Taking into account the possibilities offered by two imaging methods, X-ray microcomputed tomography (µCT) and two-dimensional optical scanning, this article discusses the possibility of using these methods to assess the internal structure of spun concrete, particularly its composition after hardening. To demonstrate the performance of the approach based on imaging, laboratory techniques based on physical and chemical methods were used as verification. Comparison of obtained results of applied research methods was carried out on samples of spun concrete, characterized by a layered structure of the annular cross-section. Samples were taken from the power pole E10.5/6c  made by one of the Polish manufacturers of prestressed concrete E-poles precast in steel molds. The validation shows that optical scanning followed by appropriate image analysis is an effective method for evaluation of the spun concrete internal structure. In addition, such analysis can significantly complement the results of laboratory methods used so far. In a fairly simple way, through the porosity image, it can reveal improperly selected parameters of concrete spinning such as speed and time, and, through the distribution of cement content in the cross-section of the element, it can indicate compliance with the requirement for corrosion durability of spun concrete. The research methodology presented in the paper can be used to improve the production process of poles made of spun concrete; it can be an effective tool for verifying concrete structure. Concrete centrifugation is the process of forming and compacting concrete mix due to the normal  force generated during the spinning of the mold around its longitudinal axis at a speed of 500–700 rpm. Due to its specificity, this method is applicable only to hollow elements. As a result of the centrifugation process, concrete with a heterogeneous and layered structure is obtained ,2,3. ThuOne of the first to describe the structure of spun concrete used in pipe production was Marquardt . Based oIn , KuranovKliukas, Jaras, and Lukoševičienė in  found th3), amount of plasticizer (0–2%), spinning speed (400–700 rpm), and its time (5–11 min). Computer image analysis allowed for graphical representation of the aggregate, cement matrix, and air-void distribution as a function of the wall thickness in individual samples. It was found that the volume fraction of aggregate decreases from the outside of the centrifuged sample to the inside, while the cement matrix content changes in the opposite direction . The air content in the cross-section of the wall was higher for internal rather than external layers. Segregation of components was found in all tested samples.Adesiyun et al. ,8,9 usedVölgyi et al. ,11 foundThis paper focuses on methods of assessing the internal structure of spun concrete, which can be used in practice to verify the selection of spinning parameters. In the first part of the work, standard methods for determining the composition of hardened concrete were used to assess its variability across the element wall. Next, based on preliminary results presented in , imagingL = 10.5 m. The annular shape of the cross-section resulted from the adopted technology of manufacturing poles by the method of concrete centrifugation in longitudinally unopenable steel mold . Th. Th2CO3 2O and CO2) was determined on the basis of calcining losses. The samples were prepared according to the procedure for determining the aggregate content in concrete; they were additionally ground on a 0.06-mm sieve. Calcining losses were determined in an oxidizing atmosphere, while the samples were heated in the air at 950 °C until a constant sample mass was obtained. The constant mass was determined by successive heating for 15 min, followed by cooling and weighing. The percentage calcining loss was determined by the following formula:om is the the mass of the sample tested, and calm is the the mass of the calcined sample. The obtained value of attC,% was converted to the content of attached ingredients expressed in kg/m3 according to the following formula:cemC was calculated from the following condition:The content of compounds attached to cement during the setting and hardening of concrete , was determined using the Le Chatelier flask method [cρ and crρ, total porosity was calculated asp,opϕ was estimated based on water absorption wn as follows:The density of concrete k method . On the obtaining an image;segmentation of the component under consideration;morphometric analysis.Research on the morphology of the spun concrete microstructure was divided into two parts due to the method of image acquisition: flat optical scanning and three-dimensional (3D) imaging in X-ray microcomputed tomography (µCT). Regardless of the method of obtaining the image, the analysis is aimed at characterizing selected morphology measures of the considered microstructure components: pores, aggregate, and cement matrix. In both cases, the following stages of research can be distinguished:R in the radial direction (perpendicular to the axis of rotation of the spun concrete element). Coordinate R increases from R = 0 on the outer edge of the element toward the center of the cross-section in accordance with In the conducted analyses, it was assumed that, due to the axial symmetry of the spun elements, the properties of the obtained material do not depend on the angular coordinate. Thus, at a fixed pole height , the parameters of the microstructure change only along the radius. The identified values were, therefore, referred to coordinate The mathematical morphology methods were used to describe the distribution of concrete components  over the wall of the spun column. The theoretical foundations for these tools, based mainly on works ,22,23, wR, a series of image subareas was selected, which are narrow circumferential bands of the concrete pole wall. The volume fraction ϕ(R) (dependent on coordinate R) is calculated in the band with the center line corresponding to coordinate R and the width ΔR. The method of selecting the aforementioned band is shown in On the basis of the analyses carried out, selected morphological statistical measures were determined: component volume fraction and so-called local thickness. The average volume fraction of the selected component is defined as the number of pixels in the component divided by the total number of pixels (in a selected area of the image). To describe the variability of the volume of the component as a function of x is defined as the largest diameter of the circle, which entirely fits within the constituent under consideration and, at the same time, contains point x in its interior. This is schematically illustrated in Local structure thickness is a scalar field, defined only in the area occupied by the considered constituent. The procedure for determining the local element thickness generally consists of filling the area occupied by the considered constituent with circles of the largest possible diameter . Then, tR), a procedure analogous to that for the volume fraction was used; specifically, the average in the appropriate circumferential band was determined as in The calculations are performed first for the entire image, resulting in a map of the local thickness of the constituent under consideration. Then, to describe the variation of local thickness as a function of the wall thickness of the concrete element , after etching it with acid, allowed quantifying the morphology of the following components: air voids (macro-pores), cement matrix, and aggregate. Thus, the scope of analyses was expanded compared to the analysis presented in , where oThe first stage of sample preparation for scanning was to level the cut surface in such a way that it was as flat, even, and smooth as possible. For this purpose, a Struers LaboPol 5 grinding and polishing machine with an MD Piano grinding disc was used. The result of the optical scan of the surface of the test sample prepared in this way (before staining) is shown in The pores were stained green by applying acrylic ink to the entire surface of the sample, which was then ground again. After this procedure, the sample was rescanned Then, after etching the matrix with hydrochloric acid, it was stained yellow . The metTo enable comparison of scans at individual stages of staining, all images were superimposed and matched to each other by appropriate rotation and shift. The pictures presented below show already “matching” images, for which the dimensions in pixels are the same and the position of the analyzed sample is the same. To exclude the background from the analysis, as well as inadequately polished fragments, edges jagged during cutting, and reinforcing bars, further analysis focused on the area of the image showing the correctly prepared surface of the concrete sample. This area is called the region of interest (ROI). The complement of ROI was not included in the analysis. For this part of the image, a white mask was applied. The image of the stained sample, limited by the aforementioned mask to ROI, is presented in R are presented for the consideration sample in R . The examination consisted of acquiring a series of X-ray projections, followed by the reconstruction of 3D image of the tested sample. The scanning parameters used are shown in Image reconstructions were made using the NRecon program based on the Feldkamp algorithm . The setThe reconstructed structure of the tested sample is shown in R is shown in R was determined in a manner analogous to that used in 2D analyses. This time, however, subsequent layers  of the 3D image were treated as circumferential bands.The first stage of the analysis was pore segmentation using the threshold method preceded by the use of a smoothing filter. The spatial morphology of the pores extracted in this way is shown in the perspective view in In general, all three methods used in the study allow determining porosity. The undoubted advantage of methods based on image analysis is the possibility of obtaining a virtually continuous function of porosity distribution, which in qualitative assessment (whether porosity changes as a function of the element thickness and what is the course of this variability) is very important. In addition, these methods make it possible to evaluate the morphology of pore space, in particular, to determine quantities such as pore width see  or shapeComparison of the results obtained with all of the methods used is only possible for average values in arbitrarily separated (four) layers of the wall of a spun pole, which corresponds to the division used in laboratory tests. For the results of optical scanning and tomography, the means were calculated on the basis of predetermined porosity distributions as a function of the