1、 ASCE STANDARD ASCE/EWRI 54-10American Society of Civil EngineersStandard Guideline for the Geostatistical Estimation and Block-Averaging of Homogeneous and Isotropic Saturated Hydraulic ConductivityThis document uses both the International System of Units (SI) and customary units.HOE_FM.indd iHOE_F
2、M.indd i 6/14/2010 2:18:28 PM6/14/2010 2:18:28 PMLibrary of Congress Cataloging-in-Publication DataAmerican Society of Civil Engineers.Standard guideline for the geostatistical estimation and block-averaging of homogeneous and isotropic saturated hydraulic conductivity.p. cm.“ASCE standard ASCE/EWRI
3、 54-10.”Includes bibliographical references and index.ISBN 978-0-7844-1092-9 (alk. paper)1. Groundwater fl owMeasurementStatistical methodsStandardsUnited States. 2. Soil permeabilityMeasurementStatistical methodsStandardsUnited States. 3. Average. I. Title.TC177.A488 2010628.114dc222010017463Publis
4、hed by American Society of Civil Engineers1801 Alexander Bell DriveReston, Virginia 20191www.pubs.asce.orgThis standard was developed by a consensus standards development process which has been accredited by the American National Standards Institute (ANSI). Accreditation by ANSI, a voluntary accredi
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12、ety of Civil Engineers.All Rights Reserved.ISBN 978-0-7844-1092-9Manufactured in the United States of America.18 17 16 15 14 13 12 11 10 1 2 3 4 5HOE_FM.indd iiHOE_FM.indd ii 6/14/2010 2:18:29 PM6/14/2010 2:18:29 PMiiiSTANDARDSIn 2003, the Board of Direction approved the revision to the ASCE Rules f
13、or Standards Committees to govern the writing and maintenance of standards developed by the Society. All such standards are developed by a consensus standards process managed by the Societys Codes and Standards Committee (CSC). The consensus process includes balloting by a balanced standards committ
14、ee made up of Society members and nonmembers, balloting by the member-ship of the Society as a whole, and balloting by the public. All standards are updated or reaffi rmed by the same process at intervals not exceeding fi ve years.The following standards have been issued:ANSI/ASCE 1-82 N-725 Guideli
15、ne for Design and Analysis of Nuclear Safety Related Earth StructuresASCE/EWRI 2-06 Measurement of Oxygen Transfer in Clean WaterANSI/ASCE 3-91 Standard for the Structural Design of Composite Slabs and ANSI/ASCE 9-91 Stan-dard Practice for the Construction and Inspection of Composite SlabsASCE 4-98
16、Seismic Analysis of Safety-Related Nuclear StructuresBuilding Code Requirements for Masonry Structures (ACI 530-02/ASCE 5-02/TMS 402-02) and Specifi cations for Masonry Structures (ACI 530.1-02/ASCE 6-02/TMS 602-02)ASCE/SEI 7-10 Minimum Design Loads for Build-ings and Other StructuresSEI/ASCE 8-02 S
17、tandard Specifi cation for the Design of Cold-Formed Stainless Steel Structural MembersANSI/ASCE 9-91 listed with ASCE 3-91ASCE 10-97 Design of Latticed Steel Transmission StructuresSEI/ASCE 11-99 Guideline for Structural Condition Assessment of Existing BuildingsASCE/EWRI 12-05 Guideline for the De
18、sign of Urban Subsurface DrainageASCE/EWRI 13-05 Standard Guidelines for Installa-tion of Urban Subsurface DrainageASCE/EWRI 14-05 Standard Guidelines for Opera-tion and Maintenance of Urban Subsurface DrainageASCE 15-98 Standard Practice for Direct Design of Buried Precast Concrete Pipe Using Stand
19、ard Installations (SIDD)ASCE 16-95 Standard for Load Resistance Factor Design (LRFD) of Engineered Wood ConstructionASCE 17-96 Air-Supported StructuresASCE 18-96 Standard Guidelines for In-Process Oxygen Transfer TestingASCE 19-96 Structural Applications of Steel Cables for BuildingsASCE 20-96 Stand
20、ard Guidelines for the Design and Installation of Pile FoundationsANSI/ASCE/T h1and 1.0 SCOPEThis standard guideline outlines procedures for the geostatistical estimation and block-averaging of homogeneous and isotropic saturated hydraulic conductivity. The procedures are described in the following
21、sections, and are applicable to 1-, 2-, and 3-dimensional data sets of saturated hydraulic conductivity.1.1 GEOSTATISTICAL ESTIMATION OF THE SATURATED HYDRAULIC CONDUCTIVITYOne purpose of this guideline is to describe a proce-dure for interpolating (or estimating) the (unknown) value of saturated hy
