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Hydraulic conductivity in layered saturated soils assessed through a novel physical model. DYNA , vol. DOI: Abstract: This paper introduces a novel physical model for measuring the hydraulic conductivity of granular materials in saturated conditions. Design methodology took issues of construction, calibration and implementation into account. Analysis of the results shows that the physical model can replicate seepage in layered soils with parallel and perpendicular flows as occurs in field.
Furthermore, it was found that it is possible to validate the experimental calibration data by use of statistical techniques. Keywords: equivalent permeability coefficient, seepage, statistical analysis, t -test. Hydraulic conductivity is one of the most important properties of soils [ 1 ].
Seepage through the soils may affect the stability of geotechnical structures such as pavement, tunnels, walls, slopes and excavations. For Nagaraj et al. Nevertheless, soil permeability also depends on several additional factors including temperature, atmospheric pressure and absorption [ 7 ]. The law is expressed by an equation for flow velocity that can be used to estimate the permeability coefficient k [ 9 ]. Flows only occur when an energy differential exists which is another way of saying when i exists.
Hence, differences of energy or potential between two points must exist into the soil. On the other hand, the soil is a non-homogenous, anisotropic and non-continuous material [ 10 ].
In nature, and at the majority of building sites, soil is layered. This means that soil properties may change from one stratum to another [ 1 ]. It can be used to monitor the hydraulic conductivity of a layered soil mass as well as flow direction within that mass [ 11 ]. Numerous methods have been developed to measure hydraulic conductivity of soils either in the field or through laboratory procedures [ 12 , 13 ].
In the field, permeability is evaluated by instrumentation of boreholes [ 12 ], but in the laboratory, the most popular procedure for evaluating hydraulic conductivity of granular soils is constant head testing which is described in ASTM standard D [ 14 ]. The falling head test method is equally popular for fine-grained soils [ 13 , 15 ]. Various groups have developed new methods and insights in this area. Ghanizadeh et al. They presented laboratory results for gas permeability measurements for the low matrix permeability Duvernay shale formation of Alberta, Canada.
Estabragh et al. Others have made new developments in the laboratory. Goh et al. This paper describes the construction, calibration and implementation of a novel physical model for measuring hydraulic conductivity in layered soils. These parameters were obtained from tests performed in perpendicular and parallel flow directions using our new physical model for permeability testing.
The study was carried out with Ottawa sand and Guamo sand which are both well-known materials in Colombia. Ottawa sand is obtained from Ottawa, Illinois in the United States and has uniform size distribution and is composed of quartz minerals [ 23 ]. Moreover, Table 1 presents the physical properties and classifications parameters of the sands. Figure 1 Grain size curve of sandy soils. Source: The authors. Table 1 Physical properties of sandy soils. A constant head apparatus was designed and developed on the basis of the apparatus suggested in ASTM standard procedure D [ 14 ].
This device is capable of measure hydraulic conductivity of soils for both perpendicular and parallel flow directions of granular soils. In addition, the apparatus was built with two square acrylic permeameters as described in Dulcey et al. The geometry of the elements was selected in accordance with the sample preparation method.
Each permeameter has seven piezometers with parallel configurations. For each permeameter, piezometer number 1 is connected to the porous stone, piezometers 2 to 4 are connected to the first soil layer and piezometers 5 to 7 are connected to the second soil layer.
Figure 2 Physical model. Several soil specimens using Ottawa and Guamo sands were prepared in order to test measurement of hydraulic conductivity by the physical new model. Each layer had a thickness of 19 cm for perpendicular flows and a thickness of 4 cm for parallel flows. Twenty different specimens, each composed of layers of the two, were compacted inside of each permeameter.
The layers were prepared to reach a thickness of 19 cm for the perpendicular direction flow tests and 4 cm for the parallel direction flow test Fig. Similarly, conventional constant head tests were developed in the model to estimate k values for sandy soils.
Figure 3 Schematic view of layered soils. Values of k were measured in the laboratory using the physical model, and computation was done according to the method described in ASTM D [ 14 ]. Values of k were also estimated through numerical models based on granulometric results and relative density parameters.
Table 2 presents the mean values of k obtained by means of tests performed with the apparatus for each sand independently plus the numerical correlations presented previously.