wall thickness and referred to four layers equal in thickness. The average values of macroporosity in the layers calculated in this way are represented by blue lines in the graphs in Due to the differences in the research methodology, it is difficult to unequivocally compare the values or mutually verify the results of laboratory and image-based tests, as different types of porosity were determined. Of course, certain constraints should be met, e.g., both macroporosity and microporosity should be less than total porosity. This condition was met.The comparison of macroporosity results obtained from optical scanning and tomography led to unexpected conclusions. Better resolution used in tomography  would suggest the possibility of extracting some portion of small pores, which cannot be observed by the second method with worse resolution. Then, the porosity of the tested sample should be lower in the case of optical scanning, in which the inferior resolution was used . The precapillary porosity (open) is basically constant in all layers and its value is around 10%;total porosity is significantly higher only in layer 3 (by approximately 20%) compared to the other layers, where the value of total porosity is between 16% and 17%;structural macroporosity (as can be seen from both imaging methods used) shows the largest relative differences between individual layers and is even several times smaller in the middle part  compared to the other layers.With regard to the assessment of porosity of the analyzed sample, thanks to the combined use of laboratory methods and imaging, the following findings were obtained:aggC is the aggregate content (kg/m3), aggϕ is the volume of aggregate, and aggρ is the specific density of aggregate.The aggregate content was determined using two methods: in laboratory tests and on the basis of plain optical scanning. General comments on the possibilities of the research techniques used are very similar to those given in aggρ in individual layers. Unfortunately, this value was not explicitly determined as part of the research. Therefore, two approaches were taken to estimate this value. In the first approach (*), a constant value equal to the average density of the aggregate used for the mixture was assumed, i.e., aggρ = 2710 kg/m3; thus, its segregation  due to centrifugation was not taken into account. In the second approach (**), it was assumed that the specific density of all solid particles is a sufficiently accurate estimation of aggregate density, i.e., aggρ ≈ crρ. This approach takes into account the variability due to centrifugation, and the estimation error should not be large, because aggregate represents the vast majority of the weight of the solids in the concrete mix ; moreover, cement density is similar to aggregate density. Finally, regardless of the adopted estimation, good compliance of laboratory test results and imaging was obtained (To apply Equation (11), it is necessary to know the specific density of aggregate obtained . Relativaggϕ was determined intrinsically. Calculation of mass content in this case required additional data, which could be determined from the recipe for the mixture and physical characteristics of its components, or even on the basis of laboratory test results. However, the obtained compliance indicates that the results of both methods are consistent; the aggregate morphology determined from scanning corresponds to the average values of its content from tests based on physicochemical methods. The results of both test methods used can be considered complementary; they can be used together to analyze spun concrete structure. In particular, thanks to the use of known relationships ), by creating an appropriate correlation, the image analysis can be used to “extend” point information (in layers) to a continuous functional distribution as a function of the wall thickness.While analyzing the results in The content of coarse aggregate decreases toward the inner cross-sectional area. The last inner layer is marked by almost zero aggregate content . It is icemC (kg/m3) was referred to, because the requirements for the minimum value of this parameter are provided by the standard [matϕ is the volume share of cement matrix (including capillary micropores) according to the estimation made on the basis of optical scanning, µp,matϕ is the cement matrix microporosity, and C* is the mass of cement used per volume unit of solid parts of hardened cement matrix (including nonevaporable gel water); according to the relationships given in [C* = 1473 kg/m3 was assumed.From the optical scan, the volume fraction of the cement matrix can be determined. Similarly to the analysis of other concrete components, it is possible to assess the variability of the matrix volume fraction as a function of the wall thickness see . The labstandard . Cement given in , C* = 14µp,matϕ can be estimated from the following inequalities:p,totϕ is the total porosity (from the laboratory test), p,mϕ is the macroporosity , matϕ is the volume fraction of cement matrix, and aggϕ is the volume fraction of the aggregate.In The specified ranges in The conclusion concerning the applied research methodology is similar to the previous analyses. The results are comparable and consistent; they complement each other. Imaging naturally results in geometrical relationships, i.e., a description of the cement matrix morphology, which is important information from the point of view of determining the effective parameters of concrete as composite using micromechanics tools or the theory of homogenization ,32,33,34The description of the cement distribution as a function of the wall thickness of the cross-section obtained by means of both methods allows for straightforward qualitative description of this distribution. Optical scanning allowed determining the volume fraction of the cement matrix , with th3  increases  comparedThe aim of the article was to compare different methods for determining porosity, as well as cement and aggregate content, in the layered structure of spun concrete. The variability of these parameters considered as a function of the thickness of the concrete wall determines the macroscopic properties such as durability, load capacity, and rigidity of spun concrete poles. The article compares the results obtained using two methodologically different approaches: laboratory determinations based on chemical and/or physical methods and image analysis. In general, mass content per unit volume is obtained in laboratory tests, and the volume fraction of individual concrete components is obtained using image analysis methods. If the specific density of the component under consideration is known, conversion of one quantity to another becomes easy.The main advantage of the methods based on image analysis is the possibility of obtaining a practically continuous function of the content of the considered concrete components as a function of the wall thickness of a spun pole. In this context, the main limitation of chemical/physical methods is the ability to determine only the average value for a few, arbitrarily separated layers of the concrete wall of a spun pole. In turn, the main limitation of image analysis methods is the pixel/voxel size and image quality, particularly due to sample preparation and image acquisition method.In terms of concrete porosity, it should be stated that the attempt to validate the results obtained from imaging the structure of concrete using laboratory techniques  was only partially successful. The results obtained cannot be directly compared due to the fact that porosities are described on different scales. The methods based on image analysis allowed describing the structural porosity  of concrete, while the laboratory methods enabled describing total and open porosity (capillary microporosity). Quite importantly, imaging methods give the opportunity to analyze the macropore morphology. In particular, it was possible to visualize the location of air voids in relation to the other concrete components , which maggϕ. Calculation of aggregate mass content per unit volume in this case required additional information about the density of the aggregate, which could be determined either from the recipe for the concrete mixture and the physical characteristics of its components or from laboratory tests. The obtained consistency of the results from both methods shows that the methods are consistent, and the aggregate morphology determined by scanning corresponds to the average values of its content coming from research based on physicochemical methods.In terms of the description of aggregate distribution as a function of the wall thickness of the cross-section, very good compatibility of both methods was obtained. The image analysis method allowed determining the volume fraction of aggregate Very good qualitative and quantitative compatibility of both methods in the field of aggregate morphology as a function of the wall thickness of the element was obtained. Thanks to the positive validation of laboratory methods and the method based on image analysis, it can be safely stated that optical scanning is a cheap, relatively fast, and effective method of assessing aggregate segregation as a function of the wall thickness of a spun concrete element.The description of cement distribution as a function of the wall thickness of the element cross-section obtained using both methods allows for straightforward qualitative description of this distribution. However, full validation success was not achieved because the results based on optical scanning allow obtaining quantitative results only after taking into account additional calculations and information from laboratory tests. Thus, in this case, to get full information about the distribution of cement as a function of the wall thickness of the element, both methods must complement each other. Nevertheless, the information obtained as a result of testing with any of methods used allows assessing the cement content, which determines the requirement for durability of columns made of spun concrete.An attempt to validate the imaging method with the use of laboratory techniques based on physical and chemical methods showed that optical scanning methods are relatively effective, and they can be a significant complement to the research methods used so far. The analyses also showed that there is a further need to conduct research in the area of spun concrete structure, with particular emphasis on the distribution of concrete porosity and cement content as a function of the wall thickness of the ring-shaped cross-section. The research methods presented in the work can be used to improve the production process of poles made of spun concrete as an effective tool for testing its structure.