22、draulic conductivity (K*) at an arbitrary location in an aquifer given a sample of saturated hydraulic conductivity measurements K1, K2, K3, . . . , Knmade at n locations in the same aquifer. The saturated hydraulic conductivity is treated as a spatially correlated random fi eld (denoted by K*). Fig
23、ure 1-1 depicts the pertinent situation in this instance. The saturated hydraulic conductivity is estimated at a location 0 (which, in the 3-dimensional case, would be referenced by Cartesian coordinates x0, y0, z0) using measurements K1, K2, K3, . . . , Knat various locations in an aquifer as illus
24、trated in Fig. 1-1 (where n = 15 for the sake of argument). K0and K*0denote the estimated (or interpolated) value and the unknown actual value of the saturated hydraulic conductivity at location 0, respectively. The measure-ments of saturated hydraulic conductivity are assumed to be made with the sa
25、me instrument or method that yields estimates of K* that are representative over the domain of infl uence of the measuring device or methodology. In the case of pumping tests, the domain of infl uence may extend hundreds of meters or farther from the pumping well. The area of infl uence of slug test
26、s, on the other hand, extends only a few meters (say, fewer than 10 m) from the test well. The mea-surements could be made on sediment or rock samples using permeameters deployed in a laboratory. One key application of K0is the estimation of the specifi c discharge at location 0 in the coordinal dir
27、ection w, q0w, via Darcys law for a given value of the hydraulic gradient at 0 in the direction w, J0w(ASCE 2008b).HOE_01-6.indd 1HOE_01-6.indd 1 6/14/2010 2:18:20 PM6/14/2010 2:18:20 PMASCE/EWRI 54-102*K2K12K4K5K6K13K14K10K8K11K9*K1*K3*K7*K9* K15*A BCD*K*(0)FIGURE 1-1. Schematic representation of a
28、n aquifer in which 15 measurements of hydraulic conductivity (denoted by K1, K2, . . . , K15) are made and used to estimate (a) the hydraulic conductivity K*0at location 0 or (b) the block-averaged hydrau-lic conductivity over the volume ABCD. The volume of aquifer over which the block-averaged hydr
29、aulic conductivity is defi ned may have arbi-trary shape.d1d2b12KV1KV2q12FIGURE 1-2. Two cells of dimensions b d1and b d2and block-averaged saturated hydraulic conductivities KV1and KV2of a fi nite-difference grid showing the groundwater discharge q12(per unit thickness perpendicular to the plane of
30、 the drawing) between the two cells shown in the drawing. d1and d2are the lengths of the cells in a direction parallel to groundwater discharge.h2denote the average hydraulic heads in cells 1 and 2, respectively; d12= (d1+ d2)/2 is the distance between the centers of cells 1 and 2; and KHis the harm
31、onic mean of block-averaged hydraulic conductivity (Freeze and Cherry 1979, p. 34):KdddKdKHVV=+121122(1-4)in which d1and d2are the lengths of the cells in a direction parallel to groundwater discharge. Estimates of KV1and KV2are obtained with the method presented in this guideline, and these estimat
32、es are used in Eq. 1-4 to approximate the harmonic hydraulic conductivity, which, in turn, is used in Eq. 1-3 to estimate the groundwater fl ow.2.0 RANGE OF APPLICABILITY: STATISTICALLY HOMOGENEOUS AND ISOTROPIC SATURATED HYDRAULIC CONDUCTIVITYStatistical homogeneity implies that the probabilistic p
33、roperties of the saturated hydraulic conductivity are the same everywhere in the aquifer in which K* measurements are made with a similar device (deployed in the fi eld or applied in the laboratory to core samples). In this case, the saturated hydraulic conductivity measurements exhibit a constant a
34、verage and a spread of K* values about the average that are devoid of spatial trends or spatial periodic patterns (ASCE 2008a). K* measurements can be statistically homogeneous and correlated simultaneously (ASCE 2008b). In the latter instance, one must resort to geostatistics, a fi eld of statistic
35、s concerned with the study of spatially correlated variables (Journel and Huijbregts 1978), or other mathematical methods that account for spatial correlation. This standard guideline adopts the geostatistical approach. From a physical standpoint, statistical homogeneity is approximated in the fi el
