Volume 8

Issue 2

##### Civil Engineering

JOURNAL OF

POLISH

AGRICULTURAL

UNIVERSITIES

Available Online: http://www.ejpau.media.pl/volume8/issue2/art-13.html

**
VARIOUS METHODS OF THE MEASUREMENT OF THE PERMEABILITY COEFFICIENT IN SOILS - POSSIBILITIES AND APPLICATION
**

Mariusz Sobolewski*
Department of Civil Engineering and Geodesy,
Warsaw Agricultural University, Poland*

The paper presents a review and classification of methods of the determination of the permeability coefficient and research instruments, well-known from literature. Special emphasis has been put on the discussion of experimental methods, as the most exact values of this parameter are obtained on their basis. Apart from this, attention has been paid to modern measuring instruments which serve to define the consolidation and permeability coefficients in coherent soils. The introduction of suggested changes in the current methodology of studies into practice makes values of the discussed parameters obtained in situ and from laboratory tests comparable.

**Key words:**
seepage, consolidation, permeability coefficient, hydraulic gradient, field tests, laboratory tests, investigative methods, measuring apparatus, cohesive soils.

**INTRODUCTION**

The permeability of soils is a very important feature which plays the crucial role in issues connected with the flow of ground water and the migration of pollutions. The occurrence of subsoil water in a building-site often complicates realization of works and requires an additional intervention with the use of special equipment. The ability of water conduction in a soil is the essential factor in the consolidation process because it decides about the intensivity of this phenomenon. The realization of structural constructions is, almost in every case, directly or indirectly connected with the flow of subsoil water. Thus the problem of water flow in soils has been the subject of scientific research for many years.

Cohesive soils deserve particular attention with regard to their low permeability. For a long time, these soils have been used to build cores of earth dams and constructions protecting hydro-engineering structures against harmful results of seepage. Natural or remould structure layers of cohesive soils are a good isolating material to be built-in. Therefore, they can successfully fulfil the role of seepage barriers protecting the environment against the expansion of pollutions. The permeability of coherent soils is of crucial importance at the design stage of vertical and horizontal mineral compacted soil liners. Classification of soils with regard to permeability has been made basically on the level of the permeability coefficient "k". For a given soil, this parameter takes a constant value in the range of validity of Darcy´s law.

**METHODS OF MEASURING THE PERMEABILITY COEFFICIENT**

We distinguish several methods which serve to determine flow parameters of soils. Methods of the determination of seepage parameters, which are described in literature, can be divided into two groups: computational (theoretical or semi-empirical) and research (experimental) methods. Examples of computational methods are: analytical and empirical formulas, numerical modelling and mathematical inverse solutions. Within experimental methods we can distinguish laboratory testing of undisturbed (NNS) or disturbed (NS) samples as well as in situ tests (field tests). All these methods can be divided into indirect and direct tests. Figure 1 illustrates a classification of methods of the determination of water flow parameters in soils.

Groups being actually discussed consist of methods which are used to establish a value of the permeability coefficient. They lead to obtaining of this parameter in a less or more exact way. The precision of obtained results depends mainly on practical adequacy of laws or empirical equations used in the model as well as on the possibility of controlling the quality of boundary conditions in examinations. The precision of a result is influenced, to a large extent, by the method of finding the permeability coefficient: whether it has been directly defined by the water flow or indirectly estimated by taking measured auxiliary parameters into consideration. The quality of results depends, to a large degree, on the accuracy of measuring devices. The strongest attention is put here mainly on problems connected with water evaporation, possibility of existing privileged paths of seepage, contamination of a sample with air, swelling or another causes. The inappropriate recognition of a permeability coefficient value can result from the mistakes having made during an experiment or from the misinterpretation of results.

Figure 1. Classification of measuring methods for determination of the permeability coefficient in saturated soils and the wide-spread apparatus in Poland [19] |

Errors can also be caused by wrong assumptions in the methodology of research, e.g. if a number of essential factors is neglected or far-fetched simplifications are introduced. Mostly, the heterogeneity of a soil or changes in a soil structure following changes in the state of stress, are not taken into consideration. The influence of processes appearing in natural conditions inside or outside the area is also disregarded. Simplifications also consist in the attribution of the mean value of the permeability coefficient to chosen layers, and next - in the generalization of this value on local or regional subsoil conditions. A one- or two- dimensional flow of water is often being assumed instead of a three-dimensional one, and parameters determinating the permeability coefficient are being assumed by analogy with the literature. Incorrect values of the permeability coefficient can also result from a poorly recognized structure of a subsoil or ground-water conditions or other causes.