Pinus tabuliformis saplings in northeastern China. A total of 49 regenerated saplings from shelterwood-cut strips and 30 from uncut strips were collected. Nonlinear quantile regression was used to develop the outermost crown profile model for the saplings from the shelterwood-cut and uncut strips. The quantile value suitable for describing the outermost crown profiles of the two types of strips was selected using nonparametric boundary regression. The difference in crown morphologies between the shelterwood-cut strips and uncut strips was compared. The results showed that with the same diameter at breast height, the crown radii of the uncut strip saplings were larger than those of the shelterwood-cut strip saplings within the range of 0.2–1.0 for the relative depth into the crown. The largest crown radius of the saplings from the uncut strips was larger than that of the saplings from the shelterwood-cut strips. The inflection points of the shelterwood-cut strip sapling crowns were larger than those of the uncut strip sapling crowns. The crown volume of the small uncut strip saplings was larger than that of the shelterwood-cut strip saplings, and the difference in crown volume decreased with increasing sapling size. The saplings in the early stage of the uncut strips showed a greater growth rate than those of the shelterwood-cut strips, but their growth rate slowed over the long term according to branch-length annual growth. The present study provides a reference for forest management strategy decision making in promoting natural regeneration.The study analysed the effect of shelterwood-cut strips on the outermost crown profiles and crown characteristics of naturally regenerated  Shelterwood-cut strips have generally been an effective method to establish adequate regeneration after harvesting given their natural conservation benefits and advantages in promoting sustainable forest management . With hiCrowns play an essential role in the productivity efficiency of individual trees since crowns serve as the location of photosynthesis, respiration and transpiration . The croThe crown profile is a suitable characteristic for reflecting the horizontal and vertical crown dimensions of an individual tree and is also useful for reflecting the crown morphology plasticity of saplings . HoweverThe parametric regression approach has been widely used in crown profile modelling . GeneralPinus tabuliformis performs well in terms of conserving water and soil and protecting the environment  to develop an outermost crown profile model for saplings from shelterwood-cut strips (sun-grown saplings) and uncut strips (shade-grown saplings) using nonlinear quantile regression, with nonparametric boundary regression being used to select the quantile value to model the outermost crown profiles of saplings, and (2) to compare the differences in the crown morphology plasticities of saplings including largest crown radius, inflection points, crown volume of upper crown and annual growth of branch length between the shelterwood-cut and uncut strips.ironment . PlantedThe research was conducted at Liaoning ecological and experimental farms located in the semiarid areas of the western part of Liaoning Province, northeastern China . The area has a continental monsoon climate in the northern temperate zone. The mean air temperature of this area is 8.3 °C, with a maximum temperature of 40.7 °C and minimal temperature of −26.4 °C with in a year. The mean annual precipitation ranges from 450 mm to 550 mm, with approximately 70% distributed within July and August. The elevation ranges from 200 m to 1074 m, and the frost-free period is usually 145–150 days. Brown forest soil is the main soil type in this area.Pinus tabuliformis plantation that is 45 years old that has a density of 1,035 trees per hectare in the Linghe experimental region of the Liaoning ecological and experimental farm. In the spring of 2014, the shelterwood-cut strip experiment was conducted. Part of the framework of the research is shown in Our study area is located in the mature At the end of the growing season in November 2017, a total of 50 saplings from the shelterwood-cut strip and 30 saplings from the uncut strip were selected. All the saplings were selected from the 2-m wide belts from the centre of the shelterwood-cut and uncut strips to ensure homogeneous conditions regarding light availability for the saplings from shelterwood-cut and uncut strips. For all saplings, the total tree height  was greater than 1.3 m, and the diameter at breast height (0.1 cm) was less than 5.0 cm. HT and DBH were measured before felling for all the sampled saplings .For the sampled saplings, the whorl containing at least one branch that was continuous to the former whorl was defined as the crown base, and the length from the sapling tip to the crown base was the crown length (CL). A straight line from the ground level to breast height was marked on the trunk to indicate the north side, which facilitated the determination of the azimuth of the branches, and the line was extended to the sapling tip after the saplings were carefully felled. After felling, the HTs of the saplings were remeasured. To facilitate the measurement, the saplings were divided into 1-m sections, while any section less than 1 m was considered a sapling tip. Each section was placed upright on the ground. For each branch from each whorl from every sapling, the vertical distance along the trunk from the branch base to the sapling tip (L) was measured first. Then, the branch diameter (BD), branch length (BL), branch chord length (BC), branch angle (VA) and azimuth, which denotes the angle deviated from the north side in the clockwise direction, were measured . To deteTo detect possible recording or measurement errors in the field work, a visual inspection of the crown profiles was carefully implemented for each sapling. One specific sapling from the shelterwood-cut strip with a DBH of 0.73 cm and a tree height of 1.4 m showed a strange profile and was considered biologically unreasonable. Thus, this sapling was removed from the data set, leaving 49 saplings from the shelterwood-cut strips with a total of 507 whorls and 1,398 branches for the analysis and modelling. For the 30 saplings from the uncut strips, a total of 363 whorls and 753 branches were harvested. The absolute depth into the crown radius of interest (DINC) was calculated as the difference between the distances from the sapling tip to the branch base and the projection of the branch onto the trunk. The relative depth into the crown radius of interest (RDINC) was calculated as RDINC = DINC/CL. The outermost crown radius (OCR) was calculated as the branch chord length multiplied by the sine value of the branch angle. The characteristics of the saplings and branches from the shelterwood-cut strips and uncut strips are shown in For the parametric regression approach, the models that perform well with other species when targeting crown profile, largest branch radius distribution and taper description of adult trees were selected as the candidate models. Due to the irregularity of the crown profiles for the saplings, the models used in the description of the crown profiles of the adult trees were reconstructed in the present study .Pinus sylvestris var. Mongolica plantation and was used in the present study  and root of mean square error (RMSE)   were useij is the outer crown radius of the jth branch from the ith sapling, jth branch from the ith sapling, M is the number of saplings, and in is the number of branches from the ith sapling.Nonlinear quantile regression with an interior point algorithm proposed by The estimation for the parameters of the specific quantile was implemented by the quantreg package of R software . In the ij is the outer crown radius of the jth branch from the ith sapling, f(·) is the nonlinear equation form, X represents the variables, θ represents the parameters, and εij is the error term.Pinus tabuliformis saplings from the shelterwood-cut and uncut strips. Nonparametric boundary regression with a polynomial frontier estimator was used to determine the specific quantile for the nonlinear quantile regression to model the outermost crown profiles. For the nonparametric boundary regression approach, the data pairs  where i indicates the number of branches per tree were used to characterise the branch tips. A single polynomial equation with a known degree parameter p was used to address the full observations as follows \doce ‘npbr’ .A set of quantile values ranging from 0.5 to 0.99 with an even interval of 0.01 was specified for the nonlinear quantile regression model. Nonparametric