CN105259088A - Method and device for quickly determining permeability functions of unsaturated soil - Google Patents

Abstract

The invention discloses a method and a device for quickly determining permeability functions of unsaturated soil. The method comprises the following steps: carrying out discretization and inverse solving on a partial differential equation of a basic soil water movement equation Richards by applying a forward Euler method and a backward Euler method to obtain two permeability coefficient expressions of the unsaturated soil; then measuring a series of data that the volumetric water content theta t at detla z in a sample and tension ht change along the time through a constant water head one-dimensional vertical unsaturated infiltration test; substituting experimental data into obtained two expressions; combining calculation results of the two expressions to quickly and accurately obtain the permeability functions of the unsaturated soil. The experimental device comprises a sample cylinder body, a measuring system, a water supply system and a water collecting system; the water supply system is used for providing constant water head water source required by the test; the water collecting system is used for collecting and measuring water yield; the measuring system comprises a sensor for measuring the theta t and the tension ht and an automatic acquiring device for acquiring data; the sensor is buried at a fixed position delta z inside the sample cylinder.

Description

A kind of method for determining unsaturated soil perviousness function fast and device

Technical field

The present invention relates to unsaturated soil infiltration coefficient measuring field, particularly a kind of method for determining unsaturated soil perviousness function fast and device.

Background technology

Funtcional relationship between Unsaturated Hydraulic Conductivity and water content of soil is called perviousness function.The soil body major part that earth surface is covered with is in unsaturated state, and along with the reduction of saturation degree, the amplitude of the Unsaturated Hydraulic Conductivity reduction of soil can produce the change of several even greater number level.Therefore, how to determine the Unsaturated Hydraulic Conductivity of soil, then become a key issue in the unsaturated seepage such as Geotechnical Engineering and the contaminant transportation analyses such as common slope project, foundation works, dam.

At present, the acquisition of the unsaturation perviousness function of soil is determined mainly through experimental formula (indirect method) and permeability test (direct method).Because unsaturated soil permeability test all requires very high for test apparatus, process of the test and test period, the soil-water characteristic curve of unsaturated soil is nearly all adopted to predict in practical application, this semiempirical defining method does not have universality, usually occur that this semiempirical unsaturated soil perviousness function is abused in a large number, and cause Calculation results and Practical Project to differ greatly.Therefore, the perviousness function of unsaturated soil is measured preferably by test.

Conventional test method is divided into steady state test method (namely flow velocity does not change in time) and unstable state test method (namely flow velocity changes in time).Due to the low-permeability of unsaturated soil under Super matrix suction, make steady state test method extremely consuming time, therefore unstable state test method is more favored, wherein the most frequently used is transient state profile method, measure in test the tension force of soil sample in nonsteady state water flow and volumetric(al) moisture content distribution and over time, in process of the test, hydraulic gradient and flow velocity change all in time, then utilize volumetric(al) moisture content to calculate flow velocity, provide infiltration coefficient by the ratio of flow velocity and hydraulic gradient.Transient state profile method process of the test is very complicated, control flow boundary condition, and prevent any position of sample from having obvious saturated surface or saturated, the time cycle is also longer.Relative to flow boundary condition, head boundary condition easily will control and stablize many, therefore research and develop a kind of by controlling head boundary condition, experimental provision and method that unsaturated soil permeability test also can obtain unsaturated soil perviousness function can being carried out fast, great for unsaturated soil theory is applied to engineering significance.

By carrying out discrete to the partial differential form of soil water movement governing equation, obtain the numerical solution formula of unsaturated soil infiltration coefficient, according to numerical solution formula, determining unsaturated soil perviousness function quickly and accurately in conjunction with simply determining the test of head One-dimensional Vertical unsaturated filtration, is basic thought of the present invention.

Summary of the invention

Technical matters to be solved by this invention is to provide a kind of method for determining unsaturated soil perviousness function fast and device, utilizing forward direction Euler method and backward Euler method by carrying out discretize to soil water movement fundamental equation Richards partial differential equation and inverting solves, obtaining two kinds of unsaturated soil infiltration coefficient expression formulas and head One-dimensional Vertical unsaturated filtration experimental provision is determined in research and development; The volumetric(al) moisture content θ at Δ z place in sample is recorded by determining the test of head One-dimensional Vertical unsaturated filtration _tand the time dependent a series of data of tension force ht, experimental data is substituted into two kinds of infiltration coefficient expression formulas of gained, the result of calculation of associating two kinds of expression formulas can obtain the perviousness function of unsaturated soil quickly and accurately.