Calculations based on analytic or empirical formulas using the grain size distribution curves as well as the estimation of the permeability coefficient according to inverse solutions or numeric analysis are little accurate. They give a possibility to obtain only rough values of permeability coefficients - mostly for well-permeable soils. Values of the permeability coefficient established by analogy or assumed according with the literature yield merely preliminary orientation on the order of magnitude of this parameter.

Experimental methods of the research are more accurate. The determination of permeability parameters of soils in an experimental way, however, constitutes a complicated problem because the permeability coefficient depends on many factors simultaneously existing during testing. The water flow through a soil, and thus the permeability coefficient, depends, to a large extent, on the structure of soil where this flow occurs. The most essential is quality of pores in the soil (their size and shape). Moreover, in coherent soils it is necessary to use considerable pressure to defeat the resistance of molecular forces and to begin movement of water. Mechanics of the water flow through a porous medium - like a soil - has already been well recognized and described. However, there is lack of well elaborated and standarized methodologies of the research. The most important thing in the methodology itself is the scale of a solved issue and the range of applied hydraulic gradients which are directly connected with the regime of moving water.

It is the quantitative research of soil microstructures in a scanning microscope (SEM), which becomes of greater importance. This research continuously requires stronger attention because in every case we can observe changes in a soil structure, which entails the necessity of developing models describing permeability parameters with large approximation and likeliness by the application of statistics.

In the last century, the engineers´ effort was put into the estimation of permeability of three-phase soil media. In 1931 Richards developed Darcy´s law for unsaturated soils and announced the dependence between the soil permeability and capillary pressure (matric suction of a soil). Since the suction of a soil was connected with the degree of its saturation, a relationship between the permeability coefficient and dampness had been sought. The hydraulic conductivity in unsaturated soils corresponds with the permeability coefficient corrected by a function describing the state of a soil. This relationship takes a less or more complicated form in different equations of various authors. Credible determination of the permeability coefficient in a saturated soil is therefore a condition of correct estimation of the permeability coefficient in a unsaturated soil.

It should be mentioned that the phenomenon of swelling can also be connected with the water flow within unsaturated cohesive soils. The swelling of a soil can affect a measurement of the permeability essentially. Therefore, during realization of a test, it is necessary to take this phenomenon into consideration. The examination of a swelling soil should be carried out till equilibrium of velocity of provided and effluent water is reached. If swelling is less than 5%, the test can be finished. If swelling exceeds 5%, the upper swelled piece of the soil should be cut off, the test should be repeated and the evaluation of the permeability of the soil - renewed [4].

**EXPERIMENTAL METHODS OF MEASURING THE PERMEABILITY COEFFICIENT**

Almost in every case, experimental determination of the permeability coefficient uses empirical Darcy´s law, which describes the correlation between velocity of a water flow "V" and a hydraulic gradient "i". Thus, the determination of the permeability coefficient in a soil requires experimental recognition of the velocity of water moving within the soil. In practice, three kinds of such investigations are known, namely: constant-head test, falling-head test and constant flow rate test. In each of these three cases, the water flow is forced by the pressure applied to the soil.

The examination of the permeability coefficient in cohesive soils brings a number of difficulties concerning time consumption of experiments as well as technical requirements needed for maintaining the water flow when the hydraulic gradient is low. Prolonged time of tests can promote growth of microorganisms as well as induce changes within the microstructure of a tested cohesive soil specimen. Because of these reasons, the falling-head method and the constant flow rate method have been specially worked out for cohesive soils. The constant-head method turns out, however, to be particularly useful for cohesiveless soils.