boundary regression was used to describe the outermost crown profiles for all the saplings from the shelterwood-cut strips and uncut strips. RDINC was divided into 10,000 intervals by an even interval of 0.0001. The crown radius of all the specified RDINCs was calculated for each sapling by a series of nonlinear quantile regression models and nonparametric boundary regression. The absolute distance between the two curves modelled by nonlinear quantile regression and nonparametric boundary regression for each sapling was calculated . The speThe outermost crown profile model developed by the nonlinear quantile regression approach was used to depict the crown morphology plasticity of the saplings from shelterwood-cut and uncut strips. The inflection points were calculated for each sapling. The difference in the inflection points of the saplings from shelterwood-cut strips and uncut strips was compared. The crown volume for the upper crown was calculated by a rotational integral using the predicted outermost crown profile curves. The crown morphology plasticity, including the largest crown radius, inflection points, and annual growth of branch length of the two types of saplings, was also compared.Radj2 and RMSE were used to compare different models, and the best model was selected for each basic equation, as shown in All parameters of the power-exponential equation and Kozak equation  were repa1, a2, and a3 were reparameterized by introducing easily measured sapling variables. The final model form is shown in For the power-exponential equation, a1–a5 are the parameters to be estimated, and the other variables are defined as those above.c1–c5 are the parameters to be estimated, and the other variables were defined as those above.For the Kozak equation, we further modified the basic equation to fit the crown profiles of the saplings, and it is shown as follows :(10)\doRadj2 for the power-exponential equation and the modified Kozak equation with only DBH and CR as independent variables was 0.62. The power-exponential equation was much more flexible in describing the outermost crown radius and was thus selected as the best model to describe the outermost crown profiles for the Pinus tabuliformis saplings.Parameter estimates and goodness-of-fit statistics for Pinus tabuliformis saplings. The nonlinear quantile regression models were developed for a set of quantile values from 0.5 to 0.99 with an even interval of 0.01 for the saplings from the shelterwood-cut strip and uncut strip. All sapling branches from the shelterwood-cut strip and uncut strip were used to estimate the model parameters. The estimates of the parameters for the 0.75, 0.85, 0.95, and 0.99 quantiles of the shelterwood-cut and uncut strips are shown in The power-exponential equation was used as the basic equation to model the outermost crown profiles for the The results indicated that the crown curves based on the nonlinear quantile regression with the same quantile value for the saplings from shelterwood-cut and uncut strips were different in terms of parameter estimates. The distances between the predicted crown profiles from the nonlinear quantile regression with crown quantiles from 0.50 to 0.99 with aneven interval of 0.01 and the fitted outermost crown profiles by nonparametric boundary regression were calculated for all saplings. For the shelterwood-cut strip saplings, the nonlinear quantile regression crown profile model with the quantile of 0.88 had the smallest distance with the nonparametric boundary regression approach. For the uncut strip saplings, the smallest distance was in the 0.92 quantile. The estimates for the two nonlinear quantile regression models for the outermost crown profilesare shown in With the nonparametric boundary regression, the nonlinear quantile regression was powerful and suitable in describing and predicting the outermost crown profile for the individual saplings from both the shelterwood-cut  and uncuThe relationship between the characteristics of the saplings and crown regularity was compared between the shelterwood-cut strip and uncut strip saplings. The CR was fixed at 0.80, approximately the mean CR value of our sampled saplings, and the relationship between the crown radius and DBH for the two strip types was analysed  and 5B. The crown characteristics of the saplings from shelterwood-cut strips and uncut strips were analysed. For the largest crown radius, saplings from the uncut strips were larger than those of the saplings from the shelterwood-cut strips when the saplings from the two strips were the same size  and 5B. p > 0.05). After 2015, the growth rate of the shelterwood-cut strip saplings increased and was significantly larger than that of the uncut strip saplings (p < 0.05).The annual growth of branch lengths for the saplings from the shelterwood-cut strips and uncut strips were analysed and compared, as shown in Shelterwood-cut strips are an effective method for developing adequate natural regeneration . GeneralGenerally, in comparison to sun-grown saplings, shade-grown saplings invest more in lateral growth to capture more light because light is the limiting factor. In contrast to shade-grown saplings, sun-grown saplings invest more in height growth than in lateral expansion because competition is the main limiting factor . For shaThe inflection points for the shelterwood-cut strip saplings were larger than those of the uncut strip saplings. The combination of the largest crown radius and inflection point determined the difference in the crown morphology of the saplings from the shelterwood-cut strips and uncut strips. This was the reason why the crown morphology of the uncut strip saplings was flatter, and the crown morphology of the shelterwood-cut strip saplings was similar to a parabola. The growth rate of the saplings was an essential factor affecting the crown morphology . TherefoThe effect of DBH and CR on the outermost crown profiles of the saplings from the two types of strips was different. We found that DBH had a significant effect on the outermost crown profiles of both the shelterwood-cut and uncut strip saplings. However, the CR significantly affected only the shelterwood-cut strip saplings but not the uncut strip saplings. This result indicated that non-functional branches would not affect the growth of saplings from the uncut strip. This process is important to the management of natural regeneration.Pinus tabuliformis saplings to develop effective management strategies to improve the growth of Pinus tabuliformis saplings in the understory. However, the sampled saplings in the present study came from only one location and the accuracy and generality of the results may be limited to some extent. In addition, a full light control was also meaningful to further analyse the effect of strip shelterwood-cuts on the crown morphology plasticity of the saplings and it was also not considered in the present study. In the next step, we will further add the quantitative light measurement and full light control in our experiment and enlarge the study area to make our results more generalised.Some studies have shown that light-demanding tree species are able to grow in a shaded understory, although at a slow rate . We alsoPinus tabuliformis from shelterwood-cut strips and uncut strips was analysed and compared in northeastern China. Nonlinear quantile regression modelled the outermost crown profiles of the saplings from both the shelterwood-cut and uncut strips well. DBH affected the outermost crown profiles of the saplings from the shelterwood-cut and uncut strips. In contrast, CR affected the outermost crown profiles of the saplings from the shelterwood-cut strips but not from the uncut strips. The saplings from shelterwood-cut strips generally had the smaller largest crown radius and larger inflection point than those from the uncut strips. The crown volume of the small uncut strip saplings was larger than that of the shelterwood-cut strip saplings of the same size, and the volume decreased with increasing sapling size. The saplings from the uncut strips tended to maintain a flat crown shape to intercept more light for the small saplings. With increasing sapling size, the sapling from the uncut strips tended to grow more slowly due to severely limited light interception.Crown morphology plasticity of the naturally regenerating saplings of 10.7717/peerj.9826/supp-1Supplemental Information 1A total of 49 and 30 saplings from clear-cut and uncut strip were provided. The sapling sample branch was selected from each whorl of each saplings were measured for the annual branch length.Click here for additional data file.