Table 2. Hydraulic conductivity of sandy soils. Results indicate that the k values obtained experimentally are within the range of soils classified as SP, according to authors including Bowles [ 11 ], Cedergren [ 12 ], Warrick [ 7 ] and Budhu [ 13 ]. This is due to the fact that eq. Conversely, the outcomes found with the method proposed by Chapuis were very close to our experimental results. This is accounted for by the fact that this method includes a parameter, relative density, which is related to the state of the soil and depends on the void ratio.
Ren et al. Twenty different two-layered samples of Ottawa sand in the upper layer and Guamo sand in the lower layer were compacted in each permeameter for a total of ten permeability tests. These equations were obtained after taking energy losses of the soil mass in each layer into account [ 13 ]. Table 3 Equivalent permeability coefficients.
Direct measurements were made by determining the differences in hydraulic potentials measured by the piezometers located in distinct layers in both permeameters. Fifty measurements were made in each permeameter. Findings show that the equivalent permeability coefficients differ according to flow direction. This is the result of the sample preparation process in which soil compaction produces a non-isotropic condition that induces modifications of hydraulic conductivity.
Computation of the mean and median, both measures of spread, show them to be equal indicating an insignificant amount of variation. Table 4 presents the findings from our statistical analysis. A comparison of the values obtained from Equations 4 and 5 with tests results shows that the relative errors between them are 0.
To verify the behavior of the results, a t -test using the null hypothesis in which the experimental coefficient mean values are equal to the mean obtained from eqs. Table 5 shows the normality test statistics: skewness presented slightly high values, but kurtosis is acceptable as can be seen in Fig.
Table 5 Normality test. According to [ 32 , 33 ], the t -test is robust to non-normality when sample sizes have more than 30 observations. Due to the previous results and a sample size of 50, normality was assumed.
In the case of perpendicular flow, the null hypothesis is rejected because the empirical value 0. However, the relative error between these two values of 0. Table 6 T-test outcomes. Based on the results, it is possible to affirm that experimental and empirical values are close and that variation is small. For all the above reasons, the physical model is capable of replicating seepage in layered granular soils.
This paper proposes an alternative physical model for evaluating the hydraulic conductivity of granular materials. This can be used to measure hydraulic conductivity directly and to establish the equivalent permeability coefficient in layered soils, and is therefore capable of replicating seepage as it occurs in the field.
The technique has proven to be efficient and relatively easy to apply. Importantly, this physical model is highly reliable for testing permeability since it generates statistically stable results as evidenced by equality between mean and median values.
In a physical context, such relative errors do not represent important changes for practical designs, even if the hypothesis of the equal means of the t -test was rejected. The t -test is a powerful tool for comparing variation in experiments with sample sizes of less than 30 observations.
Since this technique also allows evaluation of dispersion of data obtained from experimental procedures, it can contribute to the calibration and implementation of laboratory apparatuses. Our results show that the equivalent permeability coefficient varies according to flow direction. Data presented higher values for perpendicular flows than for parallel flows due to the sample preparation method. The compaction process induces an anisotropic condition within the granular soil that is reflected in the void distribution, which in turn produces an increase of the flow velocity.
The comparison of numerical methods with experimental techniques demonstrated a clear relationship between experimental correlations weighted average and direct measurements. This establishes that the assessment performed with the physical model was adjusted to the postulate of eq. Nevertheless, the numerical models in this study did present differences with respect to the direct measurements indicating that the parameters of each numerical model must be computed and adjusted according to the soil type.
Influence of thickness and position of the individual layer on the permeability of the stratified soil. Perspectives in Science, 8, pp. Journal of Geotechnical and Geoenvironmental Engineering, 12 , pp. In GeoCongress New York: Oxford University Press.
Paris: Dalmont. Revista Tecnura, 19 43 , pp.
Hydraulic conductivity in layered saturated soils assessed through a novel physical model. This paper introduces a novel physical model for measuring the hydraulic conductivity of granular materials in saturated conditions. Design methodology took issues of construction, calibration and implementation into account. Analysis of the results shows that the physical model can replicate seepage in layered soils with parallel and perpendicular flows as occurs in field. Furthermore, it was found that it is possible to validate the experimental calibration data by use of statistical techniques. Hydraulic conductivity is one of the most important properties of soils [ 1 ].
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