In the constant-head method, the permeability coefficient is established according to direct measurement of the flow of water at a steady hydraulic gradient. The quantity of transfluent water through a sample of soil is being observed in precisely defined numeral conditions. A constant-flow rate permeability method consists in the measurement of a hydraulic gradient at a precisely controlled steady value of the water flow through the soil sample. Both of these methods result in the determination of correlation between the water flow velocity "V" and the hydraulic gradient "i". Falling-head tests require application of an instrument, where a change of water volume follows a change of its pressure. These examinations consist in recording of the increase or drop of the pressure of water moving to or from the device through the soil (inside or outside test). As the character of falling-head method is different from the previous methods, it is not possible to obtain a direct relationship between the water flow velocity "V" and the hydraulic gradient "i".

Apart from the above mentioned methods, there exists an indirect way of evaluation of the permeability coefficient, which is based on the one-dimensional Terzaghi´s consolidation theory. The value of the permeability coefficient "k_{h}" may be then calculated from a formula including the oedometric modulus "M_{h}" and the consolidation coefficient "c_{h}". This method is practically useful only for cohesive soils.

The character of investigations in all of these methods is different and mainly results from physical assumptions which have been made. However, in direct investigation we can distinguish transitory and steady-state phases (figure 2).

Figure 2. Course of changes a) different pressures DH b) hydraulic gradient c) discharge of water increment DQ during introduce of water into a sample of a cohesive soil for various permeability research methods:I - falling-head test, II - constant-head test, III - constant flow rate test (flow-pump). Broken line shows the transitory phase of the experiment, continuous line shows steady flow [19] |

In constant-head tests, a constant value of the hydraulic head is applied immediately. At a constant length of the seepage path, a definite value of the hydraulic gradient is established during an experiment. The use of low gradients is unpractical and unreliable because the required time of investigation is very long. In addition, the control of low gradients and the determination of very small flows are affected by mistakes of the measurement. In these examinations, the difference of total heads is controlled outside, and the water flow evoked by this difference is measured with respect to time. In a traditional depiction of constant-head tests, the difference of total heads measured through the specimen of soil decreases in time until it achieves an equilibrium state of a flow rate "Q". Problems occurring during a measurement disable one to follow up the transitory phase and the determination of the hydraulic gradient at which the water flow in the soil stabilizes. The seepage velocity is counted from Darcy´s law. A scheme of the device used in the constant-head method is shown in figure 3.

The character of investigations in all of these methods is different and mainly results from physical assumptions which have been made. However, in direct investigation we can distinguish transitory and steady-state phases (figure 2).

Figure 3. A scheme of a measurement test-stand in the constant-head method 1-specimen of soil, 2- porous tile, k -permeability coefficient, Q -discharge (total flow), A -area of specimen, L -seepage path, DH - difference of total heads |

In falling-head tests, a hydraulic gradient usually decreases with time, asymptotically approaching the real value referring to stabilized flow conditions. It proves that the water flow rate diminishes during the experiment. The reaction of the soil in transitory and steady-state phases of the examination is modified by continuous fall of the gradient. Therefore, the conditions of the water flow never become stabilized. As in these examinations, only a change of the water pressure in the measuring system is recorded. Velocities of the water flow and hydraulic gradients can be obtained from calibration of the equipment, basing on the exact values found in other investigations. The derived formulas for the permeability coefficient mainly take more or less a complicated form [1], [14], [27]. A scheme of the device applied in the falling-head method is shown in figure 4.

Figure 4. A scheme of a measurement test-stand in the falling-head method 1-specimen of soil, 2- porous tile, H_{1} -total head at the beginning test, H_{2} -total head at the end test, DH -difference of total heads, L -seepage path |