In high humidity areas, it is necessary to improve the impermeability of concrete to water and other erosion solutions. The internal defect and pore channel of concrete are the main factors affecting the impermeability and durability. In this paper, a novel hydrophobic agent named Yellow River Engineering Consulting (YREC) was prepared. The relative internal defect degree of concrete with different curing ages and YREC contents was evaluated by ultrasonic non-destructive testing as qualitative characterization method, and the effect of YREC on hydration reaction was investigates using X-ray powder diffraction (XRD). Water permeability and contact angle tests were used to analyze the internal and external hydrophobicity induced by YREC addition, respectively. The pore structure changes of concrete mortar matrix induced by YREC were further discussed applying low-temperature liquid nitrogen adsorption (LT-NA) and mercury intrusion/extrusion porosimetry (MIP). The results indicated that YREC not only improves the impermeability of water, but also greatly enhances the mechanical strength. In the case of mixing YREC, the porosity of concrete mortar matrix decreases accompanied with the more advantage pores (micropores and transition pores) developed. Based on the relative internal defect degree and the changes of multi-scale pore structure, the functionality and durability of concrete with 4% YREC addition are the most desirable. The uaterials ,7. The paterials ,9,10,11.At present, some research foundation has been established to improve concrete durability by isolating concrete from external water through hydrophobic technology. The common method is surface coating that provides the concrete surface a protective layer, which can resist the intrusion of water . HydrophA better approach is to make concrete materials both internally and externally hydrophobic, and the hydrophobic admixture has been mixed in the concrete directly. Hartmut Herb et al.  optimizeIn the case of similar coarse aggregate properties, the mechanical properties of concrete materials are directly bound up with the microscopic characteristics  of the mortar matrix ,27,28,29In this study, the concrete materials with strong hydrophobicity are processed combining with low-heat Portland cement and hydrophobic admixture named Yellow River Engineering Consulting (YREC). The hydrophobic modification of concrete through addition of YREC is further analyzed. For the novel hydrophobic agent, the electron laser particle size analysis, scanning electron microscope (SEM) test, chemical composition analysis, and Fourier-transform infrared spectroscopy are used to investigate the properties comprehensively. Concrete specimens of different curing ages were prepared considering three kinds of content. The effect of YREC was evaluated from the four aspects of concrete: defect degree, strength, impermeability, and hydration products. The multi-scale pore structure changes of mortar matrix induced by YREC were further discussed using low-temperature liquid nitrogen adsorption (LT-NA) and MIP.2 and Al2O3, was dried in an oven at a temperature of 105 °C for 48 h. Next, the dried mica was ground in a mill and sieved using a negative pressure sieving method with a 2.5 μm thickness. Finally, a mixture composed of 98% mica, 1% silane coupling agent (KH550), and 1% polydimethylsiloxane (PDMS) by mass were added to a powder surface modification machine and processed at a temperature of 60 °C for 20 min. The specific preparation process was also introduced in our previous work [The hydrophobic admixture named YREC was selected to prepare the concrete specimens. YREC admixture is a kind of hydrophobic powder with flake inorganic material as the base material, which is processed by crushing, particle control and chemical modification. Mica powder as the substrate of YREC, comprised mainly of SiOous work ,39. Lase3 was adopted. Fine aggregate was obtained from machine sand, which had a fineness modulus of 2.78. The coarse aggregate was crushed basalt (4–20 mm), and the apparent density was 2780 kg/m3. The size of specimens is 100mm × 100mm × 100mm. The value of water-cement ratio is 0.50. The specimen without YREC was named L, and the specimens mixed with YREC were named LY, LY-2, LY-4, and LY-6 represented the 2%, 4%, and 6% YREC addition, respectively. Five different cueing ages were designed  with 95% relative humidity curing environment and a temperature of 20 °C. The mix proportions of all the concrete were listed in The cement material, P•LH 42.5 was obtained from the Huarun Company . Fly ash with the specific gravity of 2360 kg/mFor permeation test, the specimens at 7, 14, 28 and 90 days were carried on the HP.4.0 full-automatic concrete anti-permeability apparatus. The water pressure started from 0.1 MPa and increased by 0.1 MPa every 8 h . For concD was proposed to characterize the defects inside the concrete, which was expressed as: cD was the relative defect degree, tV was the wave velocity of concrete at t days (km/s), which satisfied t < 90, V90 was the wave velocity of concrete at 90 days (km/s).In a complete concrete structure, the sound wave has high amplitude. It will decay rapidly and directly affect directly the propagation speed of the wave when it encounters pores or cracks. This feature can be used to evaluate the defects of concrete. In addition, ultrasonic non-destructive test was carried out on 100 mm cubic specimens to evaluate the defect degree of concrete. The relative defect degree 2 adsorption/desorption. The mercury intrusion measurements were conducted using an AutoPore IV9500 Micrometrics Instrument . The mortar matrix specimens from L and LY groups were selected, and each particle size is between 5 and 10 mm at 28 days.LT-NA was carried on the ASAP 2020 physical adsorption device  at Tinghua University. Before LT-NA measurements, all particles were dried for 24 h at a constant temperature of 60 °C. The PSD of mortar matrix was obtained using the Barrett–Joyner–Halenda (BJH) model according to NV is the volume of adsorbed gas molecules at the equilibrium pressure P, V0 is Monolayer adsorption volume, P0 is the gas saturation pressure, α is the coefficient associated with a fractal value, δ is the y-intercept in the log-log plot. The log-log plots of ln(V/V0) vs. ln(ln(P0/P)) can be obtained from the LT-NA data [The advantages of fractal theory in surface analysis were first introduced in 1983 ,42. The -NA data ,45,46. TX-ray powder diffraction (XRD)  was used to test hydration product. The powder of cement paste from L, LY-2, LY-4, and LY-6 at 28 days was selected. The scanning range was 5–70°, and step size was 0.02°.The YREC particles mainly distributed around 90 μm. The particles less than 25 μm accounted for 10%, and the particles larger than 195 μm accounted for 10%. The dominant particles ranging from 25 to 195 μm accounted for 80%. The need for properly characterizing the microstructure of YREC will help in explaining the materials work and the interaction with concrete. The microstructure of YREC admixture using SEM is shown in −1. The functional groups corresponding to each wave peak are also shown in the FTIR spectrum was chosen to run an analysis on the functional groups of YREC. This technique is well known for its high sensitivity, accuracy, and reliability in analyzing materials . The FTISplitting tensile strength and compressive strength of concrete specimens in L and LY groups with 3, 7, 14, 28 and 90 curing days were shown in D decreased with curing days, which represents the improvement of the internal density of the concrete correspondingly. The relative defect degree of L was higher than that of LY, and the difference became smaller when the curing age reached 28 days, but LY specimens were still higher, which indicated that YREC improved the internal density obviously, especially at early times. The relative defect degree D of LY-4 was the lowest in the LY specimen.cD was closely related to the mechanical properties, the relationship considered the influence of YREC content and curing ages is further analyzed. The results are shown in Lts is the loss rate of splitting tensile strength (%), fts-t is the splitting tensile strength under t curing days (km/s), which satisfied t < 90, fts−90 is the splitting tensile strength with 90 curing days (MPa).Lc is the loss rate of compressive strength (%), fc−t is the compressive strength under t curing days (km/s), which satisfied t < 90, fc−90 is the compressive strength with 90 curing days (MPa).Since the relative defect degree cD met the exponential relationship with the loss rate of both splitting tensile strength and compressive strength, and the correlation coefficient R2 arranges from 0.09807 to 0.9991. It indicates that the characterization method of relative defect degree proposed in this paper is available to evaluate the mechanical properties of concrete. The loss rate of both splitting tensile strength and compressive strength could be obtained through these ultrasonic non-destructive test results, thus the long-term strength of concrete can be predicted based on the early strength, which was of great significance in engineering scale.It could be seen that the relative defect degree The MIP analyses are widely accepted to be capable to characterize a large scale of pore size, especially for macro-pores in the porous media. The porosities of L, LY-2, LY-4, and LY-6 were 18.20%, 16.08%, 14.13%, and 14.51%, respectively. The whole intrusion/extrusion processes of MIP show that there were different degrees of hysteresis loops in specimens, among which the hysteresis of L specimen was more serious than that of LY-2, LY-4 and LY-6 . It is g3/g. The addition of YREC has a filling effect and inhibited the generation of larger pores in the cement hydration process [2 adsorption was larger than that of the L sample.The isothermal adsorption/desorption curves of the four mortar matrix specimens are shown in  process ,47. The 0P/P)) = −0.50. It is necessary to point that the value at −0.50 corresponded to the pores with a diameter of about 5 nm [2 adsorption at low and high pressures respectively. Two fractal dimensions named D1 and D2 could be obtained by linear fitting of two parts of data. D1 corresponded to monolayer coverage in pores with the diameter less 5 nm, and D2 corresponded to multilayer coverage in the pores > 5 nm. The average fractal dimension (D) was obtained from linear regression of the whole pressure segment to evaluate the overall heterogeneity of pore structure. The values of D, D1, and D2 increased with the increasing addition of YREC, and the L sample with the minimum value indicates that the pore surface structure of LY samples were more complex than that of L sample  and the water permeability coefficient , C3S and Aft were well-developed in L and LY-2. The results once again showed that YREC promoted hydration. Moreover, the calcium hydroxide crystal (CH) of LY-4 developed better at 11.3° according to XRD patterns of L, LY-2, LY-4, and LY-6 at 28 days are shown in A method to improve the workability of concrete using YREC was explored. With this approach, the hydrophobicity, strength and compactness of the derived concrete were promoted. Several results are reached:The components of YREC and a large number of hydrophobic functional groups provided strong hydrophobicity. The structure of YREC particles is favorable for impermeability due to the complex and longer seepage path in concrete based on fractal analysis and hydrophobic tests.The defect degree of concrete can be deduced by YREC, and the splitting tensile strength and compressive strength were improved significantly due to the filling effect. The addition of 4% YREC is the most desirable method, which can promote the hydration reaction and further enhance the functionality of concrete.The porosity of the mortar matrix materials decreased with the addition of YREC, which inherently affected the diffusion of water. YREC can restrain the formation of harmful pores in concrete mortar matrix, which mainly decreased the pore volume with the pore size larger than 10 µm. Moreover, the more advantage pores (micropores and mesopores) developed in concrete mortar matrix with the addition of YREC.YREC can significantly improve the hydrophobicity of concrete materials. The next step is to study the properties of YREC in acidic environment or chlorine salt and sulfate environments. The application range of the material is desirable to further investigated.