For solving the problems of the technologies described above, the technical solution adopted in the present invention is as follows:

For determining a method for unsaturated soil perviousness function fast, it is characterized in that comprising the following steps:

1) utilizing forward direction Euler method and backward Euler method by carrying out discretize to soil water movement fundamental equation Richards partial differential equation and inverting solves, obtaining two kinds of Unsaturated Hydraulic Conductivity expression formulas:

$K_t=\frac{K_s}{1-h^{\′}\left({\mathrm{\θ}}_t\right)\·\frac{{\mathrm{\θ}}_t-{\mathrm{\θ}}_s}{\mathrm{\Δ}z}}---\left(I\right)$

$K_t=\frac{\frac{{\mathrm{\θ}}_{t+1}-{\mathrm{\θ}}_t}{\mathrm{\Δ}t}\·\mathrm{\Δ}z-K_s}{h^{\′}\left({\mathrm{\θ}}_t\right)\·\frac{{\mathrm{\θ}}_t-{\mathrm{\θ}}_s}{\mathrm{\Δ}z}-1}---\left(II\right)$

In formula:

K _trepresent volumetric(al) moisture content θ _tcorresponding infiltration coefficient;

K _srepresent saturation permeability coefficient;

represent that matric potential h is for volumetric(al) moisture content θ differentiate;

Δ z represents mensuration volumetric(al) moisture content θ _tt changes the distance of measuring point place distance water and soil surface of contact in time;

θ _srepresent saturated volume water cut;

Formula (I) is containing volumetric(al) moisture content θ and space length Δ z Two Variables, and formula (II) is containing volumetric(al) moisture content θ, time Δ t and space length Δ z tri-variablees;

2) utilize unsaturated soil permeability experimental facility, recorded the volumetric(al) moisture content θ at soil sample test point Δ z place by the test of One-dimensional Vertical unsaturated filtration _tand the time dependent a series of data of tension force ht, and obtained data are substituted into formula (I) and formula (II), determine the perviousness function of unsaturated soil fast.

For determining an experimental provision for unsaturated soil perviousness function fast, comprising sample cylindrical shell, measurement system, water gathering system and water system, it is characterized in that:

Measurement system comprises for measuring volumetric(al) moisture content θ _tsoil moisture sensor and soil tension pick-up for measuring tension force ht, and for the data collector of data acquisition, soil moisture sensor and soil tension pick-up test lead are embedded in the inner Δ z place of test specimen tube, and the other end is connected with data collector;

Filtering layer and lower filtering layer is provided with in sample cylindrical shell, upper filtering layer is respectively filter, upper woven wire, upper filter paper from top to bottom, lower filtering layer is respectively lower filter paper, lower woven wire, lower filter from top to bottom, for filling soil sample in space between upper filtering layer and lower filtering layer, sample cylindrical shell a segment distance has two openings below loaded filter, for arranging soil moisture sensor and soil tension pick-up;

Water system comprises for bucket, submersible pump, water inlet pipe and run-down pipe, submersible pump is placed on in bucket, submersible pump is connected with sample cylindrical shell by water inlet pipe, water inlet pipe one end is connected with submersible pump, the other end is positioned at above the upper filtering layer of sample cylinder inboard wall, run-down pipe one end is connected with sample cylindrical shell, and link position is positioned at the below of water inlet pipe and sample cylindrical shell link position, and the run-down pipe other end is positioned at for bucket;

Water gathering system comprises drainpipe, water storage bottle and balance, balance is placed on water gathering system base, and water storage bottle is placed on balance, the ponding that water storage bottle flows out for collecting test, drainpipe one end is placed in the below of lower filtering layer in sample cylindrical shell, and the other end stretches in water storage bottle.

In preferred scheme, described run-down pipe and the link position of test specimen tube are positioned at 5cm place above filtering layer, and for providing, 5cm's determine head boundary condition.

In preferred scheme, be provided with test sales counter below described sample cylindrical shell, sample cylindrical shell is placed on above test sales counter, and water gathering system is placed on below test sales counter.

In preferred scheme, described water storage bottle is provided with water storage bottle cap, and drainpipe stretches in water storage bottle through water storage bottle cap, and water storage bottle cap and water storage bottle, drainpipe fit tightly the sealing ensureing water storage bottle.

In preferred scheme, be provided with top cover above described sample cylindrical shell, top cover can be opened or close.

In preferred scheme, the termination that described water inlet pipe is positioned at the top of filtering layer on sample cylindrical shell is provided with sprinkler head.

A kind of method for determining unsaturated soil infiltration coefficient fast provided by the invention and device, by adopting said method and apparatus structure, have following beneficial effect:

(1) utilize forward direction Euler method and backward Euler method to carry out discrete and inverting to soil water movement fundamental equation to solve, obtain two kinds of unsaturated soil perviousness function expressions, directly just can calculate unsaturated soil infiltration coefficient by the expression formula drawn in conjunction with simple one dimension permeability intensity, obtain compared with infiltration coefficient with transient state profile method by calculating in real time the flow velocity that changes and hydraulic gradient, method is more simple, and function expression meaning clearly;

(2) only need to know Δ z place, fixed position volumetric(al) moisture content θ and tension force h _tthe relation of t in time, substituting into above-mentioned unsaturated soil perviousness function expression just can in the hope of the unsaturation perviousness function of soil, and being combined with the result of calculation under higher volumes water cut at lower volumetric(al) moisture content by two calculation expressions just to obtain the unsaturation perviousness function of soil more accurately;

(3) Design of Waterworks is become a kind of method of constant head, utilize submersible pump by the shower nozzle of the air free water in stainless steel drum by water inlet pipe end, evenly be sprayed onto above filter, by filter, water is uniformly distributed in the circular soil body of infiltration, along with the rising of water level, when water level reaches gap height, unnecessary water will overflow from water delivering orifice, thus arrive the object controlling constant head pressure, for test provides stable boundary condition.

Accompanying drawing explanation

Below in conjunction with drawings and Examples, the invention will be further described:

Fig. 1 is device one-piece construction schematic diagram of the present invention.

Fig. 2 simplification Infiltration Model of the present invention schematic diagram.

In figure: top cover 1, sprinkler head 2, water inlet pipe 3, sample cylindrical shell 4, water 5, upper filter 6, upper woven wire 7, upper filter paper 8, soil moisture sensor 9, soil tension pick-up 10, soil sample 11, lower filter paper 12, lower woven wire 13, lower filter 14, opening 15, drainpipe 16, water storage bottle cap 17, water storage bottle 18, ponding 19, balance 20, testing table 21, water gathering system base 22, run-down pipe 23, for bucket 24, submersible pump 25, water and soil surface of contact 26, data collector 27.

Embodiment

Derivation about unsaturated soil infiltration coefficient expression formula:

1. soil water movement governing equation

The One-dimensional Vertical Infiltration form of soil water movement fundamental equation is as follows:

$\frac{\∂\mathrm{\θ}}{\∂t}=\frac{\∂}{\∂z}\[K\left(\mathrm{\θ}\right)\·\frac{\∂h}{\∂z}\]-\frac{\∂K\left(\mathrm{\θ}\right)}{\∂z}---\left(III\right)$

In formula:

θ represents volumetric(al) moisture content;

T represents the time;

K (θ) represents the infiltration coefficient corresponding to θ;

H represents matric potential.

Order then formula (III) can be changed to following form:

$\frac{\∂\mathrm{\θ}}{\∂t}=\frac{\∂}{\∂z}\[K\left(\mathrm{\θ}\right)\·\frac{\∂h}{\∂\mathrm{\θ}}\·\frac{\∂\mathrm{\θ}}{\∂z}\]-\frac{\∂K\left(\mathrm{\θ}\right)}{\∂z}---\left(IV\right)$

2. the discrete and inverting of soil water movement governing equation solves

In one dimension unsaturated filtration model, if i represents locus, j represents time location, and the time interval is Δ t, and space interval is Δ z.Can adopt respectively forward Euler method and backward Euler method discrete and inverting carried out to equation (IV) solve, obtain two kinds of coefficient of permeability K (θ) expression formulas.

Set up simplification One-dimensional Vertical Infiltration discrete model as shown in Figure 2, wherein blue portion represents the water-filling layer that soil sample top is very thin, i.e. permeable stone part, and khaki part represents soil sample.Set up 0,1,2 three location point at earth pillar vertical direction, 0 and 1 is 2 points closely near water-soil environment, can think that this water cut of 2 equals saturation moisture content all the time, not change in time.

Euler method and Euler method is as follows to carrying out discrete and inverting solution procedure to equation (IV) backward forward:

2.1 forward Euler method discrete and inverting carried out to equation (IV) solve:

For $\frac{\∂\mathrm{\θ}}{\∂t}=\frac{\∂}{\∂z}\[K\left(\mathrm{\θ}\right)\·\frac{\∂h}{\∂\mathrm{\θ}}\·\frac{\∂\mathrm{\θ}}{\∂z}\]-\frac{\∂K\left(\mathrm{\θ}\right)}{\∂z}=\frac{\∂K\·(\frac{\∂h}{\∂\mathrm{\θ}}\·\frac{\∂\mathrm{\θ}}{\∂z}-1)}{\∂z}$

If $h^{\′}\left(\mathrm{\θ}\right)=\frac{\∂h}{\∂\mathrm{\θ}},f=K\·\frac{\∂h}{\∂\mathrm{\θ}}\·\frac{\∂\mathrm{\θ}}{\∂z}-1=K\·\left(h^{\′}\right(\mathrm{\θ})\·\frac{\∂\mathrm{\θ}}{\∂z}-1),$

Then:

$\frac{\∂\mathrm{\θ}}{\∂t}=\frac{\∂f}{\∂z}---\left(V\right)$

Forward direction Euler method is used to carry out discrete to Time and place,

The left side $\frac{\∂\mathrm{\θ}}{\∂t}=\frac{{\mathrm{\θ}}_i^{j+1}-{\mathrm{\θ}}_i^j}{\mathrm{\Δ}t}$

The right $\frac{\∂f}{\∂z}=\frac{f_{i+1}^j-f_i^j}{\mathrm{\Δ}z}$

$f_{i+1}^j=K_{i+1}^j\[h^{\′}\left({\mathrm{\θ}}_{i+1}^j\right)\·{\left(\frac{\∂\mathrm{\θ}}{\∂z}\right)}_{i+1}^j-1\]=K_{i+1}^j\[h^{\′}\left({\mathrm{\θ}}_{i+1}^j\right)\·\frac{{\mathrm{\θ}}_{i+1}^j-{\mathrm{\θ}}_i^j}{\mathrm{\Δ}z}-1\]$

$f_i^j=K_i^j\[h^{\′}\left({\mathrm{\θ}}_i^j\right)\·{\left(\frac{\∂\mathrm{\θ}}{\∂z}\right)}_i^j-1\]=K_i^j\[h^{\′}\left({\mathrm{\θ}}_i^j\right)\·\frac{{\mathrm{\θ}}_i^j-{\mathrm{\θ}}_{i-1}^j}{\mathrm{\Δ}z}-1\]$

Above-mentioned two formulas substitution formula (V) are obtained final discrete form as follows:

$\frac{{\mathrm{\θ}}_i^{j+1}-{\mathrm{\θ}}_i^j}{\mathrm{\Δ}t}=\frac{1}{\mathrm{\Δ}z}\{K_{i+1}^j\[h^{\′}\left({\mathrm{\θ}}_{i+1}^j\right)\·\frac{{\mathrm{\θ}}_{i+1}^j-{\mathrm{\θ}}_i^j}{\mathrm{\Δ}z}-1\]-K_i^j\[h^{\′}\left({\mathrm{\θ}}_i^j\right)\·\frac{{\mathrm{\θ}}_i^j-{\mathrm{\θ}}_{i-1}^j}{\mathrm{\Δ}z}-1\]\}$

As shown in Figure 2, as i=1, above-mentioned equation is expressed as follows the Infiltration Model schematic diagram simplified:

$\frac{{\mathrm{\θ}}_1^{j+1}-{\mathrm{\θ}}_1^j}{\mathrm{\Δ}t}=\frac{1}{{\mathrm{\Δz}}_2}\{K_2^j\[h^{\′}\left({\mathrm{\θ}}_2^j\right)\·\frac{{\mathrm{\θ}}_2^j-{\mathrm{\θ}}_1^j}{{\mathrm{\Δz}}_2}-1\]-K_1^j\[h^{\′}\left({\mathrm{\θ}}_1^j\right)\·\frac{{\mathrm{\θ}}_1^j-{\mathrm{\θ}}_0^j}{{\mathrm{\Δz}}_1}-1\]\}---\left(VI\right)$

Position i=0 and i=1 is the upper and lower 2 adjacent points of water and soil surface of contact 26, therefore with not becoming in time, is saturation moisture content θ _s, for saturation permeability coefficient K _s, then formula (VI) is changed to:

$\frac{{\mathrm{\θ}}_s-{\mathrm{\θ}}_s}{\mathrm{\Δ}t}=\frac{1}{{\mathrm{\Δz}}_2}\{K_2^j\[h^{\′}\left({\mathrm{\θ}}_2^j\right)\·\frac{{\mathrm{\θ}}_2^j-{\mathrm{\θ}}_s}{{\mathrm{\Δz}}_2}-1\]-K_1^j\[h^{\′}\left({\mathrm{\θ}}_s\right)\·\frac{{\mathrm{\θ}}_s-{\mathrm{\θ}}_s}{{\mathrm{\Δz}}_1}-1\]\}$

$0=\frac{1}{{\mathrm{\Δz}}_2}\{K_2^j\[h^{\′}\left({\mathrm{\θ}}_2^j\right)\·\frac{{\mathrm{\θ}}_2^j-{\mathrm{\θ}}_s}{{\mathrm{\Δz}}_2}-1\]+K_s\}$

Then:

$K_2^j=\frac{K_s}{1-h^{\′}\left({\mathrm{\θ}}_2^j\right)\·\frac{{\mathrm{\θ}}_2^j-{\mathrm{\θ}}_s}{{\mathrm{\Δz}}_2}}---\left(VII\right)$

As can be seen from formula (VII), the infiltration coefficient expression formula after derivation be with water content sensor to the separation delta z of water and soil surface of contact and volumetric(al) moisture content θ for dependent variable, it doesn't matter with time t.Therefore, only need be recorded soil sample volumetric(al) moisture content θ and the tension force h in any j moment at measuring point Δ z place by the test of one dimension unsaturation Vertical Infiltration, just can calculate corresponding infiltration coefficient by through type (VII), bring not test figure in the same time into formula (VII) respectively and calculate the infiltration coefficient that just can obtain corresponding to a series of different volumes water cut, and then this obtains unsaturation perviousness function K (θ).

2.2 use Euler method backward to carry out discrete and inverting to equation (IV) solves:

For $\frac{\∂\mathrm{\θ}}{\∂t}=\frac{\∂}{\∂z}\[K\left(\mathrm{\θ}\right)\·\frac{\∂h}{\∂\mathrm{\θ}}\·\frac{\∂\mathrm{\θ}}{\∂z}\]-\frac{\∂K\left(\mathrm{\θ}\right)}{\∂z}=\frac{\∂K\·(\frac{\∂h}{\∂\mathrm{\θ}}\·\frac{\∂\mathrm{\θ}}{\∂z}-1)}{\∂z}$

If $h^{\′}\left(\mathrm{\θ}\right)=\frac{\∂h}{\∂\mathrm{\θ}},f=K\·\frac{\∂h}{\∂\mathrm{\θ}}\·\frac{\∂\mathrm{\θ}}{\∂z}-1=K\·\left(h^{\′}\right(\mathrm{\θ})\·\frac{\∂\mathrm{\θ}}{\∂z}-1),$

Then:

$\frac{\∂\mathrm{\θ}}{\∂t}=\frac{\∂f}{\∂z}---\left(VIII\right)$

Forward direction Euler method is used to carry out discrete to Time and place

The left side $\frac{\∂\mathrm{\θ}}{\∂t}=\frac{{\mathrm{\θ}}_i^{j+1}-{\mathrm{\θ}}_i^j}{\mathrm{\Δ}t}$

The right $\frac{\∂f}{\∂z}=\frac{f_i^j-f_{i-1}^j}{\mathrm{\Δ}z}$

$f_i^j=K_i^j\[h^{\′}\left({\mathrm{\θ}}_i^j\right)\·{\left(\frac{\∂\mathrm{\θ}}{\∂z}\right)}_i^j-1\]=K_i^j\[h^{\′}\left({\mathrm{\θ}}_i^j\right)\·\frac{{\mathrm{\θ}}_i^j-{\mathrm{\θ}}_{i-1}^j}{\mathrm{\Δ}z}-1\]$

$f_{i-1}^j=K_{i-1}^j\[h^{\′}\left({\mathrm{\θ}}_{i-1}^j\right)\·{\left(\frac{\∂\mathrm{\θ}}{\∂z}\right)}_{i-1}^j-1\]=K_{i-1}^j\[h^{\′}\left({\mathrm{\θ}}_{i-1}^j\right)\·\frac{{\mathrm{\θ}}_{i-1}^j-{\mathrm{\θ}}_{i-2}^j}{\mathrm{\Δ}z}-1\]$

Above-mentioned two formulas substitution formula (VIII) are obtained final discrete form as follows:

$\frac{{\mathrm{\θ}}_i^{j+1}-{\mathrm{\θ}}_i^j}{\mathrm{\Δ}t}=\frac{1}{\mathrm{\Δ}z}\{K_i^j\[h^{\′}\left({\mathrm{\θ}}_i^j\right)\·\frac{{\mathrm{\θ}}_i^j-{\mathrm{\θ}}_{i-1}^j}{\mathrm{\Δ}z}-1\]-K_{i-1}^j\[h^{\′}\left({\mathrm{\θ}}_{i-1}^j\right)\·\frac{{\mathrm{\θ}}_{i-1}^j-{\mathrm{\θ}}_{i-2}^j}{\mathrm{\Δ}z}-1\]\}---\left(IX\right)$

As shown in Figure 2, as i=2, above-mentioned equation is expressed as follows the Infiltration Model schematic diagram simplified:

$\frac{{\mathrm{\θ}}_2^{j+1}-{\mathrm{\θ}}_2^j}{\mathrm{\Δ}t}=\frac{1}{{\mathrm{\Δz}}_2}\{K_2^j\[h^{\′}\left({\mathrm{\θ}}_2^j\right)\·\frac{{\mathrm{\θ}}_2^j-{\mathrm{\θ}}_1^j}{{\mathrm{\Δz}}_2}-1\]-K_1^j\[h^{\′}\left({\mathrm{\θ}}_1^j\right)\·\frac{{\mathrm{\θ}}_1^j-{\mathrm{\θ}}_0^j}{{\mathrm{\Δz}}_1}-1\]\}---\left(X\right)$

Position i=0 and i=1 is the upper and lower 2 adjacent points of water and soil surface of contact 26, therefore with not becoming in time, is saturation moisture content θ _s, for saturation permeability coefficient K _s, then formula (X) is changed to:

$\frac{{\mathrm{\θ}}_2^{j+1}-{\mathrm{\θ}}_2^j}{\mathrm{\Δ}t}=\frac{1}{{\mathrm{\Δz}}_2}\{K_2^j\[h^{\′}\left({\mathrm{\θ}}_2^j\right)\·\frac{{\mathrm{\θ}}_2^j-{\mathrm{\θ}}_s}{{\mathrm{\Δz}}_2}-1\]-K_1^j\[h^{\′}\left({\mathrm{\θ}}_s\right)\·\frac{{\mathrm{\θ}}_s-{\mathrm{\θ}}_s}{{\mathrm{\Δz}}_1}-1\]\}$

$\frac{{\mathrm{\θ}}_2^{j+1}-{\mathrm{\θ}}_2^j}{\mathrm{\Δ}t}=\frac{1}{{\mathrm{\Δz}}_2}\left\{K_2^j\[h^{\′}\left({\mathrm{\θ}}_2^j\right)\·\frac{{\mathrm{\θ}}_2^j-{\mathrm{\θ}}_s}{{\mathrm{\Δz}}_2}-1\]-K_s\right\}$

Then:

$K_2^j=\frac{\frac{{\mathrm{\θ}}_2^{j+1}-{\mathrm{\θ}}_2^j}{\mathrm{\Δ}t}\·{\mathrm{\Δz}}_2-K_s}{h^{\′}\left({\mathrm{\θ}}_2^j\right)\·\frac{{\mathrm{\θ}}_2^j-{\mathrm{\θ}}_s}{{\mathrm{\Δz}}_2}-1}---\left(XI\right)$

As can be seen from formula (XI), the infiltration coefficient expression formula after derivation be with time t and water content sensor to the separation delta z of water and soil surface of contact and volumetric(al) moisture content θ for dependent variable.Therefore, only need be recorded soil sample volumetric(al) moisture content θ and the tension force h in any j moment at measuring point Δ z place by the test of one dimension unsaturation Vertical Infiltration, just can calculate corresponding infiltration coefficient by through type (XI), bring not test figure in the same time into formula (XI) respectively and calculate the infiltration coefficient that just can obtain corresponding to a series of different volumes water cut, and then this obtains unsaturation perviousness function K (θ).

In sum, by obtaining the expression formula of two kinds of Unsaturated Hydraulic Conductivity to the derivation of One-dimensional Vertical Infiltration equation, afterwards by infiltrating the simplify processes of physical model to one dimension, draw two kinds of forms of the Unsaturated Hydraulic Conductivity expression formula under a point position control:

$K_t=\frac{K_s}{1-h^{\′}\left({\mathrm{\θ}}_t\right)\·\frac{{\mathrm{\θ}}_t-{\mathrm{\θ}}_s}{\mathrm{\Δ}z}}---\left(I\right)$

$K_t=\frac{\frac{{\mathrm{\θ}}_{t+1}-{\mathrm{\θ}}_t}{\mathrm{\Δ}t}\·\mathrm{\Δ}z-K_s}{h^{\′}\left({\mathrm{\θ}}_t\right)\·\frac{{\mathrm{\θ}}_t-{\mathrm{\θ}}_s}{\mathrm{\Δ}z}-1}---\left(II\right)$

In formula:

K _trepresent volumetric(al) moisture content θ _tcorresponding infiltration coefficient;

K _srepresent saturation permeability coefficient;

represent that matric potential is for volumetric(al) moisture content differentiate;

Δ z represents mensuration volumetric(al) moisture content θ _tt changes the distance of measuring point place distance water and soil surface of contact in time;

θ _srepresent saturated volume water cut.

By Numerical Experimental Method, reliability demonstration is carried out to formula (I) and formula (II), find can not predict preferably compared with the Unsaturated Hydraulic Conductivity under low water content condition containing the unsaturation perviousness function expression (I) of time t, the expression formula (II) containing free t can calculate the unsaturation perviousness function under high-moisture condition more accurately.The result of calculation of final decision associating two expression formulas, combine to obtain more accurate continuous print unsaturated soil coefficient of permeability K (θ) with formula (II) result of calculation under higher volumes water cut at lower volumetric(al) moisture content by formula (I), and then obtain unsaturated soil perviousness function.

Claims (8)

1., for determining a method for unsaturated soil perviousness function fast, it is characterized in that comprising the following steps:

1) utilizing forward direction Euler method and backward Euler method by carrying out discretize to soil water movement fundamental equation Richards partial differential equation and inverting solves, obtaining two kinds of Unsaturated Hydraulic Conductivity expression formulas:

$K_t=\frac{K_s}{1-h^{\′}\left({\mathrm{\θ}}_t\right)\·\frac{{\mathrm{\θ}}_t-{\mathrm{\θ}}_s}{\mathrm{\Δ}z}}---\left(I\right)$

$K_t=\frac{\frac{{\mathrm{\θ}}_{t+1}-{\mathrm{\θ}}_t}{\mathrm{\Δ}t}\·\mathrm{\Δ}z-K_s}{h^{\′}\left({\mathrm{\θ}}_t\right)\·\frac{{\mathrm{\θ}}_t-{\mathrm{\θ}}_s}{\mathrm{\Δ}z}-1}---\left(II\right)$

In formula:

K _trepresent volumetric(al) moisture content θ _tcorresponding infiltration coefficient;

K _srepresent saturation permeability coefficient;

represent that matric potential h is for volumetric(al) moisture content θ differentiate;

Δ z represents mensuration volumetric(al) moisture content θ _tt changes the distance of measuring point place distance water and soil surface of contact in time;

θ _srepresent saturated volume water cut;

Formula (I) is containing volumetric(al) moisture content θ and space length Δ z Two Variables, and formula (II) is containing volumetric(al) moisture content θ, time Δ t and space length Δ z tri-variablees;

2) utilize unsaturated soil permeability experimental facility, recorded the volumetric(al) moisture content θ at soil sample test point Δ z place by the test of One-dimensional Vertical unsaturated filtration _tand the time dependent a series of data of tension force ht, and obtained data are substituted into formula (I) and formula (II), determine the perviousness function of unsaturated soil fast.

2. a kind of method for determining unsaturated soil perviousness function fast according to claim 1, is characterized in that: described formula (I) is for the situation of low water content, and formula (II) is for the situation of high-moisture.

3. for determining an experimental provision for unsaturated soil perviousness function fast, comprising sample cylindrical shell, measurement system, water gathering system and water system, it is characterized in that: measurement system comprises for measuring volumetric(al) moisture content θ _tsoil moisture sensor (9) and soil tension pick-up (10) for measuring tension force ht, and for the data collector (27) of data acquisition, soil moisture sensor (9) and soil tension pick-up (10) test lead are embedded in the inner Δ z place of test specimen tube, and the other end is connected with data collector (27);

Filtering layer and lower filtering layer is provided with in sample cylindrical shell (4), upper filtering layer is respectively filter (6) from top to bottom, upper woven wire (7), upper filter paper (8), lower filtering layer is respectively lower filter paper (12) from top to bottom, lower woven wire (13), lower filter (14), for filling soil sample (11) in space between upper filtering layer and lower filtering layer, below the upper loaded filter of sample cylindrical shell (4), a segment distance has two openings (15), for arranging soil moisture sensor (9) and soil tension pick-up (10),

Water system comprises for bucket (24), submersible pump (25), water inlet pipe (3) and run-down pipe (23), submersible pump (25) is placed on in bucket (24), submersible pump (25) is connected with sample cylindrical shell (4) by water inlet pipe (3), water inlet pipe (3) one end is connected with submersible pump (25), the other end is positioned at above the upper filtering layer of sample cylindrical shell (4) inwall, run-down pipe (23) one end is connected with sample cylindrical shell (4), link position is positioned at the below of water inlet pipe (3) and sample cylindrical shell (4) link position, run-down pipe (23) other end is positioned at for bucket (24),

Water gathering system comprises drainpipe (16), water storage bottle (18) and balance (20), balance (20) is placed on water gathering system base (22), water storage bottle (18) is placed on balance (20), the ponding (19) that water storage bottle (18) flows out for collecting test, drainpipe (16) one end is placed in the below of lower filtering layer in sample cylindrical shell (4), and the other end stretches in water storage bottle (18).

4. a kind of experimental provision for determining unsaturated soil perviousness function fast according to claim 3, is characterized in that: described run-down pipe (23) is positioned at sample cylindrical shell (4) position of 5cm above filtering layer with the link position of test specimen tube (4).

5. a kind of experimental provision for determining unsaturated soil perviousness function fast according to claim 3, it is characterized in that: described water gathering system base (22) is provided with testing table (21), sample cylindrical shell (4) is placed on testing table (21), and water gathering system is arranged on testing table (21) below.

6. a kind of experimental provision for determining unsaturated soil perviousness function fast according to claim 3, it is characterized in that: described water storage bottle (18) is provided with water storage bottle cap (17), drainpipe (16) stretches in water storage bottle (18) through water storage bottle cap (17), and water storage bottle cap (17) and water storage bottle (18), drainpipe (16) fit tightly the sealing ensureing water storage bottle (18).

7. a kind of experimental provision for determining unsaturated soil perviousness function fast according to claim 3, is characterized in that: described sample cylindrical shell (4) top is provided with top cover (1), and top cover (1) can be opened or close.

8. a kind of experimental provision for determining unsaturated soil perviousness function fast according to claim 3, is characterized in that: the termination that described water inlet pipe (3) is positioned at the top of the upper filtering layer of sample cylindrical shell (4) is provided with sprinkler head (2).