wavelength longitudinal and shear wave velocities were measured under different normal stress levels.A Hertzian-type power model was used to fit the wave velocities,and the relationship between the two fitted parameters provided the trend of joint conditions.Numerical simulations using three-dimensional distinct element code(3DEC)were conducted to better understand how the long-wavelength wave propagates through wet bentonite-filled rock joints.

Three-dimensional mixed convection stagnation-point fow past a vertical surface with second-order slip velocity

This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.Interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.

ELASTIC BEHAVIOR ANALYSIS OF 3D ANGLE-INTERLOCK WOVEN CERAMIC COMPOSITES

A micromechanical model for elastic behavior analysis of angle-interlock woven ceramic composites is proposed in this paper. This model takes into account the actual fabric structure by considering the fiber undulation and continuity in space, the cavities between adjacent yarns and the actual cross-section geometry of the yarn. Based on the laminate theory, the elastic properties of 3D angle-interlock woven ceramic composites are predicted. Different numbers of interlaced wefts have almost the same elastic moduli. The thickness of ceramic matrix has little effect on elastic moduli. When the undulation ratio increases longitudinal modulus decreases and the other Young＇s moduli increase. Good agreement between theoretical predictions and experimental results demonstrates the feasibility of the proposed model in analyzing the elastic properties of 3D angle-interlock woven ceramic composites. The results of this paper verify the fact that the method of analyzing polyester matrix composites is suitable for woven ceramic composites.

3D elastic waveform modeling with an optimized equivalent staggered-grid finite-difference method

Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and inversion.Traditionally,the Taylor series expansion is often applied to calculate finite-difference(FD) coefficients on spatial derivatives,but the simulation results suffer serious numerical dispersion on a large frequency zone.We develop an optimized equivalent staggered-grid(OESG) FD method that can simultaneously suppress temporal and spatial dispersion for solving the second-order system of the 3 D elastic wave equation.On the one hand,we consider the coupling relations between wave speeds and spatial derivatives in the elastic wave equation and give three sets of FD coefficients with respect to the P-wave,S-wave,and converted-wave(C-wave) terms.On the other hand,a novel plane wave solution for the 3 D elastic wave equation is derived from the matrix decomposition method to construct the time-space dispersion relations.FD coefficients of the OESG method can be acquired by solving the new dispersion equations based on the Newton iteration method.Finally,we construct a new objective function to analyze P-wave,S-wave,and C-wave dispersion concerning frequencies.The dispersion analyses show that the presented method produces less modeling errors than the traditional ESG method.The synthetic examples demonstrate the effectiveness and superiority of the presented method.

Three-dimensional gravity inversion based on 3D U-Net++

The gravity inversion is to restore genetic density distribution of the underground target to be explored for explaining the internal structure and distribution of the Earth.In this paper,we propose a new 3D gravity inversion method based on 3D U-Net++.Compared with two-dimensional gravity inversion,three-dimensional(3D)gravity inversion can more precisely describe the density distribution of underground space.However,conventional 3D gravity inversion method input is two-dimensional,the input and output of the network proposed in our method are three-dimensional.In the training stage,we design a large number of diversifi ed simulation model-data pairs by using the random walk method to improve the generalization ability of the network.In the test phase,we verify the network performance by using the model-data pairs generated by the simulation.To further illustrate the eff ectiveness of the algorithm,we apply the method to the inversion of the San Nicolas mining area,and the inversion results are basically consistent with the borehole measurement results.Moreover,the results of the 3D U-Net++inversion and the 3D U-Net inversion are compared.The density models of the 3D U-Net++inversion have higher resolution,more concentrated inversion results,and a clearer boundary of the density model.

A Three-Dimensional (3D) Environment to Maintain the Integrity of Mouse Testicular Can Cause the Occurrence of Meiosis

Adhesions between different cells and extracellular matrix have been studied extensively in vitro, but little is known about their functions in testicular tissue counterparts. Spermatogonia and their companion somatic cells maintain a close association throughout spermatogenesis and this association is necessary for normal spermatogenesis. In order to keep the relative integrity of the testicular tissues, and to detect the development in vitro, culture testicular tissues in a three- dimensional （3D） agarose matrix was examined. Testicular tissues isolated from 6.5 d postpartum （dpp） mouse were cultured on the top of the matrix for 26 d with a medium height up to 4/5 of the 3D agarose matrix. The results showed that in this 3D culture environment, each type of testicular cells kept the same structure, localization and function as in vivo and might be more biologically relevant to living organisms. After culture, germ cell marker VASA and meiosis markers DAZL and SCP3 showed typical positive analysed by immunofluorescence staining and RT-PCR. It demonstrated that this 3D culture system was able to maintain the number of germ cells and promote the meiosis initiation of male germ cells.

A COMPUTER CODE FASTOR-3D FOR TRANSIENT THREE-DIMENSIONAL SIMULATION ON FLOW AND HEAT TRANS-FER WITH POROSITY APPROXIMATION

Upon the conservation of mass, momentum and energy, volume fraction and surface penetrative rate were employed to modify the conservative equations to simulate the effect of blockages on fluid flows and heat transfer. These equations were solved numerically with the finite differential method and the primitive variable approach. This method uses staggered grid and pressure correction schemes. A computer code FASTOR3D integrated the aforementioned algorithm. The preliminary results have been compared with conventional benchmark solutions. With auxiliary software DV, the numerical results were visualized in colorful images to demonstrate the variation of flow patterns and temperature profiles during the transient process. The results of the simulation code for the fluid flows and heat transfer in the sodium pool of a fast breeder reactor are acceptable.

Elastic Modulus Prediction of Three-dimension-4 Directional Braided C_f/SiC Composite Based on Double-scale Model

Double-scale model for three-dimension-4 directional（3D-4d） braided C/SiC composites has been proposed to investigate its elastic properties. The double-scale model involves micro-scale that takes fiber/ matrix/porosity in fibers tows into consideration with unit cell which considers the 3D-4d braiding structure. Micro-optical photographs of composites have been taken to study the braided structure. Then a parameterized finite element model that reflects the structure of 3D-4d braided composites is proposed. Double-scale elastic modulus prediction model is developed to predict the elastic properties of 3D-4d braided C/SiC composites. Stiffness and eompliance-averaging method and energy method are adopted to predict the elastic properties of composites. Static-tension experiments have been conducted to investigate the elastic modulus of 3D-4d braided C/SiC composites. Finally, the effect of micro-porosity in fibers tows on the elastic modulus of 3D-4d braided C/SiC composites has been studied. According to the conclusion of this thesis, elastic modulus predicted by energy method and stiffness-averaging method both find good agreement with the experimental values, when taking the micro-porosity in fibers tows into consideration. Differences between the theoretical and experimental values become smaller.