To explore if medical exercise therapy (MET) alone is comparable to arthroscopic partial meniscectomy (APM) followed by MET for knee pain, activity level, and physical function in middle-aged patients with degenerative meniscal tear (DMT) by a systematic review and meta-analysis of randomized controlled trials (RCTs).A systematic search of electronic databases  was conducted to retrieve RCTs comparing MET+APM with MET alone for DMT. Risk of bias of the studies was evaluated. Outcomes assessed were pain relief, physical function, and activity level.p = 0.004) and at 6 months (p = 0.04). And there were statistically improvements in APM + MET at 6 months compared with MET alone when changing measurement to visual analog scale (VAS) (p = 0.0003). Our analysis also found small significant differences favor the APM followed by MET group for physical function both at 2 to 3 months  and at 6 months .A total of 6 RCTs containing 879 patients were included. After pooling the data of 5 researches, we found small significant differences support the APM + MET group for pain control assessed by Knee injury and Osteoarthritis Outcome Score (KOOS) at 2 to 3 months (We found favorable results of APM + MET up to 6 months for pain control and physical function. However, there were no differences at longer follow-up. The clinical applicability of APM + MET compared with MET should be interpreted carefully, and the potential of MET to treat DMT should be valued. The menisci of the knee  are wedge-shaped semilunar disks which are consisted of fibrocartilage interposed between the condyles of the femur and the tibia . MeniscaGreat many treatments about degenerative meniscus tears (DMT) have been tried. Currently, arthroscopic partial meniscectomy (APM) has been widely used for patients with DMT . And itsTherefore, the objective of this study was to decipher the efficacy of MET compared with APM + MET in older patients with non-obstructive meniscal tears.This study was performed according to PRISMA guidelines for systematic reviews and meta-analysis  was used to conduct the meta-analysis. Heterogeneity was assessed by the Cochrane Q test and considered statistically significant if ogeneity . To enhaThe detailed retrieval process was shown in PRISMA flow diagramFig. . The seaThe sample size of the extracted studies ranged from 93 to 351. All included RCTs were published between 2007 and 2017. Overall, 445 participants were randomly allocated to APM followed by exercise group, and 434 participants were in the exercise group. The average age ranged from 48 to 59 years and females accounted for 47.8% of all enrolled participants. The follow-up time was 2 to 60 months. In terms of evaluation of knee osteoarthritis grade, two studies used Ahlbacks classification , 27, andAssessments of the outcomes were conducted at 2 to 3, 6, 12, and 24 months, respectively. Clinical results were reported as follows: pain relief of knee, physical function, and activity level. We only shown the significant results in the text. An overview of the estimated risk of bias for each study was presented in Fig. numerical rating scale (NRS) [p < 0.0001; Chi2 = 0.99, df = 2, P = 0.61; I2 = 0%, Fig. p = 0.004; Chi2 = 2.64, df = 2, P = 0.27; I2 = 24%, Fig. p = 0.04; Chi2 = 0.26, df = 1, P = 0.61; I2 = 0%, Fig. Four studies used the visual analogue scale (VAS) and le (NRS) , 26, 27,le (NRS) , 12, 27 le (NRS) , 14, 27 p = 0.02; Chi2 = 1.39, df = 2 (P = 0.50); I2 = 0%, Fig. p = 0.01; Chi2 = 0.58, df = 1 (P = 0.44); I2 = 0%, Fig. p = 0.01; Chi2 = 1.42, df = 2, P = 0.49; I2 = 0% Fig. p = 0.03; Chi2 = 1.70, df = 3 (P = 0.64); I2 = 0%, Fig. To evaluate the physical function, different methods were employed in the included articles: Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC), KOOS, and the Lysholm Knee Scoring Scale (LKSS). The same items were used in the WOMAC physical function dimension and the KOOS function in daily living dimension of activities of daily living, so they could be pooled directly. Finally, three trials including 549 patients were extracted , 27, 28 Tegner Activity Scale score was used in two articles , 14 enroAdditional sensitivity analyses were performed to confirm the results. We eliminated a study applying MET program (five times a week) quite different from others . And theWe found that APM followed by structured MET was more effective compared to MET alone in terms of VAS score, KOOS Pain dimension, Lysholm Knee Scoring Scale, WOMAC, and KOSS function score within 6 months. These findings revealed that APM followed by MET may improve both pain control and physical function in patients with degenerative meniscal tear in a short-term. However, it was found that MET could be as effective as APM + MET both in the 12th and 24th months’ follow-up since the completion of interventions.There was low statistical heterogeneity of the main positive outcomes. To increase the strength of the conclusions, we pooled the data from the included studies despite the usage of outcome measures that were various in the extracted articles. Most of the results were consistent, which improved the quality of evidence. In addition, we conducted the sensitivity analysis, and it also confirmed the results. Totally, the efficacy of APM with MET in patients with a meniscal tear was explored in 5 recent RCTs. When comparing the included studies, four of them did not show statistically or clinically significant differences in symptomatic outcomes between participants in the group of APM with MET or MET alone , 14, 26.Recently, meta-analyses were published to compare APM with conservative treatment for non-obstructive meniscal tears . It indiBesides, other aspects should also be taken into considerations. Østeras et a. l describeOur systematic review had the following limitations: (1) Only five trials evaluating a total of 797 subjects were included in this meta-analysis; if more researches available, the statistical efficacy of analysis might enhance. (2) Most of included trials were difficult to interpret because between 20% and 30% of participants initially assigned to the non-operative group crossed over to perform APM. (3) The follow-up duration was not long enough in some included studies. Long-term follow-up trials should be performed in the future. (4) Among-study heterogeneity was unavoidable because of the use of different grades of degenerative meniscal tear of patients and various programs of exercises. Despite several limitations existed, we carefully retrieved available studies based on strict inclusion criteria to ensure high quality. Moreover, Cochrane Handbook and PRISMA guidelines were employed to determine the quality of results contained in the extracted articles.No systematic review and meta-analysis were found that evaluated the effectiveness of MET alone compared to APM followed by MET in middle-aged patients with DMT. Despite the small number of patients and the heterogeneity in the extracted RCTs in this study, favorable results of APM + MET at short-term were found for pain control and physical function compared to MET, but there were no differences at longer follow-up. Our results supported the potential of MET that could be comparable to APM + MET regarding to the improvement of pain control and physical function in patients with DMT. Therefore, the clinical applicability of APM + MET compared with MET should be interpreted carefully, and the potential of MET to treat DMT should be valued.Additional file 1. PRISMA 2009 Checklist.Additional file 2. Search strategy on PubMed.Additional file 3. Sensitivity analysis by excluding the study of Sihvonen et al.