36、d when geological processes produce uncon-solidated deposits (clays, silts, sands, gravels, or combinations of these) or consolidated deposits (bedrock aquifers, in the vernacular) of similar texture, porosity characteristics, and mineral composition.An aquifer exhibits isotropic saturated hydraulic
37、 conductivity when its properties are identical in any direction chosen in the analysis of groundwater fl ow. This state of nature is approximated in consolidated deposits whose physical properties are relatively undisturbed along directional axes by formation weight, tectonism, or metamorphism. It
38、is also found in unconsolidated deposits in which the depositional mechanism leads to relatively uniform formations. In contrast, the statistical analysis of anisotropic forma-tions, wherein the saturated hydraulic conductivity exhibits different values along different directions, is much more compl
39、ex than that pertinent to isotropic formations. See ASCE (2008b) to read an in-depth discussion of anisotropic saturated hydraulic conductivity.HOE_01-6.indd 2HOE_01-6.indd 2 6/14/2010 2:18:21 PM6/14/2010 2:18:21 PMASCE/EWRI 54-103The assumptions of statistical homogeneity and isotropy of the satura
40、ted hydraulic conductivity adopted in this standard guideline are synonymous to what in the geostatistical literature is called second-order stationarity of a spatial variable (K*, in this standard guideline) (de Marsily 1986, p. 288).3.0 DEFINITIONSThe following defi nitions involve several variabl
41、es for which notation is found in Section 8.0. This section also covers all variables introduced in other sections of this document.3.1 SATURATED HYDRAULIC CONDUCTIVITY (K*)K* represents the ability of a porous material to transmit groundwater. It is equal to the groundwater fl ow (volume/time) per
42、unit area of aquifer perpen-dicular to the groundwater fl ow, when the fl ow is driven by a hydraulic gradient equal to 1. K* has units of length over time. The saturated hydraulic conduc-tivity is a spatial random variable whose value varies from location to location within an aquifer.3.2 BLOCK-AVE
43、RAGED SATURATED HYDRAULIC CONDUCTIVITY (KV)Given by the following scaled integral of the saturated hydraulic conductivity over a volume V of aquifer in which x, y, and z are the Cartesian coordinates of points contained within the volume V (de Marsily 1986, p. 298):KVK x y z dx dy dzVzVyVxV= ()1*ini
44、nin, (3-1)The spatially variable nature of the saturated hydraulic conductivity is made explicit in the integral of Eq. 3-1. The average (or mean, also called the expected value) of KVequals the average of the saturated hydraulic conductivity (herein denoted by K).3.3 HYDRAULIC HEADHydraulic head is
45、 the mechanical energy of ground-water per unit weight at a specifi c point in an aquifer. It has units of length.3.4 HYDRAULIC GRADIENTHydraulic gradient is the change of hydraulic head per unit distance along the path traveled by groundwater. It is dimensionless.3.5 SPATIAL COVARIANCESpatial covar
46、iance is a measure of the degree of spatial statistical association among measurements of saturated hydraulic conductivity made at different locations in an aquifer. The focus in this document is on measurements of saturated hydraulic conductivity that are positively correlated. The spatial covarian
47、ce is related to the spatial correlation and variance of saturated hydraulic conductivity, according to the defi nition in Section 3.6 and expressed mathematically in Section 3.7. The variance of the saturated hydraulic conductivity is a special case of the spatial covariance when the latter is eval
48、uated for a separation distance between two aquifer locations equal to 0. The variance measures the spread of the saturated hydrau-lic conductivity about its mean.3.6 SPATIAL CORRELATIONSpatial correlation is a measure of the degree of spatial statistical association among saturated hydrau-lic condu
49、ctivity measurements made at different locations in an aquifer. The spatial correlation equals the spatial covariance divided by the variance of saturated hydraulic conductivity. Its defi ning equation appears in Section 3.7. This standard guideline is concerned with positively correlated saturated hydraulic conductivity measurements, in which case the spatial correlation ranges between 0 and 1. The closer the spatial correlation is to 1, the greater the degree of statistical association among saturated hydraulic conductivity measurem