The Flow-Pump technique was introduced to enable multistage application of larger and larger flows to facilitate the determination of water flow characteristics and deviations from linear Darcy´s law. Olsen, the author of this technique was first to propose it for measuring the permeability of cohesive soils in 1966 [13]. Practically, on a wider scale, it was applied just in the 80´s in geotechnical laboratories. The theoretical basis was developed and presented by Morin and Olsen in 1987 [12]. A constant flow rate method assumes validity of Darcy´s law. The way of investigation is different from other methods, which results from physical assumptions. In the constant flow rate method, the flow of water through a soil sample is forced at a constant discharge "Q" assured by a syringe pump connected with a variable-speed step motor. Values of the flow rate can be applied in a wide range of constant velocities making hydraulic gradients grow from very small to very high values. If the quantity of the water flow into a soil sample is constant in time, the difference of pressures between both sample endings "DH" can be measured. Thus, it is possible to calculate a hydraulic gradient throughout duration of a test. Velocities of provided and effluent water in the soil sample are controlled outside the device. The hydraulic head at the bottom surface of the sample gradually grows till water reaches the opposite surface of the sample. Then the hydraulic gradient achieves a constant value. A stabilized value of the pressure difference results from steady flow conditions the equilibrium in the whole measuring system. A constant value of the discharge "Q" corresponds with the measured value of the hydraulic gradient "i". Finally, the same result is found to be the same as in the constant-head method. However, during these investigations, the direct measurement of the flow rate is avoided, and thus - the measuring errors connected with it. The unquestionable advantage of this method is the exact control of initial and boundary conditions. The high level of accuracy of measured parameters makes the required long time or high gradients no longer necessary to generate measurable velocities of the water flow. Therefore, the evaluation of the soil permeability can be carried out yet at comparatively low gradients and a shorter time of an experiment. The constant monitoring of the pressure difference enables one to capture the moment of stabilization of flow conditions through a sample. This, in turn, allows for easy distinction between transitory and steady-state phases. In a steady-state phase, practically, the course of the pressure difference "D H" is not ideally constant. It is due to influence of temperature of the environment. A scheme of the device applied in the constant-flow rate method is shown in figure 5.

Figure 5. A scheme of a measurement test-stand in the constant-flow rate method (flow-pump technique) 1 - specimen of soil, 2 - modified triaxial cell apparatus, 3 - porous tile, 4 - sensor of pore pressure, 5 - leading muff with piston, 6 - weights, 7 - displacement sensor, 8 - flow pump,9 - differential sensor of hydraulic head [19] |

**THE RESULTS OF THE COMPARISON OF EXPERIMENTAL METHODS**

As the groups of methods of the determination of the permeability coefficient, discussed above, are based on different physical or seepage assumptions, the influence of the adopted research method for obtained values of the permeability coefficient should be taken into consideration. The examinations performed on different kinds of soils, using various experimental methods and the same measuring apparatus, show satisfactory agreement of the results. Values of the permeability coefficient obtained from the constant-head method are always a bit larger than those from the falling-head method (figure 6). This dependence results because the seepage parameters in the falling-head test are evaluated at a smaller total head than in the constant-head method.

Figure 6. Comparison of results of falling-head tests (1) with results of constant-head tests (2), a) field tests of BAT probe [25], b) laboratory tests [6] |

The results of field and laboratory tests show the fundamental trend of changes the permeability coefficient along the depth [23]. The observed variability of this parameter depends mainly on kind of a soil in a subsoil as well as on the state of stress. A considerable majority of literature examples shows however large differences of the permeability coefficient obtained in situ and from laboratory tests - they reach even 2 orders of magnitude. Examples of conformity of the investigation results are also met. The comparison of direct examinations on the permeability coefficient can be found i.e. in [10], [14], [16], [21], [22], [27], where good agreement of the results was obtained. In all the mentioned methods, of course, it is not possible to skip the analysis of the affect of soil permeability by changes of physical, chemical and thermal conditions. The comparison of the results of investigations proves that the values obtained in natural conditions are higher than those measured in a laboratory [1], [2], [3], [11], [17], [18], [19], [22], [24]. According to numerous scientists, these differences are mainly the effect of scale. Moreover, the methods based on applying water into a soil by using large hydraulic gradients of an order of tens and more cause changes of the permeability which result from structural changes of the soil medium. Changes of the permeability coefficient connected with changes of the soil structure can exceed a few hundred percents.

Potential kinds of errors and possible causes of appeared divergences of results can be found out i.a. in [3], [5], [8], [9], [11], [15], [17], [20]. A majority of scientists claims that if suitable laboratory techniques are used, it is possible to obtain good agreement of results found from field and laboratory tests. According to the classification of research methods presented in this paper (see figure 1), only the results from local point space methods can be comparable with each other. The examination using these methods includes a similar, small space of a soil medium, mostly in a one-dimensional water flow and triaxial state of stress.

In geotechnical examinations of soils, at the present state of knowledge, technical and practical requirements, the accurate recognition of seepage proprieties of cohesive soils becomes indispensable. As the traditional methodology of investigations is dubious and the range of values of the permeability coefficient obtained from experimental methods is large, the elaboration and unification of investigative procedures is advisable.

**MEASURING APPARATUS**

Experimental methods use a measuring apparatus which enables the estimation of the permeability of a soil medium. To use it effectively, a number of devices has been constructed, which found applications in geotechnics and allied sciences. In certain cases, to measure the soil permeability, the equipment is adopted, which originally was designed to examine other parameters. In most of them, the measurement principle uses Darcy´s law. Depending on the type and construction of the device, one of the methods mentioned above is applied: constant-head, falling-head or constant flow rate.

Generally, direct field permeability measurements include the groundwater table raise or lowering tests in boreholes, falling-head tests in piezometers or tests using a pressure piezometers, infiltration tests using different types of opened or sealed infiltrometers, self- boring pressuremeter tests and others. The investigations based on the theory of consolidation found the application mainly for cohesive soils. The indirect way of determination of seepage parameters from the theory of consolidation consists in the examination of dissipation of excess pore pressure Du, which is generated during sounding various penetrometers, like: CPTU, DMTA, BAT probe.

The laboratory investigations on the permeability coefficient are performed by special devices, which are divided with regard to the character of seepage and to the principle of operation - between constant-head devices, falling-head devices, constant flow rate devices as well as devices using the theory of consolidation. The falling-head devices initially found wide application for fine-grained soils. Then the flow-pump permeability tests began to be developed. The range of application of individual devices is different. Systematization of the research methods and measuring apparatus employed to the estimation of the permeability coefficient is shown in figure 7.

Figure 7. Permeability of soils and range of practical usage of the apparatus based on various methods of measuring the coefficient of permeability [19] |

**THE CHOICE OF EQUIPMENT AND APPLIED RESEARCH METHODOLOGY**

There exists a problem in engineering practice, how to choose the equipment from offered numerous groups of devices. The adaptation of the chosen apparatus to local background soil conditions is another problem. In this situation, an answer to the following question may be helpful: what research methodology at the present state of knowledge and technology can be successfully applied to obtain credible values of the parameters? If we want to know this answer, we should analyse the advantages and disadvantages of individual devices. The choice of a measuring apparatus often depends on the range of its applicability (see figure 7). It may result also from usefulness of the equipment with regard to the direction of water flow in a soil (see figure 8).

Figure 8. Application of methods and apparatus for measurement of the permeability coefficient with regard to direction of flow of water into a soil |

Low time-consumption and simplicity of realization as well as comparatively low costs are characteristic attributes of field tests. The next advantage of these investigations is that they take place in natural conditions and can be carried out in large depths. The impossibility of flow control and one-dimensional (horizontal) movement of water are mainly the constrains of field tests. The field techniques are aimed only at the examination of saturated soils.

The laboratory investigations are characterized by the possibility of measuring seepage parameters in both directions: horizontal and vertical. In laboratory tests, there exists the possibility of control of the water flow, hydraulic gradients, state of stress, state of deformation, state of saturation and runoffs. The laboratory investigations make it possible to determine a relationship between the permeability and void ratio "e", which is impossible to obtain in field conditions. The examination of small samples does not permit one to survey the influence of local changes within the soil environment. The large disadvantage is that these tests are time-consuming and expensive because of the necessity of high-quality sampling of a undisturbed structure. Such factors should be taken into consideration as well as changes of temperature occurring in the environment, evaporation of water and the possibility of appearance of privileged paths of seepage or difficulty of realization of investigations at small stresses.

A test-stand for investigations on the soil permeability, especially for fine-grained soils, should have the following features:

possibility of precise measurement of the seepage velocity "V" in a large range of hydraulic gradients,

possibility of controlling changes occurring in the structure of a soil and smooth realization of the investigations without evoking such changes,

possibility to renew the in situ conditions in the soil with elimination of the air, swelling and water evaporation.

Modern investigative apparatus deserves our special attention - especially flow-pump devices [15], [27] and a Rowe's hydraulic consolidation cell [26]. A flow pump can cooperate with the cell of any device making the reconsolidation of a sample possible. Applying it, we can directly obtain a high-credibility value of the permeability coefficient. The advantage of the Rowe´s cell is the possibility to realize measurements of compressibility, consolidation and permeability in four directions: two vertical (up-down, down-up) and two horizontal (centre-boundary edge, boundary edge-centre). It creates a new potential to seek how the ratio of horizontal (c_{h}) and vertical (c_{v}) consolidation coefficients as well as the ratio of horizontal (k_{h}) and vertical (k_{v}) permeability coefficients are correlated with the internal microstructure of the same sample of a soil. The modern Rowe´s hydraulic consolidation cell is characterized by high accuracy and considerably - in comparison with traditional methods - better capabilities of laboratory soil tests. It makes it possible to examine natural and compacted soils, both in small and large samples [26]. The combination both these research methods (flow-pump and Rowe´s cell) seems to be the best solution which, in the future, will appear fruitful for the discussion about still remaining doubts connected with water flow in cohesive soils.

The investigations [19] prove that the anisotropy of the stress state expressed by the coefficient of earth pressure at rest K_{0} is correlated with the anisotropy of permeability and consolidation expressed by relation: (_{}). Heavily overconsolidated pliocene clays from Stegny in Warsaw are characterized by the coefficient K_{0DMT} = K_{0CPTU} = 1,25 within all the profile. Simultaneously, in oedometric tests the orientation of samples does not significantly affect the changes of the consolidation coefficient. In SEM analysis [7], one observes similarity, that clays do not show a significant anisotropy of the permeability coefficient.

The last thing to discuss is the agreement of values of the permeability coefficients established in field and laboratory tests. This question still causes difficulties to engineers. Thus, introduction of modern equipment and suitable methodology into practice is essential. This problem is talked over in [19], [20], [21]. Methodology of examinations of cohesive soils that aim at the determination of flow parameters as well as at the evaluation of migration of contaminations in subsoils should be based on the analysis of results of in situ observations and those obtained in a laboratory. The application of both experimental methods (field and laboratory) combines the advantages and eliminates the disadvantages. The agreement between field and laboratory results raises the credibility of investigations. Results established in field and laboratory can only be comparable if:

the soil for laboratory tests is sampled from a place near to in situ tests,

the examination is carried out in the same state of stress (at corresponding depths),

the scale of investigations is preserved, which means that the soil samples used in experiments have similar volumes (local point space research),

the natural structure of the soil is preserved in investigations,

applied pressures do not change the soil structure,

applied gradients do not change the water flow regime, and Darcy´s law is fulfilled,

the same direction of water flow is preserved,

the same saturation ratio S

_{r}is preserved.

The correct estimation of the permeability coefficient requires a properly matched and adapted measuring apparatus, well elaborated methodology of research and proper interpretation of measurement results. The introduction of suggested conditions into the methodology of research of seepage parameters will enable one to obtain conformed values of the permeability coefficient from field and laboratory tests.

**SUMMARY**

If new measuring techniques, which enable the examination of flows in directions perpendicular to each other, are applied for the same reconsolidated soil sample in the in situ conditions, it will be possible to widen the interpretation of measurement results from the consolidation and permeability tests.

So far, the best method of the determination of the permeability coefficient in cohesive soils is the constant-flow rate test (flow-pump method). Among research methods, however, the new generation of devices is represented by the Rowe's hydraulic consolidation cell and a syringe flow-pump equipped with a step motor. The Rowe's cell enables one to carry out direct examinations on the consolidation and permeability in vertical and horizontal directions.

There exists a big need to perform tests on the consolidation and permeability parameters in cohesive soils differing from each other by the coefficient of earth pressure at rest K_{0}. Therefore, investigations carried out in the Rowe´s cell with the flow-pump technique used can play an essential role in the nearest future.

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Mariusz Sobolewski

Department of Civil Engineering and Geodesy,

Warsaw Agricultural University, Poland

Nowoursynowska St. 159

02-776 Warsaw, Poland

email: mariusz_sobolewski@sggw.pl

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