The paper aims to investigate the influence of waste tire rubber and silica fume on the fresh and hardened properties of self-compacting concrete (SCC) and to design multivariate regression models for the prediction of the mechanical properties of self-compacting rubberized concrete (SCRC). For this purpose, 21 concrete mixtures were designed. Crumb rubber derived from end-of-life tires (grain size 0.5–3.5 mm) was replaced fine aggregate by 0%, 5%, 10%, 15%, 20%, 25%, and 30% of total aggregate volume. Silica fume was replaced cement by 0%, 5%, and 10% of the total cement mass. The optimal replacement level of both materials was investigated in relation to the values of the fresh properties and mechanical properties of self-compacting concrete. Tests on fresh and hardened self-compacting concrete were performed according to the relevant European standards. Furthermore, models for predicting the values of the compressive strength, modulus of elasticity, and flexural strength of SCRC were designed and verified with the experimental results of 12 other studies. According to the obtained results, mixtures with up to 15% of recycled rubber and 5% of silica fume, with 28 days compressive strength above 30 MPa, were found to be optimal mixtures for the potential future investigation of reinforced self-compacting rubberized concrete structural elements. After almost two decades, the idea to combine concrete with waste recycled tire rubber as an aggregate replacement is still the subject of a large number of experimental investigations. To date, a considerable number of authors investigated traditional concrete with recycled rubber derived from end-of-life tires (ELTs), and it is known that this type of environmentally friendly concrete has been used in non-structural concrete elements such as traffic noise barriers, sidewalks, and sport fields ,2,3,4 maThe mechanical properties of SCRC can vary significantly depending on mixture design, material properties, supplementary cementitious materials (SCMs) used in experiment, type and size of recycled rubber, etc. The use of crumb rubber (CR) and SCMs in structural self-compacting concrete (SCC) is a promising method to decrease the negative impacts of waste on the environment and to reduce cement consumption. Before structural application and full-scale experiments in the laboratory, the SCC mixture design needs to be determined, due to the desired concrete strength. In addition to the requirements for the mechanical resistance and stability of the structure, the replacement level of CR and SCMs should also be selected respecting economic criteria, since the replacement of the natural fine aggregate with crumb rubber negatively effects on the designed fresh and hardened state properties of SCC. Hence, the use of mineral and chemical additives, such as different types of SCMs and superplasticizers, are obligatory to preserve concrete design properties. SCMs are mostly used to enhance the mechanical and durability properties of SCC. Recently, there are many studies on the effect of silica fume (SLF) and other SCMs on the fresh and hardened properties of highly flowable cementitious composites. Some of these studies investigated the mutual effects of SLF and other SCMs, such as fly ash, metakaolin (MK), and ground granulated blast-furnace slag (GGBFS) on the mechanical and durability properties ,38,39,40There are two main research objectives of the present study. First, (i) to examine the coupling effect of different replacement levels of both SLF and CR on the mechanical properties of SCC. For this purpose, 21 SCC mixtures were made, with different replacement levels of natural fine aggregate  with CR and cement  with SLF. Second, (ii) to develop prediction models for the mechanical properties of SCC with CR and SLF, i.e., compressive strength, modulus of elasticity, and flexural strength. In 3 and Blaine fineness of 4378 cm2/g, which complies with the requirement of European Standards EN 197-1:2002 [3 and Blaine fineness of 20.5 m2/g, which is in accordance with the European Standards EN 13263-1:2009 [SCC mixtures were designed in accordance with the parameters given by the European Guidelines for self-compacting concrete . Ordinar7-1:2002 , was use7-1:2002 . Silica 3-1:2009 , was use3-1:2009 , was use3-1:2009  and EN 93-1:2009 . If it w3 and Blaine fineness of 5206 cm2/g was used as a filler. The density of cement, silica fume, and dolomite powder was tested according to ASTM C188-16:2011 [Dolomite powder, size < 0.063 mm, from a local quarry, with a specific gravity of 2.97 g/cm-16:2011 .3 were used as a fine (FA) and coarse aggregate (CA). Rubber aggregate, size 0.5–3.5 mm, obtained by the mechanical grinding of local waste tires, was used as a fine aggregate replacement (0–4 mm). The specific gravity of rubber aggregate, i.e., crumb rubber (CR), was 1.05 g/cm3. The appearance of silica fume and crumb rubber is shown in Natural sand and crushed stone with nominal sizes of 0–2, 0–4, 4–8, and 8–16 mm with specific gravities of 2.58, 2.79, 2.88, and 2.88 g/cm3. The water to powder ratio (w/p) was 1.07, 1.05, and 1.03 for SCC mixtures with 0%, 5%, and 10% silica fume, respectively, and these values were in accordance with the permitted values given by European Guidelines for SCC [A total of 21 self-compacting concrete mixtures were tested in fresh and hardened state, regarding two variables: crumb rubber and silica fume. Reference mixture with 0% of crumb rubber and 0% of silica fume was marked as SCC-0CR-0SLF. Three replacement levels of the cement with SLF  and seven replacement levels of the FA with CR  were investigated. A summary of the SCC mixtures is listed in  for SCC . For theDesigned SCC mixtures were stirred with a pan mixer that had a maximal capacity of 50 L . At the The hardened state properties of SCC were determined after 28 days of water curing.Tests on fresh and hardened SCC were performed according to relevant European standards. The J-ring test, L-box test, slump flow test, and segregation resistance test were performed according to EN 12350-12:2010 , EN 1235ck,cyl) was determined through testing cylinders (b) was tested on 100 × 100 × 400 mm prisms , modulus of elasticity (E), and flexural strength (fb) were presented as the average of three samples. A summary of the tested properties of SCC in fresh and hardened states is given in According to percentage values of the two main variables, i.e., silica fume and crumb rubber, a total of 126 cylinder specimens and 63 prism specimens were prepared. Three specimens were prepared for the same set of study parameters. The obtained results of compressive strength (fThe test results of the SCC properties in the fresh state are given in From T500 (s) was used as a viscosity indicator of SCC mixtures. From The passing ability of fresh concrete mixture can be of great significance during the execution of concrete works at a construction site, if reinforcement is congested. Therefore, before casting concrete into molds, their passing ability was checked with two different test methods: L-box and J-ring. From test results given in The appearance of segregation can be pronounced in high vertical-reinforced concrete elements such as columns, pylons, etc. The sieve segregation resistance test, which is defined as a percentage of concrete passed through a 5 mm sieve, can be of great help to bring conclusions regarding concrete homogeneity and concrete strength uniformity. According to the test results given in The test results of the SCC fresh state properties were in accordance with investigations carried out by different authors so far ,44,60,61The test results of the SCC properties in the hardened state are given in 3). The relative decrease in dry unit weight was approximately 7% and 15% with 15% and 30% replacement levels of fine aggregate and 0% and 5% replacement levels of cement, respectively. An almost linear relationship between a reduction in dry unit weight and increase of replacement level of natural fine aggregate with crumb rubber was observed. Lightweight self-compacting concrete with a dry unit weight around 2069 kg/m3 was obtained, with 30% of the fine aggregate replacement level, which ultimately leads to a lower total mass of the concrete structures if such concrete is intended for structural purposes.The unit weight of SCC cylinders and prisms was measured after 28 days. The results given in As expected, the mean value of three measurements of 28-day compressive strength was the lowest, i.e., 12.21 MPa, when the CR and SLF replacement levels were 30% and 0%, respectively. The negative impact of CR on the 28-day compressive strength can be described with a poor rubber