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U.S. Geological Survey Open-File Report 97-47

Cover: Sign warning motorists of subsidencehazard was erected after an earth fissuredamaged Snyder Hill Road in Pima County,Arizona, 1981.


U.S. Geological Survey Subsidence InterestGroup Conference, Proceedings of theTechnical Meeting, Las Vegas, Nevada,February 14–16, 1995By Keith R. Prince and S.A. Leake, Editors

U.S. GEOLOGICAL SURVEYOpen-File Report 97–47

Tucson, Arizona1997


U.S. DEPARTMENT OF THE INTERIORBRUCE BABBITT, Secretary

Any use of trade, product, or firm names in this publication is fordescriptive purposes only and does not constitute endorsement bythe U.S. Government.

U.S. GEOLOGICAL SURVEYGordon P. Eaton, Director

For additional informationwrite to:

Regional HydrologistU.S. Geological Survey345 Middlefield RoadMenlo Park, CA 94025-3591

Copies of this report can bepurchased from:

U.S. Geological SurveyBranch of Information ServicesBox 25286Denver, CO 80225-0286


Contents III

CONTENTS

................................................................................................................................ PageHistory of the Subsidence Interest Group by Keith R. Prince .................................................................... 1Subsidence Interest Group Conference Agenda ......................................................................................... 3Poroelasticity simulation of ground-water flow and subsurface deformation by Paul A. Hsieh ................ 5Simulation of deformation of sediments from decline of ground-water levels in an

aquifer underlain by a bedrock step by S.A. Leake and Paul A. Hsieh ................................................. 10State of subsidence modeling within the U.S. Geological Survey by Thomas J. Burbey........................... 15Deformation of a sandbar in response to changes in effective stress along the

Colorado River in the Grand Canyon, Arizona by M.C. Carpenter...................................................... 20Piezometric-extensometric estimations of specific storage in the

Albuquerque Basin, New Mexico by Charles E. Heywood .................................................................. 21Results of Global Positioning System surveys in Antelope Valley, California by Marti E. Ikehara ......... 27Deformation in the Casa Diablo geothermal well field, Long Valley Caldera,

eastern California by James F. Howle and Christopher D. Farrar ...................................................... 31Hydrogeologic effects of flooding in the partially collapsed Retsof Salt Mine,

Livingston County, New York by Dorothy H. Tepper, William M. Kappel, Todd S. Miller,and John H. Williams ............................................................................................................................ 36

CONVERSION FACTORS

In this report, temperature is reported in degrees Celsius (°C), which can be converted to degrees Fahrenheit (°F) by using the following equation:

°F = 1.8(°C) + 32

VERTICAL DATUM

Sea level: In this report, “sea level” refers to the National Geodetic Vertical Datum of 1929—A geodeticdatum derived from a general adjustment of the first-order level nets of the United States and Canada,formerly called Sea Level Datum of 1929.

Multiply By To obtain

millimeter (mm) 0.03937 inchcentimeter (cm) 0.3937 inch

meter (m) 3.281 footkilometer (km) 0.6214 milekilogram (kg) 2.205 pound

hectare (ha) 2.471 acrecubic meter per second (m3/s) 35.3107 cubic foot per secondmicroradian per year (µrad/yr) 5.73x10-5 degrees per year

liter per second (L/s) 0.2642 gallon per minuteper meter (m-1) 0.3048 per foot

Newton per meter (N/m) 0.06852 pounds per footNewton per square meter (N/m2) 0.020885 pounds per square footNewton per cubic meter (N/m3) 0.0063659 pounds per cubic foot

Pascal (Pa) 0.0001450 pounds per square inchper Pascal (Pa-1) 689.5 per square inch per pound


U.S. Geological Survey Subsidence Interest Group Conference, Proceedings of the Technical Meeting, Las Vegas, Nevada, February 14–16, 1995

HISTORY OF THE SUBSIDENCE INTEREST GROUP

By Keith R. Prince

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Land subsidence is the loss of surfaceelevation as a result of the removal ofsubsurface support. The mechanisms by whichthis can occur may be natural in origin orinduced by human activities. Common causesof land subsidence include the removal of oil,gas, and water from underground reservoirs;dissolution of limestone aquifers (sinkholes);underground mining activities; drainage oforganic soils; and hydrocompaction (the initialwetting of dry soils). Overdraft of aquifers isthe major cause of areally extensive landsubsidence, and as ground-water pumpingincreases, land subsidence also will increase.

The U.S. Geological Survey (USGS) has along-standing history of describing, mapping,and conducting process-oriented research inland subsidence. In 1955, the GeologicalSurvey formed the “Mechanics of AquiferProject” under the direction of Joseph Poland to study the processes that resultland subsidence due to the withdrawal ground water. From 1955 to 1984, thresearch team gained international renown they advanced the understanding of aquimechanics and land-subsidence theory. addition to conducting pioneering researcthis group also provided a focal point withithe USGS for the dissemination of technologand scientific understanding in aquifemechanics. In 1984, however, the “Mechaniof Aquifers Project” was terminated leaving n

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focal point for technology transfer in theUSGS.

The USGS has continued to participate inbroad spectrum of cooperative and Federafunded projects in aquifer mechanics and lasubsidence. These projects are designedidentify and monitor areas with the potentiafor land subsidence, conduct basic researchthe processes that control land subsidence the development of earth fissures, and devenew quantitative tools to predict aquifersystem deformation. In 1989, the “AquifeMechanics and Subsidence Interest Grou(referred to herein as the “Subsidence InterGroup”) was formed to facilitate technologtransfer and to provide a forum for thexchange of information and ideas amonscientists actively working in subsidence anaquifer-mechanics projects. To stimulatechnical interaction among the membscientists, periodic technical meetings are hein which the latest advances in monitoring anresearch are presented.

Introduction to Papers

This report is a compilation of short papethat are based on oral presentatiosummarizing the results of recent research twere given at the third meeting of thSubsidence Interest Group held in Las Veg

History of the Subsidence Interest Group 1


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Nevada, February 14–16, 1995. The repoincludes case studies of land subsidence aaquifer-system deformation resulting fromfluid withdrawal, geothermal developmenand mine collapse. Methods for monitorinland subsidence using Global PositioninSystem technology for the rapid and accurameasurement of changes in land-surfaaltitude also are described. The current staof numerical simulation of land subsidencin the USGS is summarized, and several the short papers deal with the developmeand application of new numerical techniquefor simulation and quantification of aquifersystem deformation.

Not all oral presentations made at thmeeting are documented in this report. Seveof the presentations were of ongoing resear

2 U.S. Geological Survey Subsidence Interest Group Conference

rtnd

t,ggtecetuseofnts

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eralch

and as such, the findings were provisional nature and were offered at the meeting stimulate scientific discussion and debaamong colleagues. The information presentin this report, although only a subset of thproceedings of the meeting in Las Vegashould help expand the scientific basis fmanagement decisions to mitigate or contrthe effects of land subsidence. The shopapers describing the results of these studprovide a cross section of ongoing researchaquifer mechanics and land subsidence aalso form an assessment of the curretechnology and “state of the science.” Thanalytical and interpretive methods describin this report will be useful to scientistinvolved in studies of ground-water hydraulicand aquifer-system deformation.

, Las Vegas, Nevada, February 14–16, 1995


SUBSIDENCE INTEREST GROUP CONFERENCE AGENDA

Las Vegas, NevadaFebruary 14–16, 1995

Time Subject Presenters

Tuesday, February 14, 1995

8:00 a.m. Welcome, Opening Comments Keith Prince, Menlo Park, Calif.

Session 1—Theoretical, Numerical, and Field Developments

8:10 Numerical simulation of two-dimensional aquifer deformation—A finite-element model based on Biot theory

Paul Hsieh, Menlo Park, Calif.

8:50 Simulation of deformation of sediments from decline of ground-water levels in an aquifer underlain by a bedrock step

Stan Leake, Tucson, Ariz.

9:30 The state of subsidence modeling Tom Burbey, Carson City, Nev.

10:10 Break

10:30 Comments on poroviscosity Don Helm, Reno, Nev.

11:10 Development and results of tilt sensors used in the study of beach deformation in the Grand Canyon

Mike Carpenter, Tucson, Ariz.

11:50 Lunch

Session 2—Measurement of Subsidence

1:00 p.m. Land-surface elevation changes associated with well-injection tests, Los Angeles County, California

Devin Galloway, Sacramento, Calif.; Don Pool, Tucson, Ariz.

1:40 Changes in subsidence patterns at Roger Lake, Edwards Air Force Base, California

James Blodgett, Sacramento, Calif.

2:20 Measurement and correlation of earth-fissure formation rates with hydrogeology, subsidence, and ground-water withdrawals in the Picacho Basin, central Arizona

Don Pool, Tucson, Ariz;Steve Slaff, Tucson, Ariz; andPhil Pearthree, Tucson, Ariz.

3:00 Break

3:20 Deformation measurements in the Albuquerque Basin of New Mexico Chuck Heywood, Albuquerque, N. Mex.

4:00 Results of Global Positioning System surveys in Antelope Valley, California Marti Ikehara, Sacramento, Calif.

4:30 IBEX—An endangered species? The design of an incremental borehole extensometer probe

Francis Riley, Menlo Park, Calif.

4:45 Adjourn

7:30 USGS Subsidence Interest Group Business Meeting

Wednesday, February 15, 1995Session 3—Subsidence Effects and Features

8:00 a.m. Land subsidence at Luke Air Force Base, Arizona Herb Schumann, Tempe, Ariz.

8:40 Deformation in the Casa Diablo and geothermal well field, eastern California Chris Farrar, Carnelian Bay, Calif.;Jim Howle, Carnelian Bay, Calif.

9:20 Break

9:40 Partial collapse of the Retsof Salt Mine, New York Dorothy Tepper, Ithaca, N.Y.

10:20 Sinkhole development in the San Xavier District, Tucson, Arizona Don Pool, Tucson, Ariz.

11:00 Lunch

12:00 p.m. Field Trip 1—Las Vegas Wash Gary Dixon, Las Vegas, Nev.;John Whitney, Yucca Mountain Project, Denver, Colo.; and Pat Glancy, Carson City, Nev.

Thursday, February 16, 1995

8:00 a.m. Field Trip 2—Subsidence in Las Vegas Valley Don Helm, Reno, Nev.; Tom Burbey, Carson City, Nev.

12:00 p.m. Adjourn

3Subsidence Interest Group Conference Agenda


This page intentionally left blank


Poroelasticity Simulation of Ground-Water Flow and Subsurface Deformation

By Paul A. Hsieh

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her

INTRODUCTION

Withdrawal of ground water causes horizontaland vertical displacements in the subsurface. If thesubsurface material is assumed to be linearlyelastic, then poroelasticity theory, originallydeveloped by Biot (1941), can be used to analyzethe coupled interaction between ground-water flowand subsurface (matrix) deformation. In this study,a finite-element model is developed to solve theaxisymmetric form of the poroelasticity equations.The model is used to analyze deformation-inducedchanges in hydraulic head, a phenomenon alsoknown as the Noordbergum effect or reversewater-level fluctuation.

POROELASTICITY MODEL

In poroelasticity theory, fluid flow is describedby Darcy’s Law and mass conservation, and matdeformation is described by Biot’s constitutivrelations and stress equilibrium. Strains aassumed to be small. In this study, it is furthassumed that (a) the subsurface is in an initial stof hydraulic and mechanical equilibrium, (bgravitational body force remains constant, (c) thmatrix grains are incompressible, and (d) the fluis compressible. Under the above assumptions, equations of poroelasticity are (Verruijt, 1969p. 342):

, (1)

and

, (2)

κ∇2h∂∂t---- ∇ u•( )

ρfgn

Kf-----------∂h

∂t------+=

G∇2uG

1 2ν–---------------∇ ∇ u•( ) ρfg∇h–+ 0=

Poroelasticity

rixereerate)e

idthe,

where h is change in hydraulic head from the initiahead, u is displacement vector of the skeletamatrix, t is time, κ is hydraulic conductivity, n isporosity, ρfg and Kf are the specific weight andbulk modulus of the fluid, respectively, and G andν are the shear modulus and drained Poisson’s rof the skeletal matrix, respectively. A numericamodel has been developed to solve taxisymmetric form of equations (1) and (2following the finite-element method of Smith anGriffiths (1988, chap. 9). In this formulationmaterial properties are assumed uniform witheach element, but properties may vary from oelement to the next. The model, therefore, may applied to solve problems with a nonuniformdistribution of properties.

SIMULATION OF DEFORMATION- INDUCED CHANGES IN HYDRAULIC HEAD

The poroelasticity model is applied to simuladeformation-induced changes in hydraulic hethat often are observed in aquitards when watepumped from an adjacent aquifer. A hypotheticsetting consists of a 100-meter thick, lateralextensive aquifer that is confined above and belby aquitards (fig. 1). The upper aquitard is 100 thick, and the lower aquitard extends to a gredepth. The water table coincides with the lansurface, which is the top of the upper aquitard.well is screened over the entire thickness of taquifer, and for simplicity, the well is assumed tbe cased throughout both aquitards. Ground wais pumped at a constant rate of 5×10-2 m3/s. Thehydraulic and mechanical properties used in tsimulation are shown in table 1. The aquife

Simulation of Ground-Water Flow and Subsurface Deformation 5


A Q U I F E R

well screen

U P P E R A Q U I T A R D

L O W E R A Q U I T A R D

land surface & water table

z

r

well

100 m

100 mcasing

casing

Q

Figure 1. Hypothetical setting of an aquifer confined aboveand below by aquitards.

properties are characteristic of an unconsolidated,sandy formation. The two aquitards have identicalproperties that are characteristic of unconsolidatedsilty deposits.

In the numerical model, the aquifer andaquitards extend laterally from the well radius of0.1 m to an outer boundary 10 km away. The outerboundary is impervious, and there is no change instresses. The lower aquitard extends vertically to abottom boundary 10 km below land surface. Thebottom boundary is impervious, and there is nodisplacement. These two remote boundaries aresufficiently distant from the well screen so thatslight variations in boundary conditions would notaffect the solution in the region affected bypumping. The top boundary (land surface) is freeof boundary traction, and drawdown of the watertable is assumed negligible. At the well, there is noradial displacement and no change in the vertical

6 U.S. Geological Survey Subsidence Interest Group Conference

Table 1. Values of physical properties used in simulation

Physical property

Hydraulic conductivity, κ, in meters per second ..............

Shear modulus, G, in Newton per square meter ...............

Drained Poisson’s ratio, ν (dimensionless).......................

Porosity, n (dimensionless) ...............................................

Fluid bulk modulus, , in Newton per square meter ....Kf

component of boundary traction. This boundarycondition allows the matrix along the well screenand (or) casing to move vertically but nothorizontally. A uniform flux of water is withdrawnfrom the entire thickness of the aquifer so that noflow crosses the casing in the aquitards. The10-kilometer by 10-kilometer model domain isdiscretized into a 40-column by 100-row mesh ofrectangular elements with variable sizes. Toprevent numerical oscillation, elements as thin as0.1 m are used along aquifer-aquitard interfaces.The first time step is 15 seconds, and this time-stepsize is successively increased by 1.2 times until atotal simulation time of 50 days is reached.

A 300- by 300-meter vertical section of aquiferand aquitards in their initial, undeformed states(before pumping) is shown in figure 2A. The wellis on the left, land surface is at the top, and only theupper 100 m of the lower aquitard is shown.Horizontal and vertical grid lines, spaced 20 mapart, are superimposed on the section. By movingwith the skeletal matrix, these grid lines illustratethe deformation of the aquifer and aquitards duringpumping. Note that the grids shown in figure 2 arenot the finite-element mesh used in the numericalmodel.

The simulated deformation of the aquifer andaquitards after 10 minutes of pumping is shown infigure 2B. For the sake of illustration, displace-ments are exaggerated 40,000 times so that, forexample, a displacement of 40 m in figure 2Bwould correspond to an actual displacement of 1mm. Contraction of the aquifer is evident.Horizontal contraction near the well is seen by thedeflection of vertical grid lines towards the screen.A point initially at A in figure 2A has movedabout 0.1 mm in the horizontal direction to A’ infigure 2B. Vertical contraction can be seen by a

, Las Vegas, Nevada, February 14–16, 1995

Value in aquifer Value in aquitards

1 × 10-4 1 × 10-7

3 × 108 3 × 107

.25 .25

.30 .40

2.3 × 109 2.3 × 109


ureres.

e inst

pert 50ree

tsthecm

rtrytheheadsttheingneandoutentby

0 100 200 300

010

020

030

0

HORIZONTAL DISTANCE FROM PUMPING WELL, IN METERS

DE

PTH

FR

OM

IN

ITIA

L L

AN

D

0

010

020

030

0

100 200 300

A’A

(A) t = 0(B) t = 10 minutes

displacement exaggerated 40,000 times

SUR

FAC

E, I

N M

ET

ER

S

Figure 2. Deformation of a 300- by 300-meter vertical section of aquifer and aquitards with grid lines superimposed. Unshadedarea indicates aquifer. Shaded area indicates aquitard. t is time since pumping began.

decrease of aquifer thickness. Immediatelyadjacent to the well, the decrease of thickness isabout 1 mm, and the aquitards also have deformed.Near the well, the aquitards have contracted in thehorizontal direction and extended in the verticaldirection, and shear distortion increases toward theaquifer-aquitard interface.

The horizontal contraction and verticalextension in the aquitards cause local changes ofpore volume. In some parts of the aquitard,pore volume increases, and in other parts, porevolume decreases. Understanding the relationbetween pore-volume change and head change isthe key to understanding deformation-inducedeffects. During early time after the start ofpumping, there is essentially no fluid flow in theaquitards. Under this condition, change inhydraulic head is inversely proportional to changein pore volume. At any point in the aquitard, ifdeformation results in a net increase in porevolume, hydraulic head drops. Conversely, ifdeformation results in a net decrease in porevolume, hydraulic head rises.

Progressive changes occur in hydraulic head inthe 300- by 300-meter vertical section of aquiferand aquitards (fig. 3A–F). After 10 minutes ofpumping (fig. 3A), two zones of induced head drophave developed—one above and one below thewell screen. The head drops in both zones

generally are between 0 and 1 cm. (The contoline for 1 cm of head drop lies close to thaquifer-aquitard interface). These two zones aregions of pore-volume increase in the aquitardTwo separate zones of induced head rise emergthe upper aquitard. The shallower zone is jubelow land surface and near the well. The deezone occurs at the base of the aquitard and aboum radially outward from the well. The zones athe regions of pore-volume reduction in thaquitard.

As pumping continues, the aquifer contracfurther and induces greater head changes in aquitards. The maximum head rise exceeds 3 after 1 hour of pumping (fig. 3B), and 6 cm after 6hours (fig. 3C). Head rise is greater in the uppeaquitard than in the lower aquitard. The asymmeis due to the presence of land surface where absence of traction allows more deformation of tnear-surface material. Of the two zones of herise in the upper aquitard, the shallower one (jubelow land surface) has greatly expanded, and deeper one has almost merged with the expandcontours. Of the two zones of head rise, the oabove the well screen has almost disappeared, the one below the well screen has remained abthe same. These results show that, in the prescase, head rise is the dominant effect induced

Poroelasticity Simulation of Ground-Water Flow and Subsurface Deformation 7

8 U.S. Geological Survey Subsidence Interest Group Conference, Las Vegas, Nevada, February 14–16, 1995


0

0

.01

.01.02

.02

.03

-1

-2

.01

.010

0

-1

-2

-1

-2-3

0.02

.06 .04.08

.02

.020

-1

.1

-4

-1-2

-3

0

.02

.06 .04

.08

.02

.020

(B) t = 1 hour

(A) t = 10 minutes

(E) t = 3.2 days

(D) t = 1 day

0.01

.01

.02.03.04.05.06

0

.01

.02

-1-2

-3

-2

-3

-4

.04 .02

0

.02

-1

-1

0

HORIZONTAL DISTANCE FROM PUMPING WELL, IN METERS

(C) t = 6 hour (F) t = 8.1 days

0 100 200 300 0 100 200 300

0

100

200

300

0

100

200

300

0

100

200

300

DE

PTH

FR

OM

IN

ITIA

L L

AN

D S

UR

FAC

E, I

N M

ET

ER

S

Figure 3. Changes in hydraulic head, in meters, in 300- by 300-meter vertical section of aquifer and aquitards. Unshaded areaindicates aquifer. Shaded area indicates aquitard. Positive numbers indicate head rise, in meters. Negative numbers indicate headdrop, in meters, Contour interval is irregular. t is time since pumping began.


ehn

:

pumping. Head drop is confined to a relativelysmall region above and below the well screen.

The deformation-induced head rise isdissipated over time by: (1) fluid flow from regionsof higher head to regions of lower head (includingthe water table) and (2) propagation of head dropfrom the aquifer into the aquitards (fig. 3D, E, andF). After 1 day of pumping, head drop haspropagated into the lower quarter of the upperaquitard. Above this zone of head drop, hydraulichead is still increasing (exceeding 8 cm), but flowto the water table has displaced the maximum to alower position than before. After 3.2 days, themaximum head rise exceeds 10 cm; however, theregion of head rise in the upper aquitard nowencompasses only its upper half. By 8.1 days, themaximum head rise has decreased to about 4 cm,indicating significant dissipation of deformation-induced effects. After 14 days (not shown), headdrop has propagated throughout the upper aquitard,and deformation-induced effects are no longerobservable.

CONCLUSIONS

A simulation using a poroelasticity model withtypical aquifer and aquitard properties shows thatthree-dimensional deformation caused by ground-

water withdrawal from a confined or semiconfinedaquifer can induce hydraulic-head changes inadjacent aquitards. The deformation-induced headchanges range from about 1 cm of head drop toabout 10 cm of head rise. These results areconsistent with reported field observations. Thesimulation suggests that in a thick aquitard,induced head rise could persist for many days afterthe start of pumping but is eventually dissipated by(1) fluid flow from regions of higher head toregions of lower head and (2) propagation ofdrawdown from the pumped aquifer into theaquitard. The poroelasticity model developed forthis analysis is useful in understanding thehydraulic response to ground-water withdrawal inlayered aquifer-aquitard systems.

REFERENCES CITED

Biot, M.A., 1941, General theory of three-dimensionalconsolidation: Journal of Applied Physics, v. 12,p. 155–164.

Smith, I.M., and Griffiths, D.V., 1988, Programming thfinite element method, 2nd ed.: Chinchester, JoWiley and Sons, 469 p.

Verruijt, A., 1969, Elastic storage of aquifers, in DeWiest, R.J.M., ed., Flow Through Porous MediaNew York, Academic Press, p. 331–376.

Poroelasticity Simulation of Ground-Water Flow and Subsurface Deformation 9


Simulation of Deformation of Sediments from Decline of Ground-Water Levels in an Aquifer Underlain by a Bedrock Step

By S.A. Leake and Paul A. Hsieh

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INTRODUCTION

Land subsidence occurs in many areas whereground-water pumping lowers water levels withincompressible aquifer systems. In the southwesternUnited States, aquifer-system compaction and landsubsidence have resulted in earth fissuresparticularly along the margins of aquifers ialluvial basins that have extensive ground-wapumpage. One explanation for the developmentfissures is horizontal extensional strain that coudevelop over buried bedrock highs or ste(Jachens and Holzer, 1982; Carpenter, 199Commonly applied methods of evaluating aquifesystem compaction (Leake and Prudic, 1991) aapplications of the Terzaghi theory, in which acompaction is assumed to be vertical. Neglectithe horizontal components of deformation does nallow for complete analysis of problems of earfissuring. Furthermore, the one-dimensionapproach raises questions regarding the validitycomputed distributions of head and verticdeformation in systems where horizontal defomation is significant. The more rigorous Bio(1941) theory of deformation accounts for horzontal as well as vertical components of elasdeformation. The purpose of this analysis is evaluate relative importance of horizontal anvertical components of deformation in an aquifunderlain by a bedrock step.

APPROACH

Deformation around a bedrock step wasimulated in a vertical plane for an idealizeaquifer system (fig. 1). The right side of the plan

10 U.S. Geological Survey Subsidence Interest Group Conferenc

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is analogous to an edge of an alluvial basin, and left side is analogous to an interior part of a baswhere ground-water pumping causes water levto decline. The aquifer system includes an uppunconfined compressible aquifer, a middle compressible confining unit, and a lower compressibconfined aquifer.

Ground-water flow and deformation in thhypothetical system were simulated using twdifferent methods. The first method used thMODFLOW finite-difference ground-water modeprogram (McDonald and Harbaugh, 1988) simulate ground-water flow in the vertical planeVertical compaction, ∆b, is computed using therelation

,

where Ssk is the skeletal component of specifistorage, b is thickness of compacting sedimentand ∆h is change in head computed bMODFLOW. The relation is consistent with theTerzaghi theory (Leake and Prudic, 199equation 5). Compaction is computed for each ceand vertical displacement is computed as half the compaction for a cell plus the sum ocompaction values for the cells below. The secomethod is a finite-element solution of flow andeformation in two dimensions. Fluid flow isdescribed by Darcy’s Law and mass conservatioand matrix deformation is described by Biotconstitutive relations and stress equilibrium. Fmore details on this method, see paper entit“Poroelasticity Simulation of Ground-Water Flowand Subsurface Deformation” on page 5 in threport. In this paper, the two methods are referrto as the Terzaghi method and the Biot methorespectively.

∆b Ssk– b∆h=

e, Las Vegas, Nevada, February 14–16, 1995


UPPER AQUIFER—CONSTANT HEADCOMPRESSIBLE CONFINING UNIT

BEDROCK STEPCOMPRESSIBLE CONFINED AQUIFER

0 500 1,000 METERS

0 1,000 3,000 FEET

VERTICAL EXAGGERATION X 5

2,000

CBC

A

A

A

B

D

E

A

EXPLANATION

BOUNDARY SEGMENTIDENTIFIER

Figure 1. Hydrologic system used in simulations of flow and deformation.

For simplicity in simulating flow and defor-mation in vertical sections, the head in the upperaquifer was specified to remain constant for theentire period of simulation; therefore, nocompaction occurs in that aquifer. The hydraulicboundary conditions (table 1) allow for a specifieddecline in head in the lower aquifer along the leftside of the model. Along boundary-segment E(fig. 1), head is specified to linearly decline by60 m over a 10-year period (fig. 2).

The Terzaghi method as applied for thisanalysis does not compute displacements along theedges of the model, but allows for verticaldisplacement at the centers of all model cells. Themechanical boundary conditions for the Biot

method (table 1) allow for vertical displacementeverywhere except along the lower boundaryincluding the step. Horizontal displacement isallowed along the top boundary.

In the finite-difference and finite-elementmodels, the hydrologic system is represented using26 horizontal rows and 65 vertical columns of cellsand elements. Rows are 20 m thick in the aquifersand 4 m thick in the confining unit, and eachcolumn is 80 m wide. The hydraulic and physicalproperties used in the simulations are given intable 2. The values are within ranges expected inalluvial basins in the southwestern United States(Hanson, 1989). Simulations with the Terzaghimethod used a single skeletal specific-storage

Simulation of Deformation of Sediments from Decline of Ground-Water Levels in an Aquifer Underlain by a Bedrock Step 11

Table 1. Boundary conditions used in simulations of flow and deformation

Boundary-segment identifier Hydraulic boundary condition

Mechanical boundary conditionused in Biot method

A No flow No horizontal or vertical displacement

B No flow No horizontal displacement

C Specified head (constant) No horizontal displacement

D Specified head (constant) Free surface

E Specified head (declining) No horizontal displacement


oddnt

onnshickinan

in iserehehey ant

ulg.byrehd

0 2 4 6 8 10SIMULATION TIME, IN YEARS

0

20

40

60HE

AD

DE

CL

INE

, IN

ME

TE

RS

Figure 2. Specified decline in head along boundary-segment E.

Table 2. Hydraulic and physical properties used in simulations of flow and deformation

Hydrologic unit

Hydraulic conductivity(meter day-1)

Skeletal specific storage

(meter-1)Young’s modulus(Newton meter-1) Poisson’s ratio

Upper aquifer ............................ 25 1×10-5 8×108 0.25

Middle confining unit ............... .01 1×10-4 8×107 .25

Lower aquifer............................ 25 1×10-5 8×108 .25

value rather than elastic and inelastic specific-storage values. The values of 1×10-5 m-1 for theaquifers and 1×10-4 m-1 for the confining unit arein the range of typical values for the skeletalcomponent of inelastic specific storage. Usingthese values, this analysis is valid only for the casein which pore pressures do not increase (fig. 2).The Biot method does not use specific storage butrather uses Young’s modulus and Poisson’s ratio.The values given in table 2 are consistent with thespecific-storage values used in the Terzaghimethod. Although the Biot method is applicable toan elastic medium, the application here withproperties corresponding to typical inelasticspecific-storage values is appropriate as long as theYoung’s modulus and Poisson’s ratio can beassumed to remain constant.

RESULTS

A comparison of results of the two methodscan be used to evaluate the effects of ignoringhorizontal deformation on computed head change.The results for the 10-year simulations using theTerzaghi and Biot methods are the same except atthe extreme edge of the basin (fig. 3A); therefore,

the assumptions inherent in the Terzaghi methhave little effect on the computation of heachange. Similarly, computed vertical displacemeis almost identical over most of the area (fig. 3B).Within a distance of about one aquifer thickness each side of the bedrock step, the distributiodiffer. The distribution computed by the Terzagmethod includes a discontinuity over the bedrostep. The displacement in the upper cell in the thpart of the aquifer adjacent to the step is less th0.08 m, and the displacement in the upper cellthe thick part of the aquifer adjacent to the stepmore than 0.18 m. The displacement in the uppcell in the thin part of the aquifer computed by thBiot method also is less than 0.08 m; however, tdisplacement computed by the Biot method in tupper cell in the thick part of the aquifer is onl0.10 m. Furthermore, the Biot method results insmooth continuous distribution of displacemeacross the step.

The results of the Biot method can be useffor analysis of conditions leading to earth fissurinThe horizontal strain at land surface computed the method (fig. 4) shows a tensional strain of mothan 1×10-4 on the upside of the step. Althougstrain at failure is not well known, Jachens an



EXPLANATION

LINE OF EQUAL HEADCHANGE COMPUTED50 40

30

BY TERZAGHI METHOD

LINE OF EQUAL HEADCHANGE COMPUTEDBY BIOT METHOD

A

EXPLANATION

LINE OF EQUAL VERTICALDISPLACEMENT COM-PUTED BY TERZAGHIMETHOD

LINE OF EQUAL VERTICALDISPLACEMENT COM-PUTED BY BIOT METHOD

B

60

0.04

0.08

0.12

0.16

0.20

0 500 1,000 METERS

0 1,000 3,000 FEET

VERTICAL EXAGGERATION X 5

2,000

Figure 3. Results of simulations of flow and deformation using the Terzaghi and Biot methods. A, Computed head change, inmeters. B, Computed vertical displacement, in meters.

Holzer (1982) calculate values in the range of2×10-4 to 2×10-3.

CONCLUSIONS

Head changes computed by the Terzaghi andBiot methods were almost identical throughout thesimulated flow system. Vertical displacementscomputed by the two methods were almost thesame except near the bedrock step. For theconditions simulated, the simpler Terzaghi methodadequately describes deformation on a regional

scale. For analysis of smaller-scale deformationaround the bedrock step, the more rigorous Biotmethod is needed to adequately simulate verticaland horizontal deformation. The deformationcomputed by the Biot method can be used tocalculate potential horizontal strains that lead todevelopment of earth fissures.

REFERENCES

Biot, M.A., 1941, General theory of three-dimensionalconsolidation: Journal of Applied Physics, v. 12,p. 155–164.

Simulation of Deformation of Sediments from Decline of Ground-Water Levels in an Aquifer Underlain by a Bedrock Step 13


f a

m

e

y

s,

y

s,

2×10-4

1×10-4

1×10-4

0

HO

RIZ

ON

TA

L S

TR

AIN

2,000 5,0002,000 2,500 3,000 3,500 4,000 4,500

DISTANCE, IN METERS

Bedrock step

Com

pres

sion

Ten

sion

Figure 4. Horizontal strain at land surface at the end of the 10-year simulation computed by the Biot method.

Carpenter, M.C., 1993, Earth-fissure movementsassociated with fluctuations in ground-water levelsnear the Picacho Mountains, south-central Arizona:U.S. Geological Survey Professional Paper 497–H,49 p.

Hanson, R.T., 1989, Aquifer-system compaction,Tucson basin and Avra Valley, Arizona: U.S.Geological Survey Water-Resources InvestigationsReport 88–4172, 69 p.

Jachens, R.C., and Holzer, T.L., 1982, Differentialcompaction mechanism for earth fissures near CasaGrande, Arizona: Geological Society of AmericaBulletin, v. 93, no. 10, p. 998–1012.

Leake, S.A., and Prudic, D.E., 1991, Documentation o

computer program to simulate aquifer-syste

compaction using the modular finite-differenc

ground-water flow model: U.S. Geological Surve

Techniques of Water-Resources Investigation

book 6, chap. A2, 68 p.

McDonald, M.G., and Harbaugh, A.W., 1988, A

modular three-dimensional finite-difference

ground-water flow model: U.S. Geological Surve

Techniques of Water-Resources Investigation

book 6, chap. A1, 586 p.



State of Subsidence Modeling Within the U.S. Geological Survey

By Thomas J. Burbey

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alge canuidrin

ntinseghrly ofeing is,e

aisd

ereer,

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renddeat

Much of the current knowledge of landsubsidence and aquifer deformation came from theU.S. Geological Survey’s Mechanics of AquiferProject led by Joseph F. Poland from 1955 throu1984. Until the advent of efficient and powerfucomputers, many of the calculations used estimate vertical subsidence were done wanalytical models (Poland and Davis, 1969Beginning in the 1970’s, Terzaghi’s principle oeffective stress coupled with Hubbert’s forcpotential and Darcy’s Law provided the basis fone-dimensional subsidence modeling (Gamboland others, 1974; Helm, 1975, 1976). Helmone-dimensional consolidation model wadeveloped for constant and stress-dependparameters, but was not linked to a ground-waflow model. Although Helm’s model remains apowerful tool for detailed analysis of verticaeffects at a specific site, it is not a model fobasin-wide analysis. The first subsidence modincorporated into a ground-water flow model wawritten by Meyer and Carr (1979). This modeallowed for elastic- and inelastic-storage valuesbe incorporated into a three-dimensional grounwater flow model (Trescott, 1975). After the development of the three-dimensional MODFLOWground-water flow model (McDonald and Harbaugh, 1988), Leake and Prudic (1991) wroteone-dimensional subsidence program fMODFLOW called the Interbed Storage Packag(IBS1). This subsidence model is more versatthan the Meyer and Carr (1979) model and is ustoday as the standard for modeling subsidenceground-water basins. Although this program donot contain the stress-dependent paramecapabilities of the earlier Helm model, it allows focontinuous calculation of subsidence due pumping in the areal extent of the model gri

sghltoith).feorati’ssentter

lrelsl

tod--

- aore

ileed inesterrtod.

Leake (1990) added other capabilities to thoriginal code by allowing the evaluation of delayedrainage from interbeds within an aquifer systein an experimental version of the Interbed StoraPackage (IBS2). Leake (1991) developed anothInterbed Storage Package (IBS3) in which totload can be treated as a variable and storaparameters as stress dependent. These modelsbe used to evaluate vertical subsidence due to flwithdrawal; however, they do not account fohorizontal displacement resulting from changes stress.

The surface effects of horizontal displacemehave been evaluated by measuring radial stra(Wolff, 1970), by observance of failed surfacstructures (Poland and Davis, 1969) and throuthe presence of earth fissures (Holzer, 1984). Eaexplanations have associated the occurrencehorizontal movement with differential subsidencand compared the process to that of a bendbeam failing at the point of greatest stress. Thathorizontal movement occurs primarily above thaquifer in the brittle unsaturated zone and isdirect consequence of vertical displacement. Ththeory does not apply to many fissures anstructural failures that have been observed whminimal subsidence has been measured (Holz1984; Anderson, 1989). In recent years, eafissures have been shown to be directly relatedhorizontal aquifer movement due to pumping unconsolidated aquifers (Helm, 1994a). addition, many fissures are known to havmigrated upwards from depth thus contradictinthe earlier bending-beam theory of fissudevelopment. Theoretical developments (Bear aCorapcioglu, 1981; Helm, 1994b) and fielmeasurements of horizontal land-surfacmovement (Poland and Davis, 1969) indicate th

State of Subsidence Modeling Within the U.S. Geological Survey 15


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horizontal aquifer movement is significant and canbe the same order of magnitude as verticalsubsidence. Furthermore, Helm (1994b) indicatesthat horizontal movement due to pumping canoccur beyond where measurable drawdown orsubsidence occurs. Thus, the problems associatedwith land subsidence are three dimensional inscope. The calculation of both vertical and hori-zontal movement provides the necessaryinformation water managers need to optimizepumping and reduce the potential for earth-fissuredevelopment. Earth fissures have resulted in manylitigation cases because of structural damagecaused to buildings, foundations, fences,railroads, roads, sidewalks, pipelines, and wellcasings. The next step in advancing the state ofsubsidence modeling is to include the mathematicsneeded to produce a model capable of simulatingboth horizontal and vertical aquifer-systemdeformation.

Development of a tractable field-based three-dimensional displacement model to simulateaquifer-system response to changes in appliedstress is the next goal. Earlier subsidence modelscannot provide the foundation for a three-dimensional displacement model because three-dimensional poroelastic theory is different from thetheory used in one-dimensional subsidence modelsthat are based solely on stress changes due towater-level declines. In Biot’s (1941, 1955)development of three-dimensional consolidation(poroelastic) theory, the directional components ofdisplacement and pressure or hydraulic head aredependent variables. This development incor-porates the principle of effective stress andinherently assumes stress equilibrium and anelastic stress-strain constitutive relation. Theresulting governing equation can be expressed as

, (3)

where ρw is the density of water, g is thegravitational constant, h is hydraulic head, us is thedisplacement field of solids, G is the shearmodulus (and one of Lamé’s constants), and λ isthe other Lamé constant. Lamé’s constant λ isdefined in terms of the shear modulus G andPoisson’s ratio ν as

, (4)

Equation (1) represents a system of threquations with four unknowns. Another equationneeded that relates hydraulic head to tdisplacement field of solids. The fourth equation obtained by first writing Darcy’s Law in terms othe velocity of solids,

, (5)

where υw is the velocity of water, υs is the velocityof solids, κ is hydraulic conductivity, and n isporosity. Assuming constant water and solid-gradensity, applying the principle of conservation ofluid and solid mass, taking the divergence of athe terms of equation (3), and relating volumstrain to displacement yields the fourth equation,

. (6)

Equations (1) and (4) are Biot’s fundamentexpressions of consolidation and have been uby P.A. Hsieh (see paper entitled “PoroelasticiSimulation of Ground-Water Flow and SubsurfacDeformation, p. 5, this report) for developing two-dimensional axisymmetric finite-element displacement model (referred to in this report HDM).

Capabilities for simulating three-dimensionaporoelasticity combined with the power anflexibility of MODFLOW would result in avaluable tool for analysis of aquifer deformationEquation (4), however, is not compatible witMODFLOW, which uses specific storage insteaof displacement or strain. Rice and Cleary (197use an alternative formulation of poroelasttheory. Their governing equation can be expressas

, (7)

where ρσm is the incremental change in mean totstress. Skeletal specific storage (Ss) for three-dimensional problems is defined as

. (8)

λ G+( ) us∇•( ) G∇2us+∇ ρwg h∇=

λ 2Gν1 2ν–---------------=

n υw υs–( ) κ– h∇=

t∂∂ us∇•( ) κ∇2

h=

t∂∂h κ 3λ 2G+

3ρwg--------------------

∇2h–

1ρwg----------

σmδ( )∂

∂t------------------=

Ss

3ρwg

3λ 2G+--------------------=



,

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cets:s

al,

a

A.,ofn,77.f,

Where and when the change in mean totalstress appropriately is assumed to be negligiblewithin a ground-water basin, equation (5) becomesidentical to the traditional ground-water flowequation used in MODFLOW and other ground-water flow models. Assuming the change in meantotal stress is negligible may eliminate the ability tosimulate reversals of direction of change in waterlevels (Noordbergum effect) frequently observedduring early times of pumping. None- theless,using this traditional expression with equation (1)results in a powerful coupling of equations tosimulate three-dimensional consolidation(referred to here as the granular displace- mentmodel, or GDM) and three-dimensionalground-water flow within MODFLOW. Becausebasin-wide subsidence studies generally involvelong time periods (simulation time of decades withindividual time steps of a month or more), thechange in mean total stress and the occurrence ofreversals of direction of change in water levelsprobably are less significant. Neglecting thechange in mean total stress, therefore, may notsignificantly affect results for long-termbasin-wide simulations.

To evaluate the legitimacy of this approach,the HDM and GDM models are compared for threeperiods assuming an isotropic, confined-aquifersystem with zero-displacement boundaries alongthe bottom and sides and a zero-traction boundary(zero total load) at the aquifer top. The side orlateral boundaries are more than 10,000 m from thepumping well and do not affect simulation results.Aquifer properties and initial conditions used in thesimulations are shown in table 1. The calculatedvertical and horizontal displacements resultingfrom the two models are shown in figures 1 and 2.Results indicate that for modeling aquifer-system

displacements due to fluid withdrawal, the changein mean total stress may not be large, even for shorttime steps. Results indicate that the small,simulated differences in horizontal displacementmay be due to the different numerical schemes orcoordinate systems used in the two models. TheGDM is an improvement over other modelsbecause it offers the power and flexibility ofMODFLOW with the ability to simulateaquifer-system deformation in three dimensions.This model will help provide a betterunderstanding of location and severity ofpotentially damaging fissures.

REFERENCES CITED

Anderson, S.R., 1989, Potential for aquifer compaction,land subsidence, and earth fissures in Avra Valley,Pima and Pinal Counties, Arizona: U.S. GeologicalSurvey Hydrologic Investigations Atlas HA–7183 sheets, scale 1:250,000.

Bea r, Jacob , and Corapc iog lu , M .Y. , 1981Mathematical model for regional land subsidencdue to pumping—2. Integrated aquifer subsidenequations for vertical and horizontal displacemenAmerican Geophysical Union, Water ResourceResearch, v. 17, no. 4, p. 947–958.

Biot, M.A., 1941, General theory of three-dimensionconsolidation: Journal of Applied Physics, v. 12p. 155–164.

__ 1955, Theory of elasticity and consolidation for porous anisotropic solid: Journal of AppliedPhysics, v. 26, p. 182–185.

Gambolati, Giuseppe, Gatto, Paolo, and Freeze, R.1974, Mathematical simulation of the subsidence Venice—2. Results: American Geophysical UnioWater Resources Research, v. 10, no. 3, p. 563–5

Helm, D.C., 1975, One-dimensional simulation oaqu i fe r sys tem compact ion nea r P ix ley


Table 1. Aquifer properties and initial conditions used in the simulations to produce the results shown in figures 1 and 2

Property or condition Value

Pumping rate, Q, in cubic meters per second ................................................. 6.3×10-3

Hydraulic conductivity, κ, in meters per second............................................. 1×10-4

Drained Poisson’s ratio, ν, dimensionless ...................................................... .25

Shear modulus, G, in Newton per square meter.............................................. 6.533333×106

Specific weight of water, ρwg, in Newton per cubic meter ............................ 9.8×103

Lamé’s constant, λ, in Newton per square meter............................................ 6.533333×106



-16

0

-16

-14

-12

-10

-8

-6

-4

-2

HO

RIZ

ON

TA

L D

ISPL

AC

EM

EN

T, I

N M

ILL

IME

TE

RS

0 5,0001,000 3,000

DISTANCE FROM PUMPING WELL, IN METERS

EXPLANATION

GDM (0.7 day)

GDM (6.5 days)

GDM (58 days)

HDM (0.7 day)

HDM (6.5 days)

HDM (58 days)

0

16

0

2

4

6

8

10

12

14

VE

RT

ICA

L D

ISP

LA

CE

ME

NT

, IN

MIL

LIM

ET

ER

S

0 1,0000 200 400 600 800

DISTANCE FROM PUMPING WELL, IN METERS

EXPLANATION

GDM (0.7 day)

GDM (6.5 days)

GDM (58 days)

HDM (0.7 day)

HDM (6.5 days)

HDM (58 days)

Figure 1. Simulated horizontal displacement for three time periods using the granular displacement model (GDM) and the Hsiehdisplacement model (HDM).

Figure 2. Simulated vertical displacement for three time periods using the granular displacement model (GDM) and the Hsiehdisplacement model (HDM).


eys,

ys,

r

ter

ce

g,

esssof1.

el

le lr

California—1. Constant parameters: AmericanGeophysical Union, Water Resources Research,v. 11, no. 3, p. 465–478.

___1976, One-dimensional simulation of aquifersystem compaction near Pixley, California—2.St ress -dependen t pa rame te rs : Amer icanGeophysical Union, Water Resources Research,v. 12, no. 3, p. 375–391.

___1994a, Hydraulic forces that play a role ingenerating fissures at depth: Bulletin of theAssociation of Engineering Geologists, v. 31, no. 3,p. 293–303.

___1994b, Horizontal aquifer movement in aThe is -Th iem conf ined sys tem: Amer icanGeophysical Union, Water Resources Research,v. 30, no. 4, p. 953–964.

Holzer, T.L., 1984, Ground fai lure induced byground-water withdrawal from unconsolidatedsediment: Geological Society of America, Reviewsin Engineering Geology, v. 6, p. 67–105.

Leake, S.A., 1990, Interbed storage changes andcompaction in models of regional ground-waterf low: American Geophysical Union, WaterResources Research, v. 26, no. 9, p. 1939–1950.

___1991, Simulation of vertical compaction in modelsof regional ground-water flow, in Johnson, I.A., ed.,Land Subsidence: International Association ofHydro log ica l Sc iences Pub l i ca t io n 200 ,Proceedings of the Fourth International Symposiumon Land Subsidence, p. 565–574.

Leake, S.A., and Prudic, D.E., 1991, Documentation of acomputer program to simulate aquifer-system

compaction using the modular finite-differencground-water flow model: U.S. Geological SurveTechniques of Water-Resources Investigationbook 6, chap. A2, 68 p.

McDonald, M.G., and Harbaugh, A.W., 1988, Amodular three-dimensional finite-differenceground-water flow model: U.S. Geological SurveTechniques of Water-Resources Investigationbook 6, chap. A1, 586 p.

Meyer, W.R., and Carr, J.E., 1979, A digital model fosimulation of ground-water hydrology in theHouston area, Texas: Texas Department of WaResources Report LP–103, 27 p.

Poland, J.F., and Davis, G.H., 1969, Land subsidendue to withdrawals of fluids, in Varnes, D.J., andKiersch, George, eds., Reviews in EngineerinGeo logy—Volume 2 : Boulder, Co lo radoGeological Society of America, p. 187–269.

Rice, J.R., and Cleary, M.P., 1976, Some basic strdiffusion solutions for fluid-saturated elastic poroumedia with compressible constituents: Review Geophysics and Space Physics, v. 14, p. 227–24

Trescott, P.C., 1975, Documentation of finite-differencmodel for simulation of three-dimensionaground-water flow: U.S. Geological SurveyOpen-File Report 75–438, 32 p.

Wolff, R.G., 1970, Relationship between horizontastrain near a wel l and reverse water- levfluctuation: American Geophysical Union, WateResources Research, v. 6, no. 6, p. 1721–1728.



Deformation of a Sandbar in Response to Changes in Effective Stress Along the Colorado River in the Grand Canyon, Arizona

By M.C. Carpenter

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1,e

toalee

edr

y

ebard isgerr

fed

lyck

Discharge from Glen Canyon Dam on theColorado River can fluctuate from about 85 to800 m3/s on a daily basis. Correspondingriver-stage fluctuations on downstream beachescan exceed 3.4 m. Rill erosion, slumping, andfissuring on seepage faces of many sandbarsobserved at low river stage are a response toground-water flow caused by residualhydraulic-head gradients in the sandbars, which isthe result of river-stage fluctuation.

From April 1991 to March 1993, a sandbar wasinstrumented with sensors for continual monitoringof river stage, pore pressure, temperature, andbiaxial tilt to determine relations amongground-water flow, changes in effective stress,seepage stresses, and sandbar deformation. Fiveclusters of deep, intermediate, and shallow pairs ofpore-pressure and temperature sensors wereinstalled in a vertical plane orthogonal to theriver’s edge. The clusters were spaced a few meapart in the sandbar face above, within, and belthe zone of fluctuating river stage to determine tvertical component of ground-water flow in thdeforming sandbar face. The clusters were spamore than 10 m apart in the middle and back of tsandbar. Seven tilt sensors were installed parawith and orthogonal to the river’s edge in thdeforming sandbar face.

The sandbar consisted of homogeneous finemedium sand overlying medium sand at a depth


tersowheecedhellele

to of

6 m. The back boundary was talus with a narrodeep, return channel underlain by a thin claysilty sand. The zone of fluctuating river stage wassteeply sloping face that exhibited rill erosionslumping, and fissuring.

A sequence of tilts occurred from July 7, 199through July 17, 1991. The tilts were at least fivtimes greater orthogonal to the river than parallelthe river. The sign convention for tilts ortho- gonto the river is positive for tilts upward toward thriver and negative for tilts downward toward thriver. On July 7, a tilt of 5.5∞° occurred orthogonalto the river. On July 12, a tilt of -0.5°∞ occurred;and on July 17, an additional tilt of -3.3°∞occurred. These major occurrences were followby continued negative tilt orthogonal to the rivefrom July 18 to July 26, punctuated with dailspikes of about -0.4°π. All sudden tilts occurred ondownward limbs of the daily hydrographs when theffective stress (intergranular stress) in the sandface was increasing. The hypothesis sug- gestea slump-creep sequence: (1) outward- flowinground water caused oversteepening of the lowpart of the slope in the zone of fluctuating rivestage by rilling; (2) slumping (rotational failure) othe metastable slope was triggered by increaseffective stress; and (3) leveling of the slightuplifted mound on the toe slope of the slump blooccurred by downslope creep.



Piezometric-Extensometric Estimations of Specific Storage in the Albuquerque Basin, New Mexico

By Charles E. Heywood

l

ermrinle-s

inesalsi-

edoferere atll.glayedrsnse

reof inthe

Appropriate values of skeletal specific storage(Ssk) and hydraulic conductivity are required fornumerical simulations to achieve useful predic-tions of ground-water level responses to futurepumping. These parameters often are estimatedfrom the measured hydraulic response to short-duration pumping tests, which may effectivelystress only the more permeable parts of the aquifersystem within a previously stressed magnituderange. Because the magnitude of Ssk may dependon the time period of the applied hydraulic stress aswell as the stress history of the aquifer system(Helm, 1976; Galloway, 1995), estimates of Sskfrom such tests often are applied inappropriately inground-water flow simulations for systems withsignificant low-permeability lithologies or acomponent of inelastic compressibility.

Early in a test close to the pumped well,horizontal strain of the aquifer matrix may induceappreciable pore-pressure changes before thehydraulic propagation of drawdown. Such effectswere observed in the test described in this paper.Analytical solutions of radial ground-water flowproblems are most sensitive to the storagecoefficient (S) during early time and typically arebased on models that neglect horizontal strain. Ifpiezometric data close to the pumped well areanalyzed with such a model, erroneous parameterestimates may result. For these reasons, directin-situ measurement of vertical aquifer-systemmatrix compressibility is preferable for estimatingaquifer-system specific storage.

In the Albuquerque Basin of New Mexico,ground-water withdrawals result in depletion ofaquifer-system storage and of surface-water flowin the Rio Grande. Because the economics andadministration of these water sources differ, animproved understanding of ground-water andsurface-water interaction near the Rio Grande was

Piezometric-Extensometric Estima

desired, and an aquifer test was carried out duringthe winter of 1995. A 3-month recovery periodpreceded 54 days of pumping at about 147 L/s,which was followed by a 1-month recovery period.The production well was screened from 71 to244 m; however, post-test televiewing and flow-metering revealed that the screen was encrustedand did not produce significant water below 195 m(Condé Thorn, hydrologist, U.S. GeologicaSurvey, oral commun., 1995).

Before the test in the fall of 1994, a 315-metborehole extensometer was installed 378 m frothe test well as part of an effort to monitoaquifer-system compaction that would result land subsidence. This counter-weighted borehopipe extensometer design followed guidelinedescribed by Riley (1984) to achieve high-strasensitivity. A precision transducer measurvertical displacements with a resolution of severmicrons corresponding to a vertical-strain sentivity of 10-8. A nest of four piezometers wasinstalled 5 m from the extensometer and equippwith transducers capable of detecting 2 mm water-level change. During the aquifer test, watlevels also were recorded in three shallowpiezometers approximately 80 m from thextensometer and in 12 other observation wellsvarious distances farther from the pumped weThe electrical-resistivity borehole-geophysical loillustrates the depth and thickness of sand and cinterbeds of the aquifer-system interval penetratby the extensometer (fig. 1). Clay and silt layecorrelate with lower resistivity. Piezometer screewere placed in high-resistivity intervals that werassumed to be sands of high permeability.

The relation between aquifer pore-pressudecrease and vertical strain for the period drawdown and subsequent recovery is shownfigure 2. Pore pressure was measured 6 m from

tions of Specific Storage in the Albuquerque Basin, New Mexico 21



Water level

Piezometer screen

EXPLANATION

TableLegs

Ep

Longnormal

L

Slipjoint

Slipjoint

Slipjoint

Shortnormal

Shortnormal

Longnormal

DE

PT

H,

IN M

ET

ER

S B

EL

OW

LA

ND

SU

RF

AC

E

120

140

160

180

200

220

240

260

280

300

320

100

80

60

40

20

0

RESISTIVITY, IN OHM-METERS

40 60 80200

Figure 1. Summary of Montaño extensometer-piezometer installation.


Piezometric-Extensometric Estimations of Specific Storage in the Albuquerque Basin, New Mexico 23

VERTICAL STRAIN x 10– 6

1

B

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

10

0

20

30

40

PO

RE

PR

ES

SU

RE

DE

CR

EA

SE

, IN

TH

OU

SA

ND

S O

F P

AS

CA

LS

A

10

0

20

30

Day 1

Day 7

Day 54

Day 55

Day 75

40

Figure 2. Pore-pressure change at a depth of 171 meters compared to aquifer-system strain. A, Test-pumping and recovery period.B, Test-pumping and recovery period and subsequent period of uncontrolled pumping at multiple wells.


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bythereroesss

ivee theatst,nit

extensometer at a depth of 171 m, and verticalstrain was measured over the interval of theextensometer (fig. 1). A 27-minute pump failurethat occurred 1 day into the aquifer test causedmeasurable elastic recovery at the extensometerand resulted in a small loop in the plot. Ananalogous effect was observed on day 55 when thepumped well was inadvertently turned back on forabout 2 hours. Piezometer hydrographs flattenedapproximately 1 week into the drawdown andrecovery periods of the test and indicate thatdrawdown approached steady state in permeableparts of the aquifer system where piezometers werescreened. As shown in figure 2A, the flatter slopefrom day 7 to day 54 probably reflects compactionof interbedded sediments of low permeability asthey slowly drained excess pore pressure to thesurrounding aquifer. This decrease in slope alsomay be due to apparent strain attributable touncompensated long-period temperature effects inthe extensometer apparatus. The controlled-testdata from figure 2A and an additional 60 days ofsuperimposed post-test data are shown in figure2B. During the latter 60 days, normal “uncon-trolled” pumping from multiple wells near theextensometer resulted in many drawdowns ofvarious magnitudes on a daily basis. Thestress-strain plot during this period is shifted to theright of the plot for the controlled test suggestingthat (1) some inelastic compaction resulted fromthe test, (2) an uncompensated temperature effecton the extensometer has resulted in apparent strain,or (3) the recovery period was 39 percent of thedrawdown period, which was insufficient for thepore pressure in less permeable parts of the aquifersystem (above or below the piezometer screened at171 m) to return to prepumping levels. Since thelate 1950’s, production wells near theextensometer generated approximately diurnaldrawdowns of a similar magnitude to drawdownsgenerated in the aquifer test; however, it is possiblethat the aquifer system has not experienced thatmagnitude of constant drawdown for a period aslong as the aquifer test (54 days). During theaquifer test, the middle of the thick interbeds oflow permeability may have had more time to drainexcess pore pressure than at any previous timeresulting in effective stress magnitudes above aprecon- solidation level in the middle of theinterbeds. Resulting inelastic compaction totaling

0.45 mm would generate the apparent inelasstrain shown in figure 2B. Additional seasonalstress-strain and temperature data will enabdiscrimination of these three possibilities for thright shift of the stress-strain plot.

Riley (1969) demonstrated the utility of similastress-strain plots for determining elastic- aninelastic-storage coefficients. The magnitude of tinverse slope of this stress-strain plot would bemeasure of the compressibility of the averaaquifer matrix over the interval spanned by thextensometer if the change in pore pressure wuniform in that interval. The distribution ofaquifer-system pore-pressure change was sampwith piezometers over seven depth intervaSample hydrographs, in conjunction with thvertical-permeability distribution inferred from theborehole-resistivity log, were used to estimate tchange in vertical pore-pressure distribution durinthe aquifer test. The average pore-pressure chaover the sampled aquifer-system interval wapproximated by the average drawdown recordin the four deepest piezometers. For thaquifer-system interval spanned by the extesometer, the resulting estimated matrcompressibility, α, is 5×10-10 Pa-1. For an averagematrix porosity, n, of 0.3 and water compressibility, β, of 4.4×10-10 Pa-1, the correspondingspecific storage, Ss, [ρg(α+nβ)] is 7×10-6 m-1,where the weight density of water, ρg, is9,800 kg m-2 s-2.

The shallowest piezometer near the extesometer was screened across the water taDuring the pumping period of the test, thwater-table elevation recorded in this well declineless than 0.3 m. Assuming a specific yield of 0.the resulting decrease in geostatic stress underlying sediments was less than 6×102 Pa.Measured pore pressure decreased by 3.6×104 Pain the piezometer at a depth of 171 m and somewhat less in the piezometers screened at odepths. For sediments in the producing aquifinterval (from a depth of approximately 60 t200 m), the magnitude of decreased effective strresulting from water-table lowering, therefore, waon the order of 2 percent of the increased effectstress due to decreased pore pressure. Becauseffect of water-table lowering on effective stress depth generally was minor during the aquifer tethe water table was assumed to be static. A u



of

c

decrease in measured pore pressure, therefore,corresponded to a unit increase in effective stress.

Piezometric responses to earth tides enabledan independent estimation of specific storages ofthe aquifer sands surrounding each piezometerscreen. Three 3-week series of hourly pressuredata were filtered to pass frequencies between 0.8and 3.0 cycles/d by a digital 9th order ellipticfilter with 0.01 decibels of ripple in the passbandand a stop band that was 100 decibels lower thanthe peak value in the passband. The theoreticalmagnitude of volumetric strain due to earth tideswas calculated from tidal theory (Harrison, 1971)assuming a Poisson ratio of 0.25. The magnitudesof aquifer volumetric strain and resulting piezo-metric responses at six principal tidal frequencieswere determined by Fourier regression fromwhich values of Ss were calculated for the M2and O1 frequencies by assuming grain incom-pressibility (Bredehoeft, 1967). Figure 3 showsthe mean Ss calculated from the M2 tidal responsecompared to screen depth for the four deepestpiezometers adjacent to the extensometer (darkercircles and lines). Error-bar widths are 2 standarddeviations. These values of Ss are smaller thanthat of the aggregate aquifer system and suggestthat aquifer sands are stiffer than the aquifer

Piezometric-Extensometric Estima

0

350

DE

PT

H,

IN M

ET

ER

S

SPECIFIC STORA

Error bar widths are 2standard deviations

El Paso piezometer

Albuquerque piezometer

300

250

200

150

100

50

3.5 4.0 4.53.0

Figure 3. Specific storage for aquifer sands in Rio Grande alluviu

system, which includes interbedded clay aquitards.The data suggest that sand-matrix compressibilitydecreases approximately linearly with increasingoverburden stress. Open circles representing asimilar analysis (Heywood, 1995) of twopiezometers in a similar setting in El Paso, Texas,follow a similar trend. Barometric efficiency (BE)was estimated as a function of frequency(Rojstaczer, 1988) for the Albuquerquepiezometers and was found to be about 0.2 in thetidal-frequency range. This magnitude of BE andestimated Ss suggests sand-matrix porosities ofabout 0.3. The flat frequency response in the tidalspectrum suggests that piezometric earth-tideresponses probably are not significantly attenuatedby pressure diffusion.

REFERENCES CITED

Bredehoeft, J.D., 1967, Response of well-aquifersystems to earth tides: American GeophysicalUnion, Journal of Geophysical Research, v. 72,no. 12, p. 3075–3087.

Galloway, D.L., 1995, The frequency dependence aquifer-system elastic storage coefficients—Implications for estimates of aquifer hydrauli

tions of Specific Storage in the Albuquerque Basin, New Mexico 25

GE (x 10–6 PER METER)

6.55.0 5.5 6.0

m from M2 tidal response.


laln

er

f,

s,f

6.

ton,1,

properties and aquifer-system compaction, inPrince, K.R., Galloway, D.L., and Leake, S.A., eds.,U.S. Geological Survey Subsidence Interest GroupConference, Edwards Air Force Base, AntelopeVal ley, Ca l i f o rn ia , November 18–19 ,1992—Abstracts and Summary: U.S. GeologicalSurvey Open-File Report 94–532, 84 p.

Harrison, D.H., 1971, New computer programs for thecalculation of earth tides: Boulder, University ofColorado, Cooperative Institute for Research inEnvironmental Sciences.

Helm, D.C., 1976, One-dimensional simulation ofaquifer system compaction near Pixley, California2.—Stress dependent parameters: AmericanGeophysical Union, Water Resources Research,v. 12, no. 3, p. 375–391.

Heywood, C.E., 1995, Investigation of aquifer-systemcompaction in the Hueco basin, El Paso, Texas,

USA, in Proceedings of the Fifth InternationaSymposium on Land Subsidence: InternationAssociation of Hydrological Sciences Publicatio234, p. 35–45.

Riley, F.S., 1969, Analysis of borehole extensometdata from central California, in Tison, L.J., LandSubsidence: In ternat ional Assoc ia t ion oHydrological Sciences Publication 89, v. 2p. 423–431.

__ 1984, Developments in borehole extensometry,inJohnson, A.I., Carbognin, L., and Ubertini, L., edLand Subsidence: International Association oHydrological Sciences Publication 151, p. 169–18

Rojstaczer, S.A., 1988, Determination of fluid flowproperties from the response of water wells atmospheric loading: American Geophysical UnioWater Resources Research, v. 24, no. 1p. 1927–1938.



Results of Global Positioning System Surveys in Antelope Valley, California

By Marti E. Ikehara

ostes. interof

Ssrs).ndn.seds,chchd

oredisy ae

in

man

ineon asndalm)nch

Land subsidence has been occurring inAntelope Valley, California, because of a longhistory of ground-water pumping that has exceedednatural recharge. Water demand is expected toincrease rapidly with the projected increase inpopulation from about 320,000 in 1994 to about600,000 by the year 2010 (Templin and others,1995). Much of this demand probably will be metthrough increased ground-water withdrawal. Theflexibility of accurately measuring land-surfaceelevations of bench marks distributed at bothregional and local-scale spacing can be achievedby Global Positioning System (GPS) surveying. Astatic survey of 85 geodetic stations throughoutAntelope Valley and a kinematic survey of 85stations concentrated along a 4-mile-long(6.4-kilometer) rocket-testing track at Edwards AirForce Base were done using GPS surveying. Theobjectives of the first survey were to measurecurrent land-surface elevations for calculations ofhistorical land subsidence and to establishellipsoidal heights for future subsidencemonitoring using repeated GPS measurements.The objective of the second survey was to establishhorizontal and vertical positions for crustal-motionmonitoring before the onset of pumping at newground-water wells along the track.

Antelope Valley is in the western part of thearid Mojave Desert in southern California and isabout 50 mi (80 km) northeast of Los Angeles. Thetriangular-shaped valley is bounded on the southby the southeastward-trending San GabrielMountains, on the northwest by the northeastward-trending Tehachapi Mountains, and by smallerridges and buttes to the north and east. AntelopeValley is considered high desert, and elevations ofthe valley floor range from about 2,260 to 2,950 ft(690 to 900 m) above sea level. The valley is atopographically closed basin, and surface-water

Results of G

drainage terminates in several playas—the mnotable of which are Rogers and Rosamond LakFine-grained sedimentary deposits predominatethe center of the basin and within the Lancasground-water subbasin, which is the source much of the valley’s water.

In the spring of 1992, the regional-scale GPsurvey of 85 stations in Antelope Valley wacarried out using from four to seven receivesimultaneously (Ikehara and Phillips, 1994Dual-frequency signals were recorded at 15-secointervals for 5- to 7-hour durations at each statioThe network included 7 horizontal-control stationand 10 stable vertical-control stations and resultin 332 vectors, or relative-position coordinatebetween two simultaneously observed benmarks. The least-squares adjustment in whicoordinates for all control stations were held fixeproduced a vertical-standard error (2σ) that rangedbetween 0.03 and 0.081 ft (0.9 and 2.4 cm) andaveraged 0.05 ft (1.5 cm). The maximum errassociated with the geoid model (GEOID90) usto compute orthometric heights (elevations) in thsurvey was about 0.2 ft (6 cm), as determined bcomparison with recent leveling for a 20.3-mil(32.7-kilometer) line along Sierra Highwaybetween gravity and topographic highs and lowsthe valley (fig. 1).

Between about 1930 and 1992, the maximucalculated magnitude of subsidence was more th6.0 ft (1.83 m) in Lancaster, the largest city Antelope Valley (fig. 2). Estimates of subsidencat other nearby bench marks, partially based estimated values for the period before 1960, arehigh as 6.6 ft (2.01 m). Between Lancaster aRedman, which is a predominantly agriculturarea 12.5 mi (20 km) to the northeast, 4 ft (1.22 or more of subsidence has been measured at bemarks (fig. 2).

lobal Positioning System Surveys in Antelope Valley, California 27



DISTANCE, IN MILES

ELE

VA

TIO

N, I

N F

EE

T

DE

VIA

TIO

N B

ET

WE

EN

LE

VE

LED

AB

OV

E M

EA

N S

EA

LE

VE

L

AN

D G

PS

-DE

RIV

ED

ELE

VA

TIO

ND

IFF

ER

EN

CE

, IN

FE

ET

EXPLANATION

Land-surface profile GEOID90 deviation, relative to BM 5159GEOID93 deviation, relative to BM 5159GEOID90 deviation, relative to F1147 1961 GEOID93 deviation, relative to F1147 1961

62 40

2,700

2,600

2,500

2,400

2,300

2,200

BM 5159

BM 4217

BM 471

BM 474BM 479 BM 5204

U56 1926

F1147 1961

-0.05

-0.10

-0.15

-0.20

-0.25

-0.30

-0.358 10 12 14 16 18 20

Figure 1. Land-surface profile on Sierra Highway between Palmdale and Rosamond and error for Global PositioningSystem-derived elevation differences relative to leveled differences of bench-mark pairs (modified from Ikehara and Phillips, 1994,fig. 1).

0 5 10 MILES

0 5 10 KILOMETERS

EXPLANATION

Line of equal magnitude of subsidence, in feet --Dashed where approximately located. Interval 1 foot

°45'00"

118°15'

°37'30"

118°00' 117°52'30"

AVE B

AVE D

AVE E

AVE F

AVE H

AVE I

AVE J

AVE M

AVE G

AVE J

AVE I

110

90TH

W

60TH

W

30TH

W

DIV

ISIO

N S

T

30TH

E

50TH

E

90TH

E

120T

H E

140T

H E

LAN

CA

STE

R B

LVD

SIE

RR

A

Redman

Lancaster

KERN COLOS ANGELES CO

Edwards Air Force

Base

2

2

1

3 4

56 5

2

4

3

3

33

2

2

1

1

5

6

4

3 21

14

118°07'30"

2

1 2

HIG

HW

AY

Figure 2. Magnitude of calculated or estimated subsidence in central Antelope Valley, 1930 to 1992 (modified from Ikehara andPhillips, 1994, fig. 8).


bel

ereses aedly-ores.nsg

iltseeleeree

Land subsidence in Antelope Valley is causedby aquifer-system compaction that is related towater-level declines and the presence of fine-grained compressible sediments. The potentio-metric surface and water-level declines of theLancaster ground-water subbasin were mapped forseveral periods since the 1950’s and compared tosubsidence-rate maps. As expected, the correlationbetween water-level declines and the distributionand rates of subsidence were highest wherecompressible sediments were present generallytoward the lowest parts of Antelope Valley. Incontrast, areas, such as Palmdale, that are closer tothe mountains and underlain by coarser sedi-mentary material showed little or no land sub-sidence even when water levels had declined tensof meters over decades.

The mechanics of land subsidence might better understood if horizontal and verticageodetic measurements of the land surface wmade before as well as after the onset of stresimposed on the aquifer. The establishment ofhorizontal and vertical base line was accomplishby a recent local-scale geodetic survey of densespaced reference marks that was done befproduction in two new nearby ground-water wellA kinematic GPS survey of 82 reference statiowas done in August 1994 at a straight, 4-mile-lon(6-kilometer-long) abandoned track that was bufor testing rocket sleds at Edwards Air Force Bain the northeastern part of Antelope Valley. For thfirst part of the survey, the two nearest stabvertical-control stations that are part of thregional-scale network established in 1992 weobserved in static mode simultaneously with th

Results of Global Positioning System Surveys in Antelope Valley, California 29

0.36

0.34

0.32

0.30

0.28

0.26

0.24

0.22

0.20

0.18

0.16

0.14

0.12

0.10

0.08

0.06

DIF

FE

RE

NC

E B

ET

WE

EN

GP

S-D

ER

IVE

D A

ND

LE

VE

LED

ELE

VA

TIO

NS

, IN

FE

ET

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000

DISTANCE ALONG ROCKET TRACK, IN FEET

Figure 3. Comparison of Global Positioning System-derived elevations relative to leveled elevations of rocket-track stationsmeasured at Edwards Air Force Base, Antelope Valley, August 1994.


sehendine of

i, inlrt

two base stations established for the kinematicsurvey. The static observations were made at15-second intervals for 2 hours at the trackstations; the kinematic observations were made at10-second intervals for 15 epochs (2.5 minutes). Inkinematic surveys, an offset to the base station,called a swap station, is established for use by therover, which is the antenna that visits all stationsfor which coordinates are to be determined. Duringpostprocessing, horizontal and vertical coordinateswere computed for 2 base stations, 1 swap station,and 80 track stations.

A leveling survey that included most of the 80track stations was done during the same week. Thesurvey was not double run because of timeconstraints; however, the data allowed a generalcomparison between elevations obtained by GPSand leveling methods (fig. 3). Relative to leveledelevations, GPS-derived values differed by 0.08 to0.35 ft (2.4 to 10.7 cm). One possible explanationfor the bimodal distribution of elevationdifferences is that the base station for the trackstations between 8,000 and 20,000 ft (2,438 and6,096 m) was not included in the leveling.Although the leveled elevations are considered

known for this comparison, unadjusted levelingerror at the breakpoint—the switch between bastations—may account for the abrupt change in tdifferences. The GPS-computed positions aellipsoidal heights would be used as the base-lvalues with which future geodetic measurementstrack stations could be compared.

REFERENCES CITED

Ikehara, M.E., and Phillips, S.P., 1994, Determination ofland subsidence related to ground-water-leveldeclines using global positioning system andleveling surveys in Antelope Valley, Los Angelesand Kern Counties, California, 1992: U.S.Geological Survey Water-Resources InvestigationsReport 94–4184, 101 p.

Templin, W.E., Phillips, S.P., Cherry, D.E., DeBortolM.L., and others, 1995, Land use and water usethe Antelope Valley, California: U.S. GeologicaSurvey Water-Resources Investigations Repo94–4208, 97 p.



Deformation in the Casa Diablo Geothermal Well Field, Long Valley Caldera, Eastern California

By James F. Howle and Christopher D. Farrar

fereng

k,ls

fore

9283d87;y,tondce

alh0

e

d

118°37'30"119°00' 118°52'30" 118°45'

37°45'

37°37'30"

0 5

5 0

10 MILES

10 KILOMETERS

Mammoth Lakes Hot

Creek

Owens

River

Glass

Creek

Dea

dman

Creek

MonumentW 911

geothermal well field

Long Valley Caldera margin

ResurgentDome

LAKECROWLEY

Tom'sPlace

SanFrancisco

LONG VALLEY

LosAngeles

CA

LI F

OR

NI A

(figure 2)

LEE VINING 20 KM

Casa Diablo

Mamm ot h Cree k

203

Owe ns River

395

395

CALDERA

Figure 1. Location of Long Valley Caldera, California.

0

0

0.5 MILE

0.5 KILOMETER

F FF

FF

F

F

F

F AZ

AZ

N

MP-1

21

20

1918

1716

1514

1312

1110

9 87

65

43

21

MP

-2P

LES

-1

5EGE

L-shapedTilt-array

F

EXPLANATION

Normal fault (dashed where uncertain)

Production well

Production well with bench marks

Injection well

Injection well with bench mark

Observation well

L-shaped array bench mark and number

Steam vent

Geothermal powerplant

Long baseline bench mark

Monument AZ

Bench mark established in 1993

2

395

203

Figure 2. Casa Diablo geothermal well field, monumentnetworks, and bounding normal faults.

Long Valley Caldera in eastern California hasbeen the site of seismic swarms and deformation inresponse to magmatic intrusions since 1980 (Hilland others, 1985; Langbein, 1989; Langbein andothers, 1993). Magmatic intrusions are causingregional uplift of the land surface across theresurgent dome and the Casa Diablo geothermalwell field (figs. 1 and 2). Superimposed on theregional uplift is local subsidence in and around thewell field caused by pumping of geothermal fluid.This paper presents a time-series overview ofland-surface deformation in the well field andrelates the deformation to the two principal sourcesof stress—magmatic inflation and pumping ogeothermal fluid. Leveling data from threnetworks that overlap areally and temporally apresented beginning with the bench marks aloHighway 395.

The Highway 395 long base-line networextends 65 km from Lee Vining to Tom’s PlaceCalifornia. Bench marks are spaced at intervaless than or equal to 1 km. Elevation changes bench marks in the Highway 395 long base-linnetwork for three periods between 1983 and 19are shown in figure 3. Elevation changes for 19to 1985 indicate uniform uplift across the well fielthat totals about 20 mm (Savage and others, 19Dan Dzurisin, geologist, U.S. Geological Survewritten commun., 1993). Elevation data for 1983 1985 provide a preproduction base line of the lasurface and indicate that no significant subsidenoccurred before geothermal fluid was pumped.

Electric-power generation using geothermfluid in the Casa Diablo field began in 1985 witone powerplant (MP-1) that produced about 1megawatt gross electric power (Mwe). All of th0.8×106 kg/hr of fluid is pumped from wells andcirculated through the MP-1 powerplant an

Deformation in the Casa Diablo Geothermal Well Field, Long Valley Caldera, Eastern California 31


returned to the subsurface through injection wells.Fluid with a temperature of about 170°C ispumped from a 150- to 200-meter-deep productionzone and loses about 70°C in the heat-exchangeprocess before it is injected into a zone 600 to 700m deep.

Between 1985 and 1988, bench-mark elevationchanges indicate that monument W911, 2 km northof the well field, moved up about 80 mm inresponse to regional inflation caused by magmaticintrusions (fig. 3). Monument AZ moved up onlyabout 30 mm, which is equivalent to about 50 mmof local subsidence for that period. In figure 3,elevation change is for a particular period and isnot cumulative from 1983. From 1983 to 1992, thecumulative elevation change for monument W911is about 200 mm. All monuments within about 1km of monument AZ subsided relative to theregional uplift and clearly define the extent of thelocalized subsidence caused by pumping ofgeothermal fluid along the Highway 395 long baseline. For 1985 to 1988, subsidence related togeothermal pumping counters but does not entirelymask the regional uplift from magmatic intrusions.

In December 1990, two additional powerplants(MP-2 and PLES-1) became operational. Aboutfour times as much geothermal fluid is required to

operate all three powerplants as was needed forMP-1 alone. Bench-mark elevation changes on theHighway 395 long base line between 1988 and1992 (fig. 3) show that W911 was uplifted about100 mm; however, monument AZ subsided about20 mm. The increase in pumping from 0.8×106

kg/hr to 3.0×106 kg/hr caused the local area ofsubsidence to expand almost 2 km on either side ofmonument AZ (fig. 3) and completely maskedregional uplift of monument AZ and nearbymonuments.

The second leveling network is the L-shapedtilt array, a network of closely spaced monumentsalong two nearly perpendicular lines (fig. 2). Datafrom this network also show subsidence caused bypumping of geothermal fluids. Differences inmonument elevations between consecutive surveysare resolved into north and east components ofground tilt. Data for the north component of tilt for1984 to 1994 are shown in figure 4. Through 1984,the data show a tilt to the south of 5 µrad/yr inresponse to magmatic inflation north of the wellfield. The next leveling of the tilt array in 1985revealed a reversal in the tilt direction as a result ofthe onset of geothermal production. Subsequentsurveys through 1989 reveal a linear tilt rate of38±2 µrad/yr to the north toward the well field.


N S120

100

80

60

40

20

0

-20

-4037 38 39 40 41 42 43 44 45

ELE

VA

TIO

N C

HA

NG

E, I

N M

ILLI

ME

TE

RS

DISTANCE FROM LEE VINING, IN KILOMETERS

W911

5EGE

AZ

1988-92

1985-88

1983-85

Well Field

Figure 3. Elevation changes in the Highway 395 long base line for three periods between 1983 and 1992. Elevation change is foran individual period and is not cumulative from 1983 (modified from Sorey and others, 1995).


hemene

duld,

ofof

he

edionsedw

1,lsthedin

heceld

1984 1986 1988 1990 1992 1994

Power ProductionBegins (MP-1)

Renewed Inflationof Resurgent Dome

Power ProductionIncreases (MP-2, PLES-1)

CU

MU

LAT

IVE

TIL

T, I

N M

ICR

OR

AD

IAN

S P

ER

YE

AR

38+_ rad/yr2

99+_12 rad/yr

0

100

200

300

400

500

600

700

-50

Individual surveys --the height of vertical barsrepresents one standard deviation

Figure 4. Cumulative land-surface tilt (modified from Sorey and others, 1995).

Renewed inflation of the resurgent dome in late1989 (Langbein and others, 1993) could be thecause of the slight decrease in tilt observedbetween the 1989 and 1990 surveys. In December1990, pumping was increased by 2.2×106 kg/hr tosupply two additional powerplants (MP-2 andPLES-1). This increase in pumping nearly tripledthe tilt rate into the well field. From 1990 to 1994,the north component is fit reasonably well by alinear rate of 99±12 µrad/yr.

In June 1988, the third leveling network wasestablished to provide a more detailed picture ofthe deformation and consists of 45 monumentswithin the well-field graben and across thebounding faults. Data from this leveling networkshow significant changes in the location andmagnitude of maximum subsidence in the wellfield between 1988 and 1994 (figs. 5A–C). Theobserved changes probably were caused by acombination of factors and processes includingchanges in pressure and temperature, infiltration ofcold shallow ground water, venting of steam fromthe reservoir, variations in rock compressibilities,and changes in well locations and injection depths(Sorey and others, 1995). Prior to 1992, the area ofmaximum subsidence was 500 m east of theproduction wells that are centered around

monument AZ (fig. 5A). The offset between thearea of maximum reservoir pressure drop at tproduction wells and the area of maximusubsidence at monument AZ could have becaused by lateral differences in lithology. Thproduction wells are completed in silicifiedrhyolite of low compressibility. The area arounmonument AZ, where subsidence is greatest, cobe underlain by hydrothermally altered rhyolitewhich is highly compressible.

Data collected in 1993 show that the area maximum subsidence had shifted 500 m west monument AZ and was centered around tproduction wells (fig. 5B). The change in locationand magnitude of maximum subsidence resultpartly from pressure decreases in the productreservoir. A 10-meter decrease in head was cauby a pumping-rate increase to supply the two nepowerplants in December 1990. In mid-199shallow perforated zones in the injection welwere sealed to prevent thermal breakthrough of cooled injectate to the production wells anresulted in an additional 15 m of head decline the production reservoir.

The delay between the pressure drop in tproduction reservoir in 1991 and the subsidencentered around the production wells in 1993 cou



0

0

0.5 MILE

500 METERS

1988-91

FF

F

F

F

F

FAZ

8050 40

30

30

20

10

10

0

20

3040

50

8070 60

N

F

0F

FF

F

F

F

F

10

20

20

30

30

0

0

0.5 MILE

500 METERS

1991-93

F

AZ

N

40

5

0

-5-10

-5

-20

BA

0

0

0.5 MILE

500 METERS

1993-94

F F F

FF

F

F

FAZ

55

20

1510

10 15 20 25

0

N

C

F

EXPLANATION

Normal fault (dashed where uncertain)

Production well

Production well with bench marksInjection well

Injection well with bench marks

Observation well

L-shaped array bench mark

Steam vent

Geothermal powerplant

Long baseline bench mark

Bench mark established in 1993

AZ Monument AZ

Line of equal elevation change--Interval is variable10

Figure 5. Land-surface elevation change, in millimeters, in the Casa Diablo geothermal well field. A, 1988–91. B, 1991–93. C,1993–94. Modified from Sorey and others, 1995.

have been caused by thermal expansion of rocks

above the production reservoir. A large increase in

the volume of steam discharged from fumaroles

and along faults was observed during 1991 and

most of 1992. The increase in steam discharge was

caused by boiling in the reservoir induced by the

pressure drop. Thermal expansion was reversed

when cold shallow ground water moved toward the

pressure low at the production wells.

The data for 1994 show a shift in the area ofmaximum subsidence towards the center of thegraben (fig. 5C). The greater degree of isolationbetween the injection and production reservoirspossibly allowed the pressure drop in theproduction reservoir to spread across the well fieldto include the central part of the graben. If veryfine-grained materials compose the central part ofthe graben, the reduction in pore pressure wouldinitiate a slow dewatering process that would



,

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ore,ynl

,onrnl0,

propagate from the production wells to the centerof the graben. The changes in the location ofmaximum subsidence between 1993 and 1994 alsocould be related to changes in the production andinjection rates of individual wells in the geothermalfield.

REFERENCES CITED

Hill, D.P., Bailey, R.A., and Ryall, A.S., 1985, Activetectonic and magmatic processes beneath LongValley Caldera, eastern California—An overview:American Geophysica l Union, Journal o fGeophys ica l Research , v. 90 , no . B13 ,p. 11,111–11,129.

Langbein, J., 1989, Deformation of the Long ValleyCaldera, eastern California, from mid-1983 tomid-1988: American Geophysical Union, Journal of

Geophys ica l Research , v. 94 , no . B4p. 3,833–3,850.

Langbein, J., Hill, D.P., Parker, T.N., and WilkinsonS.K., 1993, An episode of reinflation of the LonValley Caldera, eastern California, 1989–199American Geophysica l Union, Journal oGeophys ica l Research , v. 98 , no . B9p. 15,851–15,870.

Savage, J.C., Cockerham, R.S., Estrem, J.E., and MoL.R., 1987, Deformation near the Long ValleCaldera, eastern California, 1982–1986: AmericaGeophysical Union, Journal of GeophysicaResearch, v. 92, no. B3, p. 2,721–2,746.

Sorey, M.L., Farrar, C.D., Marshall, G.A., and HowleJ.F., 1995, Effects of geothermal development deformation in the Long Valley Caldera, easteCalifornia, 1985–1994: American GeophysicaUnion, Journal of Geophysical Research v. 10no. B7, p. 12,475–12,486.



Hydrogeologic Effects of Flooding in the Partially Collapsed Retsof Salt Mine, Livingston County, New York

By Dorothy H. Tepper, William M. Kappel, Todd S. Miller, and John H. Williams

The Retsof Salt Mine is in Livingston County,New York, about 25 mi (40 km) southwest ofRochester (fig. 1). This mine, which has been inoperation for 110 years and is about 1,100 ft(335 m) below land surface, supplies road salt to14 States in the Northeast. Retsof Salt Mine is thelargest salt mine in the Western Hemisphere andincludes an underground area that is roughly thesize of Manhattan (6,500 acres or about2,630 hectares). An underground room near thesouthern end of the mine near Cuylervillecollapsed on March 12, 1994, and an adjacentroom collapsed in early April. Two large, circularcollapse features that are several hundred feet aparthave developed at land surface above the twocollapsed mine rooms. The northernmost feature,which is about 700 ft (213 m) in diameter, includesa central area about 200 ft (60 m) wide that hassubsided about 20 to 30 ft (6 to 9 m). Thesouthernmost feature, which is about 900 ft(274 m) in diameter, includes a central area that isabout 700 ft (213 m) wide that has subsided about70 ft (21 m). The subsidence in the collapse areahas forced the closure of a section of State Route20A as a result of the partial collapse of a NewYork State Department of Transportation bridge.

During the formation of these collapsefeatures, hydraulic connections formed betweenaquifers and the mine that had been previouslyisolated from each other by confining units. Thesenew connections have provided routes for rapidmigration of ground water downward to the minelevel. Since March 12, ground water draining fromoverlying aquifer systems has been progressivelyflooding the mine at inflow rates averaging about18,000 gal/min (1,135 L/s). This aquifer drainagehas caused inadequate water supplies in a numberof local wells, and some wells actually have gonedry. The U.S. Geological Survey (USGS) has beenworking with the Livingston County Department


of Health since March 1994 to provide technicalexpertise in dealing with this situation. A regionalground-water-level monitoring network has beenestablished to observe the rate, magnitude, andextent of aquifer drainage related to the minecollapse. Data collected since the initial collapseshow that water levels in some wells drilled in theflood-plain sediments and upland bedrock units areshowing only expected seasonal changes.Significant water-level declines resulting fromaquifer drainage into the mine have been observedin some wells completed in glacial deltaic depositsalong the valley walls in an extensive basalsand-and-gravel aquifer in the Genesee Valley andin the uppermost bedrock near the collapse features(fig. 1). The basal sand-and-gravel aquifer and thethin water-bearing zone at the top of bedrock arehydraulically connected.

A conceptual model of the ground-water flowsystem has been developed on the basis ofknowledge of the hydrogeology of similar valleysin central and western New York, boreholegeophysical surveys of 18 wells drilled in andadjacent to the collapse features, and marineseismic-reflection profiling on the Genesee River.The complex ground-water flow system involvesmultiple aquifers in the glacial sediments and thebedrock. In June 1994, a team of specialists fromthe USGS examined the environmental effects ofthe partial collapse of the mine. The team compileda list of options for further short-term andlong-term studies to address the major issues ofpublic safety, aquifer drainage, and subsidence.The USGS, the mining company, and theLivingston County Department of Health continueto monitor ground-water levels in the area, and theUSGS is constructing a preliminary numericalmodel to assess the long-term effects of the partialmine collapse on the regional ground-water flowsystem.



Figure 1. Location of Retsof Salt Mine, area of collapse, and hydrograph of water-level decline in a well 3.5 miles from the mine.

575

450

550

500

400

1 MILE

Retsof MineArea of the

Mt.

Geneseo

Collapse area

N

Genesee

Canaseraga

Creek

Well in basal gravel

Leicester

Route 63

Route 20A

Rou

te 3

9

Route 20A

Cuylerville525

475

425

Livingston

NEW

LOCATION OFSTUDY AREA

WA

TE

R L

EV

EL

EL

EV

AT

ION

, IN

FE

ET

AB

OV

E S

EA

LE

VE

L

1994 1995Apr Jul Oct Jan Apr

Well no longermeasured,

venting naturalgas

County

Morris

YORK

Estimated water-level

decline

Recordedwater-leveldecline

River

Genesee River

EXPLANATION

Well that has gone dryor experienced largewater-level decline as

Genesee River Valley

Genesee Uplands

of April 1995

Direction of streamflow

Collapse feature

0 1 KILOMETER

0Route 63

Route 408

Hydrogeologic Effects of Flooding in the Partially Collapsed Retsof Salt Mine, Livingston County, New York 37

Documents

Report Documentation PageU.S. Geological Survey Open-File Report 97-47 U.S. Geological Survey Subsidence Interest Group Conference, Proceedings of the Technical Meeting, Las Vegas,