granule–cement paste bond and with a low rubber modulus of elasticity compared to natural aggregates ,62. On tValues of the 28-day modulus of elasticity were in a direct link with the compressive strength values, although in this case, the negative effect of replacing natural fine aggregate with crumb rubber is more pronounced, since with 5% of silica fume, the negative impact of rubber granules on the elasticity modulus values cannot be annulled . CompareFlexural strength also experienced a negative impact with replacing natural fine aggregate with crumb rubber, but this was still at smaller percentage compared to the compressive strength and modulus of elasticity . Thus, iThe experimental dataset for the present work is based on 63 values of the observed mechanical properties: three for each of 21 SCC mixtures . To predict the three main mechanical properties of SCC—compressive strength, modulus of elasticity and flexural strength—a multivariate regression technique was applied for each of the observed mechanical properties by using two independent variables: the amount of crumb rubber (0–30%) and silica fume (0–10%). Regression models were extracted by using software “Statistica 13” and “R”. The final models are given in Multivariate regression models have been developed for the partial replacement of natural fine aggregate with crumb rubber (0–30%) and the partial replacement of cement with silica fume (0–10%). For the estimation of unknown parameters of modulus of elasticity, the least squares (LS) method was used. However, when applying the LS method for the estimation of unknown parameters of the other two mechanical properties, i.e., compressive strength and flexural strength, the variability of the variance of the residuals was observed, depending on the silica fume replacement level. Hence, for an estimation of unknown parameters of compressive strength and flexural strength, the weighted least squares (WLS) method was used. In these cases, weights for WLS were determined by modeling squares of residuals in the initial model with the silica fume replacement level. The results of the regression analysis and estimated coefficients for all three mechanical properties are given in With estimated coefficients of the selected models, the relation between mechanical properties and the amount of crumb rubber and silica fume were presented graphically in For the chosen regression models, non-constant variance score tests (NCV test) were conducted , and theThe practical application of prediction models and the graph given in The positive impact of silica fume on SCRC compressive strength, even with a minor replacement level of cement, can be seen from Concrete type is SCC, not traditional concreteCR is replacing FA, not CACR is replacing fine aggregate by total aggregate volume/fine aggregate volume, not by total aggregate weight/fine aggregate weightSLF is replacing cement by total cement mass, not by total powder/binder contentAvoid experimental investigation with multiple supplementary cementitious material, such as combination of SLF and metakaolin, fly ash, or ground granulated blast furnace slagObserved CR and SLF replacement level is 0–30% and 0–10%, respectivelySCC compressive strength and modulus of elasticity is calculated from the experimental investigation of the cylinder specimen, whilst SCC flexural strength is calculated from the prism specimens, respectively.In this section, 12 experimental studies from the literature are compared with the developed models: 7 for the compressive strength model ,43,65,66As it was mentioned in ck/fck, model obtained from 39 verification values has a range of values from 0.77 to 1.33, with a total average of 1.03 and median of 1.05. Ratio fb/fb, model obtained from 44 values has a range from 0.79 to 1.27, with a total average of 0.97 and median of 0.91. However, the verification of the developed model for the modulus of elasticity is a little less reliable than the other models. Ratio E/Emodel obtained from 30 values has a range from 0.7 to 0.97, with a total average of 0.81 and median of 0.80.Verification of the prediction models based on existing test results from the available literature is given in Material properties Mix proportions Mixing procedure and curing conditions (specimen preparation)Test methods (standards and specimen dimensions)In all three cases, factors that are possibly affecting the difference between experiment values and model values are listed as follows:For future investigations and further development of the SCC model with SLF and CR, it can be suggested that additional laboratory work needs to be done, with a variation of more than two variables, such as w/b ratio, binder content, cement type, etc. With additional variables included in the models, a larger database of the experimental results of the other researches can be used in the model verification process.An increase in the replacement level of fine aggregate with crumb rubber and cement with silica fume had a negative impact on the flowability of SCC mixtures; however, slump flow values were within acceptable limits for SCC mixtures with up to 25% of crumb rubber and 10% of silica fume.SCC mixtures with up to 15% of crumb rubber and up to 10% of silica fume can be classified as viscosity class VS1 (T500 < 2 s).J-ring and L-box test results show a satisfactory passing ability of SCC mixture with up to 15% of crumb rubber and 10% of silica fume.Segregation was not present when 5% and 10% of cement was replaced with silica fume, but slight segregation was present in all mixtures without silica fume.A linear relationship between reduction in the dry unit weight and increase of replacement levels of natural fine aggregate with crumb rubber was observed.Considering the compressive strength of SCC, at a 30% replacement level of fine aggregate with crumb rubber, silica fume can reduce the negative effect by up to 14%.Values of the 28-day compressive strength of the SCC mixtures SCC-15CR-5SLF and SCC-10CR-0SLF were above 30 MPa, which can be taken into account if there is an intention for future investigation of self-compacting concrete on the structural elements and systems. Still, according to the obtained results, it can be suggested that the silica fume should be used in combination with recycled rubber only up to a 5% replacement level of the cement.Values of the 28-day modulus of elasticity were over 20 GPa with a fine aggregate replacement level of up to 20%.Replacing natural fine aggregate with crumb rubber also caused negative effects on the value of the flexural strength, but still at a smaller percentage compared to the compressive strength and modulus of elasticity.The positive impact of replacing cement with silica fume is more obvious for a lower replacement level of the natural fine aggregate with crumb rubber, i.e., up to 10%.According to the developed model for the prediction of the compressive strength, with 10% and 15% of CR and 0% and 5% of SLF, a concrete compressive strength of 30 MPa can be obtained.The verifications of the prediction models for the compressive strength and flexural strength give good agreement with the experimental results of the other research studies, while the prediction model for the modulus of elasticity is less reliable than that of the other two models.Values of the experiment/model ratio are affected by several factors such as the material properties, mix proportions, mixing procedure, and test methods.In the present study, the fresh and hardened properties of SCC mixtures with different amounts of crumb rubber (0–30%) and silica fume (0–10%) were investigated. Furthermore, the test results of SCC in the hardened state were used for creation of the prediction models. Developed models were verified with 12 experimental studies. Several conclusions arise from the conducted experimental research and development of the statistical models:Favorable fresh and hardened SCC properties can be obtained with up to 15% of crumb rubber and 5% of silica fume.Models for the prediction of mechanical properties of SCC with crumb rubber and silica fume were developed and successfully verified.Future research directions:With an extensive laboratory work, create a database for defining an extended model with more than two variables included, such as the w/b ratio, binder content, cement type etc.Detailed analysis of the durability, thermal, long-term and micro-level properties (SEM) needs to be done, and thereafter full-scale models of SCRC beams, columns, and frames with selected optimal SCC mixtures need to be investigated.The following are the overall conclusions drawn out of the obtained test results and observations made in this study: