Numerical simulation and prediction of regional land ...

Engineering Geology 201 (2016) 6–28

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Numerical simulation and prediction of regional land subsidence caused by groundwater exploitation in the southwest plain of Tehran, Iran Masoud Mahmoudpour a, Mashalah Khamehchiyan a,⁎, Mohammad Reza Nikudel a, Mohammad Reza Ghassemi b a b

Department of Engineering Geology, Faculty of Basic Science, Tarbiat Modares University, Tehran, Iran Research Institute for Earth Science, Geological Survey of Iran (GSI), Tehran, Iran

a r t i c l e

i n f o

Article history: Received 12 October 2014 Received in revised form 19 November 2015 Accepted 5 December 2015 Available online 9 December 2015 Keywords: Regional land subsidence Groundwater withdrawal Numerical simulation PMWIN Tehran

a b s t r a c t This study characterizes land subsidence in southwest plain of Tehran using numerical modeling and predicts the trend through 2018. Excessive groundwater withdrawal has caused severe land subsidence in Tehran; in the past 28 years (1984–2012), groundwater level has decreased 11.65 m. The multi-layered aquifer system in the southwestern plain of Tehran contains three aquifers and three aquitard units. The present model was developed simulation using PMWIN (MODFLOW for Windows). First, groundwater level and land subsidence were simulated for the end of 2004. The model was calibrated using hydraulic head measurements and InSAR data. The simulation results were in fairly good agreement with the measurement results. The calibrated and evaluated model was then used to assess the future evolution of land subsidence and for prediction of subsidence through the end of 2018. Numerical results show that, assuming a constant rate of pumping in the future, land subsidence in the southwestern plain of Tehran will reach 33 cm by 2018. The study confirmed that land subsidence caused by groundwater pumping is a serious threat to southwest Tehran. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Land subsidence includes both the gentle downwarping and sudden sinking of discrete segments of the ground surface (Galloway and Burbey, 2011). In many areas in the United States underlain by soluble rocks, land subsidence is a common phenomenon. Consequently, the most common type of sudden collapse is from erosion of underground soil and/or rock caused by leakage of sewage pipes or water mains. A second type of sudden collapse results from dissolution of carbonate rocks beneath the surface in these areas (Zeitoun and Wakshal, 2013). Underground mining is another cause for man-induced subsidence. Mining activities that remove materials (such as coal and salt) from below the surface can result in a sudden subsidence (Zeitoun and Wakshal, 2013). Displacement is principally vertical, although horizontal deformation often causes significant damage. The extraction of groundwater plays a direct role in land subsidence by causing the compaction of susceptible aquifer systems. Subsidence accompanying the extraction of fluids such as water, crude oil and natural gas from subsurface formations is perhaps the best known cause of land subsidence. Subsidence can disturb the existing infrastructure, including buildings, roads, railways and pipelines, and also signifies a major deficiency in sustainable water management (Galloway and Burbey, 2011). ⁎ Corresponding author. E-mail address: [email protected] (M. Khamehchiyan).

http://dx.doi.org/10.1016/j.enggeo.2015.12.004 0013-7952/© 2015 Elsevier B.V. All rights reserved.

Land subsidence caused by long-term excessive groundwater withdrawal is a worldwide phenomenon. It is often observed in semiarid and arid environments. Over 150 major cities worldwide have experienced substantial subsidence (Hu et al., 2004). The severe consequences to the environment and economy of the global distribution of land subsidence demonstrate that it requires research and technology transfer on an international level (Hu et al., 2004). Geohazards caused by land subsidence from excessive pumping of groundwater have been reported in Jakarta and Samarang, Indonesia (Chaussard et al., 2013), Venice, Italy (Teatini et al., 2012), Mexico City, Mexico (Osmanoğlu et al., 2011; Yan et al., 2012; Chaussard et al., 2014), Shanghai, China (Hu, 2006), Beijing, China (Ng et al., 2011), Tianjin, China (Yi et al., 2011), Antelope Valley, California, USA (Galloway et al., 1998), Houston–Galveston, Texas, USA (Gabrysch, 1984), San Joaquin Valley, California, USA (Ireland et al., 1984), Santa Clara Valley, California, USA (Poland and Ireland, 1988), Bangkok, Thailand (Phien-wej et al., 2006), and Quetta Valley, Pakistan (Khan et al., 2013). In Iran, it has been reported in Rafsanjan (Mousavi et al., 2001; Rahnama and Moafi, 2009), Mahyar, Nayshabour and Kashmar (Lashkaripour et al., 2010, 2007, 2006) and Mashhad (Motagh et al., 2007). Table 1 records recent subsidence rates worldwide. Land subsidence can be explained by poroelasticity or poroelastic consolidation theory, which was first formulated by Biot (1941). Poroelasticity theory is a valuable method for analysis of the interaction between fluid flow and skeletal-matrix deformation (Hsieh, 1996). The principle of effective stress, first proposed by Karl Terzaghi in 1925, is

M. Mahmoudpour et al. / Engineering Geology 201 (2016) 6–28

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Table 1 Recent worldwide measured subsidence rates for selected locations. Rates represent the local maximum measured rate for the specified period (modified from Galloway and Burbey, 2011). Location

Rate (mm/year)

Period

Measurement method

Source

Aguascalientes Valley, Mexico Anthemountas Basin, Northern Greece Bandung, Indonesia Bangkok, Thailand Beijing City, China Bologna, Italy Coachella Valley, California, US Datong, China Gioia Tauro plain, Italy Guangrao, Yellow River Delta, China Houston-Galveston, Texas, US Jakarta, Indonesia Mashhad Valley, Iran Mexico City, Mexico Murcia, Spain Quetta Valley, Pakistan Saga Plain, Japan Semarang, Indonesia Tehran Basin, Iran Thessaloniki plain, Northern Greece Tianjin, China Tokyo, Japan Toluca Valley, Mexico West of Villa de Arista, Mexico Yunlin, Taiwan Zamora, Mexico

111 23 230 30 115 40 70 20 23 65 40 220 280–300 380 35 100 160 130 205–250 45 30–40 40 90 184 100 128

1993–2003 1995–2001 2006–2009 2006 2003–2009 2002–2006 2003–2009 2004–2008 1992–2006 2002–2008 1996–1998 1997–2010 2003–2005 2002–2007 2008–2009 2006–2009 1994 2007–2009 2004–2008 1995–2001 2007–2010 1977–1988 2003–2008 2007–2011 2002–2007 2007–2011

Global positioning system Differential interferometry Differential interferometry Leveling Differential interferometry Differential interferometry Differential interferometry Differential interferometry Differential interferometry Leveling Differential interferometry Global positioning system Differential interferometry Differential interferometry Differential interferometry Global positioning system Leveling Global positioning system Differential interferometry Differential interferometry Leveling ? Differential interferometry Differential interferometry Leveling Differential interferometry

Pacheo-Martínez et al. (2013) Raspini et al. (2013) Chaussard et al. (2013) Phien-Wej et al. (2006) Ng et al. (2011) Bonsignore et al. (2010) Sneed (2010) Zhao et al. (2011) Raspini et al. (2012) Liu and Huang (2013) Buckley et al. (2003) Chaussard et al. (2013) Motagh et al. (2007) Yan et al. (2012) Herrera et al. (2010) Khan et al. (2013) Miura et al. (1995) Chaussard et al. (2013) Dehghani et al. (2013) Raspini et al. (2014) Yi et al. (2011) Hayashia et al. (2009) Calderhead et al. (2011) Chaussard et al. (2014) Hung et al. (2010) Chaussard et al. (2014)

often used to explain the occurrence of land subsidence as related to groundwater withdrawal (Galloway et al., 1999). Excessive groundwater withdrawal from aquifer systems causes pore water pressure to decrease and effective stress to increase. The increase in effective stress results in compaction of hydrostratigraphic units, including aquitard and aquifer units, and land subsidence. It is often thought that aquitard units, which consist primarily of clay and silty clay, experience higher compressibility and greater compaction than aquifer units consisting primarily of sand (Calderhead et al., 2011). Aquifer-system deformation is elastic (recoverable) if the stress imposed on the skeleton is smaller than the previous maximum effective stress. When the stress is greater than the preconsolidation stress, the pore structure (granular framework) of the fine-grained sediments rearranges into a configuration that becomes more stable at higher stress. This results in an irreversible reduction in pore volume and in inelastic compaction of the aquifer system (Sneed et al., 2003). Preconsolidation stress is the maximum effective stress a soil has experienced throughout its life. It separates elastic and reversible deformation from inelastic and partially-irreversible deformation and marks the starting point of high compressibility (Tomás et al., 2007). Calderhead et al. (2011) have shown that numerical models are useful tools for evaluation of the evolution of land subsidence caused by groundwater pumping. They are at present the most powerful predictive tools for assessing future land subsidence (Cao et al., 2013). MODFLOW numerical modeling has been used to simulate groundwater flow (Mc Donald and Harbaugh, 1988) and the interbed storage package (IBS1) in MODFLOW to simulate land subsidence (Leake and Prudic, 1991), determine the layer compaction coefficient, and estimate the groundwater safe yield in Los Banos–Kettleman City, California (Larson et al., 1999). Hoffmann et al. (2003a) used inverse modeling in MODFLOW code and the SUB package to simulate land subsidence and estimate the inelastic storage coefficient and time constant for Antelope Valley, California. Taiyuan basin in China was simulated using IBS. The modeling results show that compression of different clay layers contributes differently to land subsidence (Ma et al., 2006). Kihm et al. (2007) analyzed 3D fully-coupled groundwater flow and land deformation caused by groundwater pumping in southeast of Seoul, Korea.

A new 3D groundwater flow model and a 1D instantaneous compaction finite element numerical model were verified and applied to the Toluca Valley in Mexico (Calderhead et al., 2011). Their study showed that the use of different sources of data was beneficial for estimating and constraining the vertical component of the inelastic skeletal specific storage. Also, the study of Toluca aquifer system was carried out for establishment of a management policy for the sustainable development and management of this aquifer for minimizing land subsidence. Simulation results show that much of the land subsidence could have been avoided by implementing water policies to restrict pumping in regions with compressible materials (Calderhead et al., 2012). A 1D deformation model was developed to simulate deformation for development of groundwater resources under land subsidence control (Shi et al., 2012). Land subsidence analysis in Changhua in central Taiwan was conducted using the COMPAC 1D compaction model. The results provide a key reference for water management in central Taiwan (Hung et al., 2012). Simulation of Hangzhou–Jiaxing–Huzhou plain in China was carried out under transient conditions using MODFLOW 2000 (Harbaugh et al., 2000). The results showed the main cause of land subsidence to be inelastic compaction of the aquifer system resulting from continuously declining water levels (Cao et al., 2013). InSAR data has been used to calibrate numerical methods that reproduce aquifer deformation due to groundwater withdrawals. The relationship between the temporal evolution of the displacement and the groundwater level changes has been used for model calibration. This method can be found for instance in Tomás et al. (2010); Herrera et al. (2009) and Ezquerro et al. (2014). In Iran, land subsidence caused by withdrawal of groundwater has occurred in the cities of Tehran, Mashhad, Kashmar, Varamin, Kashan, and Rafsanjan (Sharifikia, 2010). Simulation of aquifer and land subsidence prediction have been applied with PMWIN to the Shirvan aquifer (Mohammadi et al., 2014), Hamedan–Bahar aquifer (Mahdavi et al., 2013), Shiraz plain (Karimipour and Rakhshandehroo, 2011) and Shahryar plain (Fotovat-Eskandari and Karami, 2009). The prediction model indicates that the maximum rate of subsidence recorded in Shahryar plain was 30 cm/year in 2014.

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Tehran and its surrounding cities (Tehran province) have more than 12 million inhabitants (SCI, 2012). The area is also the site of substantial agricultural and industrial activity. Land subsidence in Tehran, which is the capital of Iran, has been observed since the 1990s (Amighpey et al., 2006). The present study is an analysis of land subsidence caused by groundwater exploitation in southwestern Tehran. This paper is focused on the land subsidence that occurred during 2003–2005 period by groundwater withdrawal in Tehran Plain. The paper is arranged as follows. Section 2 an updated description of the geologic and hydrogeologic characteristics of the Tehran Plain. Leveling, GPS survey method and InSAR results for southwest plain of Tehran are presented in Section 3. Then, Section 4 is devoted to present simulation results of groundwater flow and subsidence prediction, including its formulation, calibration, sensitivity and validation with the available time series of data. The main conclusions are summarized in Section 5. 2. Geological and hydro-geological setting Tehran Basin is a semiarid-to-arid region with an area of approximately 2250 km2 located in Tehran province between the Alborz Mountains to the north and the Arad and Fashapouye Mountains to the south (Fig. 1). The topography of Tehran Basin is relatively flat and gently sloping. The annual temperature ranges from 10 to 42 °C, average annual rainfall is approximately 200 mm, and evaporation is 2500 mm. The southwestern part of the basin has been subject to land subsidence caused mainly by withdrawal of groundwater (GSI, 2005). Subsidence was first revealed by geodetic measurement from precise leveling surveys across the area between 1995 and 2002 (Arabi et al., 2005). A subsidence area of 415.64 km2 is located at 35° 30′ N to 35° 42′ N latitude and 50° 55′ E to 51° 23′ E longitude (GSI, 2005). Alluvial aquifers usually contain different proportions of gravel, sand, silt and clay deposited as layers and lenses of varying thicknesses. Tehran alluvial deposits consist of four stratigraphic units (Rieben, 1955): A (Hezardarreh formation), B (Kahrizak formation, Qt1), C (Tehran alluvial formation, Qt2), and D (recent alluvium), (Fig. 2). The ancient alluvial deposits of Hezardarreh formation comprise conglomerates with a few lenses of sandstone, siltstone and mudstone

and show regular stratification. The thickness is estimated to be about 1200 m. Hezardarreh formation is an impermeable rock unit with extensive cementation and high compaction. This formation folded during the earliest tectonic movement of the Quaternary era. The Kahrizak formation is a heterogeneous early Quaternary formation which forms a flat-layering sheet of alluvial sediment outcropping between the Hezardarreh anticlinal folds and the Alborz margin. This formation consists of clayey silt. The thickness of the Kahrizak formation is uncertain in the southern region of Tehran plain. Faulting has affected the formation in many places; however, it lays horizontally without tilting. Tehran alluvium refers to the sub-recent alluvium of the late Quaternary deposits that have been exposed between the Alborz and antiAlborz. This unit is predominantly exposed in the southern part of the Tehran plain. In the northern part, the unit consists mainly of irregularly layered gravels. Silty loam deposits increase progressively towards the south. The river deposits consist of young alluvium. The maximum thickness of this formation is estimated to be about 60 m. The age of the Tehran alluvial formation is estimated to be 50,000 to 10,000 years (late Pleistocene). No tilting is visible in this formation. The D Unit is the youngest stratigraphic unit in the Tehran region and presents as alluvial and fluvial deposits. This unit is composed of fine silt that is gray in color, sandy and pebbly in places. Fine materials such as silt and clay predominate in the southwestern part of the plain. The oldest rock outcrops in the study area are represented by tuff, andesitic and pyroclastic rocks of the Eocene age (Fig. 2). Tehran alluvium and the Kahrizak formation dominate the central Tehran plain and represent potential aquifers with good hydraulic conductivity. The folded beds of the Hezardarreh formation dominate the northern part of the plain and show poor aquifer characteristics resulting from high cementation with low conductivity. Tectonically, the study area comprises the Tuchal, Karaj and Rudehen blocks that were thrust up and towards the south-southwest by the Musha–Fasham fault (Fig. 3). The Tuchal block has acted as a central wedge, imparting westward movement to the Karaj block and eastward movement to the Rudehen block. The pediment zone confined between these three blocks and in which the subsidence area of Tehran is located, reacted to the surrounding deformations after the Pliocene by

Fig. 1. Shaded relief map of central northern Iran, a) black box: area of the InSAR study (Tehran province), b) thick black lines: location of subsidence profiles derived from InSAR data, c) light gray area: subsidence zone in southwest of Tehran (study area).


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Fig. 2. Regional geological map of study area (modified after GSI, 1993).

the folding and faulting of the surface alluvium and probably downfaulting of the basement rock. The continuity of the directions and sense of tectonic movement that raised the Alborz range above the Central Basin from the late Eocene to the present day makes it difficult to establish a strict chronology for the movement of these blocks. On the scale of the region studied, a dominant thrust from the northeastern sector explains most of the structures encountered, but does not necessarily signify that all blocks were simultaneously active (Tchalenko et al., 1974). Bagha et al. (2014) classified the relative tectonic activity of Tehran area based on geological conditions using analytical hierarchy process method (Fig. 4). The significant morphometric indices evaluated were stream length gradient, drainage basin asymmetry, hypsometric integral, ratio of valley floor width to valley height, drainage basin shape

and mountain front sinuosity. The combined indices represent relative active tectonics. This classification is divided into class 1 (very high activity), class 2 (high), class 3 (moderate), and class 4 (low). This method determined that 11.85% of the Tehran basin falls into class 1, 14.19% into class 2, 48.70% into class 3, and 25.27% into class 4. Southwestern Tehran plain shows the lowest relative tectonic activity (class 4). Recent active tectonic studies have discovered no active faults or tectonic movement and the tectonic deformation rates are lower than the subsidence rates in this area. Geodetic data from several permanent global positioning system (GPS) stations in the area indicate that the shortening rate (N–S) is 5 mm/year and the shear strain rate is 3 mm/year (Vernant et al., 2004). The hydrogeological units of the southwestern plain are divided into the aquifers and aquitards that constitute the region's aquifer system.

Fig. 3. Physiographic units of the Tehran region (Tchalenko et al., 1974).

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Fig. 4. Distribution of relative tectonic activity of Tehran Basin (Bagha et al., 2014); Red box: study area. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Six boreholes were drilled in the study area to a depth of 100 m (except for borehole 1, with a depth of 65 m). The lithology from hydraulic and geotechnical data (399 grain size distribution tests and Atterberg limits, 18 consolidation tests and seismological study) from the ground surface downward shows that the hydrogeological units consist of three aquifers and three aquitards. Evaluation of the logs of more than 31 water drills distinguished the following three aquifer systems: • Aquifer 1 (shallow aquifer) extending down from 7 m to more than 30 m. • Aquifer 2 extending down from 35 m to more than 65 m. • Aquifer 3 (deep aquifer) extending downward from 70 m.

Deep aquifer (3) is the major aquifer for groundwater extraction in the region. This aquifer is mainly composed of alluvial fine sand and silty sand with a thickness of 2 to 20 m. The maximum depth of drilling in this area is 100 m; thus, the lower boundary of the aquifer 3 is not precisely known. It appears that the thickness of this aquifer is greater than of the other two. Fig. 5 is a hydrogeological cross-section of southwestern Tehran plain. The aquitards are formed of mostly silty clay and clayey soil, which play a significant role in land subsidence. Compressible sediments in aquifer system occur as discontinuous interbeds within aquifers, and as extensive confining units adjacent to aquifer (Fig. 6a). In basin-scale groundwater models, simulation of flow and storage changes in individual discontinuous interbeds within

Fig. 5. Hydrogeological cross-section showing the multi-layered aquifer system in the study area (location of the cross section is given in Fig. 2).


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Fig. 6. Compressible beds in an aquifer system and two approaches representing the confining unit in the MODFLOW simulation of aquifer system compaction using IBS1 package. a) Vertical section of an aquifer system with compressible sediments within and adjacent to aquifer, b) use of one model layer to simulate flow and storage changes in the confining unit, c) use of five model layers to simulate flow and storage changes in the confining unit (Hoffmann et al., 2003b).

aquifers is not practical because of difficulties in mapping the interbeds. In contrast, flow and storage changes in individual confining units can be simulated in basin-scale flow models. To simulate flow and storage changes in confining units, one or more layers must be used to present each confining unit (Fig. 6b, c), (Hoffmann et al., 2003b). For Tehran aquifer system, compressible sediments like to Fig. 6b are assumed. Each aquitard is a confining unit. Thus, each of the aquitards was represented as individual model layer. Layers 1, 3 and 5 (Fig. 5) are compressible fine-grained confining units. Layers 2, 4 and 6 (Fig. 5) are aquifers including fine-grained interbeds. The thicknesses of hydrogeological units in southwestern Tehran plain differ. The thickness is greatest in aquitard 3 at BH2 and BH3 (Sabashahr and Eslamshahr, respectively), (Table 2). The clays of Sabashahr are of low-to-high plasticity. The increase in these parameters is significant for the land subsidence rate in this area. The characteristics of the hydrogeological units are shown in Table 3. Compression index (Cc), recompression index (Cr) and void ratio has been obtained from 18 consolidation tests. Liquid limit (LL), plastic limit (PL) and soil unified classification has been obtained from 399 grain size distribution tests. The engineering geological parameters presented show that aquitard 3 probably plays a more important role in progressive subsidence than aquitards 1 and 2. Significantly, the void ratios, liquid limits, plastic limits and layer thickness of aquitard 3 are greater than these values for the other two aquitards. The thickness of aquitard 3 is 9 to 41 m; the thickness at borehole 2 near Sabashahr is greatest (41 m). The clays of the Sabashahr region show high plasticity (CH) (GSI, 2008b). The topography map of the bedrock indicates that the highest and lowest bedrock elevations are about 1138 m and 853 m, respectively. The bedrock is composed of andesitic and pyroclastic rocks

with tuff and shale. The maximum and minimum thicknesses of the saturated zone in this region are 84 and 34 m, respectively (GSI, 2008a, 2007). The groundwater flow direction is from the north to the southsoutheast. The major water uses in Tehran plain are agricultural (51%), domestic and drinking (34%), and industrial (7%). Other uses comprise 8% of total volume demand (TRWC, 2012). In 2012, about 1.9 billion m3 of water were extracted from Tehran aquifer. In 2003, the number of wells permitted in the Tehran plain was 26,070; by 2012, this number had risen to 32,518 (Table 4). Despite the fact that the number of wells tripled from 2003 to 2012, the total discharge decreased. This reduction in water discharge was the result of the decline in groundwater levels and the increase in water consumption. Fig. 7 shows the groundwater level in the Tehran plain from October 1984 to March 2012. Major drops of 4 m from 1984 to 1991, 6 m from 1995 to 2004, and 1.65 m from 2007 to 2012 are evident. There are small increases in the groundwater level from 1991 to 1995 and 2005 to 2006. In March 2012, the groundwater level was 1056.5 m. The total decrease in groundwater level over 28 years was about 11.65 m, which signifies an average of 42 cm/year The depth to groundwater is generally from 22 to 55 m in the study area. A comparison of the number of pumping wells and the volume of water extracted from 1968 and 2003 indicates that the ability of the aquifer system to yield water has significantly decreased because of insufficient recharge (GSI, 2005). Water balance calculations indicate that 6848 wells extract about 810.09 million m3 per year of groundwater from the aquifer system, whereas the annual recharge is only about 793.74 million m3. The annual mean variation in reservoir volume is 16.3 million m3. In other words,

Table 2 Thickness of hydrogeological units in the boreholes (m), values in parenthesis are total thickness. units

BH1

BH2

BH3

BH4

BH5

BH7

Fill materials

0–0.6 (0.6) 0.6–7.80 (7.2) 7.80–14 (6.2) 14–36.36 (22.36) 36.36–54 (17.64) 54–63.50 (9.5) 63.50–68.40 (4.9)

0–0.7 (0.7) 0.7–16.2 (15.5) 16.20–19.40 (3.2) 19.40–36.60 (17.2) 36.60–50.50 (13.9) 50.50–92 (41.5) 92–100 (8)

0–2 (2) 2–16.50 (14.5) 16.50–25.90 (9.4) 25.90–53.30 (27.4) 53.30–59.80 (6.5) 59.80–92.60 (32.8) 92.60–100 (7.4)

0–2 (2) 2–29.5 (27.5) 29.5–41.60 (12.1) 41.60–58.10 (16.5) 58.10–71.45 (13.35) 71.45–89 (17.55) 89–100 (11)

0–0.5 (0.5) 0.5–18.55 (18.05) 18.55–25.30 (6.75) 25.30–54.70 (29.4) 54.70–67.70 (13) 67.70–98 (30.3) 98–100 (2)

0–0.5 (0.5) 0.5–14.40 (13.9) 14.40–21.95 (7.55) 21.95–37.70 (15.75) 37.70–47.30 (9.60) 47.30–80 (32.70) 80–90 (10)

Aquitard 1 Aquifer 1 Aquitard 2 Aquifer 2 Aquitard 3 Aquifer 3

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Table 3 Engineering geological properties of hydrostratigraphic units. Hydrogeological units

Lithology

Thickness (m)

Unified classification

Liquid limit LL (%)

Plastic limit PL (%)

Unit weight γ (KN/m3)

Void ratio e (−)

Shear wave velocity Vs (m/s)

Compression index, Cc (−)

Recompression index, Cr (−)

Aquitard 1 Aquifer 1 Aquitard 2 Aquifer 2

Silt and clay Silty sand, clayey sand Clay and silt Silty sand, clayey sand, poorly graded sand Clay and sand Silty sand, clayey sand

7–27 3–12 16–29 6–18

CL-ML SM-SC CL SM-SCSP CL-ML SM-SC

24.7–44.6 20.1–37.5 27–46.8 22.4–31.5

17–29.3 16–20 14.8–26.2 18.4–20.8

16.19–16.90 16.30–16.53 16.22–17.54 18.86–20.88

0.58–0.75 0.25–0.32 0.52–0.76 0.25–0.34

228–348 266–297 235–398 626–830

0.26–0.35 – 0.16–0.34 –

0.18–0.21 – 0.11–0.24 –

23.3–48.8 22.6–39.4

10–32.4 24.4–26.3

20.15–20.88 21.12–22.41

0.64–0.82 0.25–0.34

794–907 437–1536

0.14–0.52 –

0.10–0.46 –

Aquitard 3 Aquifer 3

9–41 2–20

over 10 years from 1994 to 2004, the volume of the aquifer system decreased by 163 million m3 (Ghasemi and Shemshaki, 2009). More than 1200 wells are estimated to exist in the study area. These wells are generally agricultural and domestic and extract water from aquifers 2 and 3. Also, 13 piezometric wells are existed in this area (Fig. 8). Their characteristics are presented in Table 5. Temporal evolution of piezometric level for 6 wells is shown in Fig. 9. 3. Leveling, GPS and InSAR data Land subsidence in Tehran basin has been measured over the years using precise leveling, the GPS survey method and InSAR. 3.1. Leveling and GPS data Leveling measurements were carried out by the National Cartographic Center of Iran. Land subsidence was first demonstrated using geodetic observations from precise leveling surveys across the area between 1995 and 2004 (for lines AB and CD), and between 1989 and 2004 (for line EF). Measurements of 78 benchmarks located in three general directions were used, with 42 benchmarks located within the study area (Fig. 2). The first leveling profile was along line AB located to the east and includes 13 benchmarks. This line begins from station Z1, ends at station Z13, and is approximately 16.36 km in length with a maximum land subsidence rate of 1.86 m from 1995 to 2004 (20.7 cm/year) (line AB; Fig. 2). The second leveling profile was along line CD, is approximately 38 km in length, is located south of the study area in the NE–SW direction, and includes 18 benchmark stations. This line begins at station S1 and ends at station S18. The maximum land subsidence on this line was observed at station S6 at 1.52 m from 1995 to 2004 (17 cm/year) (line CD; Fig. 2). The last line is a north–south line west of the study area with 11 stations (line EF; Fig. 2). This line starts from station K5 and ends at station K15. The average land subsidence rate was about 6.5 cm/year from 1989 to 2004. Fig. 10 shows the accumulative subsidence for 3 profiles at Tehran plain. Table 6 shows the measurement results of different benchmarks in the study area. Table 4 Discharge of wells and Infiltration galleries (Tehran Regional Water Company, TRWC, 2012). Year

Number of wells

Discharge of wells (million m3)

Discharge of Infiltration galleries (million m3)

Number of Infiltration galleries

Total discharge (million m3)

1968 1983 1994 2003 2012

3906 7304 8950 26,076 32,518

638.8 985.7 961.9 901.4 1881.8

393 – 272 71 26

522 – 286 76 167

1031.8 – 1233.9 972.4 1907.8

Fig. 11 presents the subsidence rates of benchmarks located in the Tehran plain. The maximum subsidence rates at study area are 20.7, 20 and 17 cm/year, respectively. Ground level changes were also studied using time series methods. Two GPS stations (SAFA and AVRZ) located in the southwestern region of Tehran (Fig. 2) form a portion of the local geodynamics network of Tehran province (NCC, 2007). Local networks are created for specific purposes and are generally temporary. This study was conducted from 2006 to 2008. At present, the two stations have been removed from this network and are now abandoned. GPS data indicates that southwestern Tehran is subsiding at a high rate (Fig. 12). 3.2. InSAR data The area of subsidence in southwestern Tehran is based on satellite data using the InSAR method. Remote sensing radar interferometry measurements were carried out by the Center for Observation and Modeling of Earthquake and Tectonics at Oxford University, UK (GSI, 2005). The 10 ENVISAT images were ordered from the European Space Agency (ESA) and 6 interferograms were processed using the Repeat Orbit Interferometry Package, Shuttle Radar Topography Mission (SRTM) and ESA orbital data. Temporal decorrelation of the InSAR signal, which increasingly introduces noise over time to the interferograms, affected the main part of the subsidence zones. The data set for the temporal and spatial baseline is shown in Fig. 13. Each interferogram is identified by a pair of image acquisition dates (yyyymmdd). The interferograms are sorted by time interval from shortest to longest (Fig. 14). These images were acquired from September 2003 to March 2005. In the Fig. 13 (Fig. 14a to f), each color cycle corresponds to a range change of 2.8 cm between the ground and the satellite; the blue–pink–yellow succession corresponds to subsidence. As the satellite line-of-sight is nearly vertical (incidence angle = 24.6°), assuming that ground displacement for subsidence is also vertical, a color cycle can be interpreted as defining about 3 cm of subsidence. Note that the long wavelength signal in the interfrogram is probably the result of orbital errors and/or atmospheric effects that should not be interpreted as subsidence. A deformation map was obtained by differencing the phase measurements from two radar images acquired at different times. A phase difference is an interferometric phase consisting of different components. One component is introduced by the topography of the area and was removed using an external digital elevation model (DEM), resulting in a differential interferogram. Atmospheric artifacts are mitigated using the smoothed time series of the refined interferometric phase. Vertical displacement (D) derived from InSAR measurements (InSAR_d) is calculated as: D ¼ −InSAR− d

.

cos

ipi

.

180

where i is the incidence angle (24.6°).

ð1Þ


13

Fig. 7. Groundwater level for the Tehran aquifer system between 1984 and 2011.

In the interferogram (Fig. 15), one typical subsidence zone features a number of fringes (transition from blue to pink) that increase over time. InSAR data processing was conducted for 2, 3, 4, 6, 12 and 18 months periods (Sep. 2004 to Mar. 2006). The data for a period of 6 month with the least temporal decorrelation (Sep. 2004 to Mar. 2005) specifies a subsidence region of 415.64 km2. The subsidence area correlates with the locations of wells from which groundwater is exploited for agricultural purposes (GSI, 2005).

The interferograms were unwrapped (color-cycle ambiguity was removed) and geo-referenced to produce a map of total displacement between two dates. Subsidence was analyzed for four dates (A: 9 May 2004, B: 26 September 2004, C: 9 January 2005, D: 20 March 2005) using a subset of 3 unwrapped interferograms with small baselines and small temporal intervals (interferograms 20040509–20040926; 20040926–20050109; 20050109–20050320). Because temporal decorrelation is smaller at small time intervals, short time interferograms

Fig. 8. Distribution of the pumping and piezometric wells of the study area.

14


Table 5 Characteristics of piezometric wells for the 2003–2004 period. Well

Drilling date

Depth of drilling (m)

Piezometric level (m a.s.l.)

Piezometric head (m a.s.l.)

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13

1983 1983 1989 1983 1984 1984 1984 1984 1989 1983 1983 1984 1984

50 63 55 58 75 61 76 55 84 72 65 65 65

1135.75 1108.58 1096.82 1104.50 1114.44 1074.02 1138.75 1091.20 1127.03 1057.81 1085.14 1086.88 1102.35

22 45 63 34 49 34 45 24 75 28 54 35 48

were used to construct longer ones. Interferogram BD (using dates B and D) was constructed by summing interferograms BC and CD. Interferogram AD is the sum of interferograms AB, BC and CD. This method decreased decorrelation noise in long-term interferograms. It was assumed that all InSAR signals relate to displacement and other effects such as atmospheric perturbations were neglected. This assumption implies centimetric accuracy of the results. Long wavelength signals were also removed from the unwrapped interferograms. The center of the city of Tehran was arbitrarily fixed as the reference point for unwrapping; this point is assumed to have null displacement. The reference date was fixed at 20 March 2005. The maps in Fig. 16 show displacements in cm relative to 20 March 2005 and the center of Tehran. In the figure, unwrapped interferograms are superimposed on a shaded DEM. The black lines denote the locations of the profiles. The color scale shows the amount of displacement (dark blue: ≥10 cm towards satellite; green: 0 cm; dark red: ≥ 10 cm away from satellite). Gaps in the interferograms show where the fringes were successfully unwrapped because of noise. The areas covered by agricultural fields contain fewer pixels because of the low temporal coherence of vegetation. The subsidence map was studied at periods of 70, 175 and 315 days. The color spectra of the satellite data processing and displacement values were detected for profiles 1 and 3 having NE–SW and N–S strikes. The land subsidence pattern in this area is V-shaped (Fig. 17). The maximum rate of land subsidence in profile 1 was 15 cm and in profile 3 was 16 cm (GSI, 2005).

Satellite data analysis indicates that maximum accumulated subsidence in a 110 days period (spring to summer 2010) was about 110 mm. This signifies a land subsidence rate of about 1 mm/day for this period. Maximum accumulated subsidence for this region over a period of 3 years (2007–2010) was about 59 cm. This region covers an area of nearly 530 km2 (Fig. 18; Sharifikia, 2010). In Iran, the summer drawdown season typically occurs from May to October and the rest of the year is the recovery season. Fig. 18 shows the summer season in which most groundwater is extracted by wells.

3.3. Analysis of measurements Validation of the results was not possible because the GPS measurements and precise leveling observation cover time intervals that differ from the time span for the InSAR data. Fig. 19 compares the subsidence rates for benchmarks along lines AB, CD and EF (Fig. 2) from InSAR (2003–2005) and leveling. The subsidence rates derived from each method were different, but the pattern and shape of the subsidence area for both methods were the same.

4. Numerical simulation of groundwater flow and land subsidence Groundwater flow and land subsidence were simulated by PMWIN5.3 processing. MODFLOW for Windows (PMWIN) is a simulation system that models groundwater flow and transport processes using the modular 3D finite difference groundwater model MODFLOW 96 of the U.S. Geological Survey. Application of MODFLOW to the description and prediction of the behavior of groundwater systems has increased significantly. Since the publication of MODFLOW, different codes have been developed to simulate specific features of a hydrologic system. PMWIN also supports calculation of elastic and inelastic compaction of an aquifer from changes in hydraulic heads (Chiang, 2005). Land subsidence was simulated using the interbed storage (IBS1) modular package for PMWIN5.3. IBS1calculates the volume of water released from storage and simulates elastic and inelastic compaction of compressible fine-grained beds in an aquifer caused by groundwater extraction. The term “interbed” denotes a poorly permeable bed within a relatively permeable aquifer (Leake and Prudic, 1991). The package is based on 1D (vertical) consolidation which assumes that the principal stress and deformation is vertical and the total stress does not vary. IBS1 calculates vertical compaction using the Jacob–Terzaghi theory in

Fig. 9. Graph showing piezometric level changes from 1991 to 2012 from six piezometer wells in study area. The location of these wells is shown in Fig. 8.


15

Fig. 10. Leveling results of land subsidence mentioned by National Cartographic Center of Iran.

which volume strain is calculated as:

ε ¼ εzz ¼

Δb b

ð2Þ

Table 6 Elevation changes and rates at the benchmarks in the Tehran plain. Benchmark no.

Accumulated displacement (m)

Subsidence rate (m/year)

Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Z13 S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 K5 K6 K7 K8 K9 K10 K11 K12 K13 K14 K15

−0.001 −0.009 −0.027 −0.021 −0.0361 −0.043 −1.870 −1.2571 −1.176 −0.922 −0.713 −0.651 −0.756 −0.64 −0.7671 −1.021 −1.329 −1.410 −1.523 −1.1761 −1.2179 −0.9511 −0.739 −0.582 −0.492 −0.602 −0.152 −0.115 −0.104 −0.1721 −0.102 −0.004 −0.006 −1.00 −2.236 −3.025 −2.656 −1.982 −1.34 −0.575 −0.25 −0.03

0.0001 0.001 0.003 0.0023 0.004 0.0048 0.2078 0.1397 0.1307 0.1024 0.0792 0.0723 0.084 0.071 0.0852 0.1134 0.1476 0.1566 0.1692 0.1307 0.1353 0.1057 0.0821 0.0647 0.0547 0.0669 0.0169 0.0128 0.0115 0.0191 0.0113 0.0004 0.0006 0.0670 0.1490 0.2020 0.177 0.132 0.089 0.038 0.0167 0.002

where ε is the volume strain, εzz is the component of volume strain in the vertical direction, b is the aquifer thickness, and Δb is the change in aquifer thickness or compaction. The relation between groundwater head change and soil compaction is based on the principle of effective stress developed by Terzaghi (1925), where the vertical effective stress (σ´) is expressed as the difference between total stress (σ), which is the total overburden load (geostatic stress), and fluid or pore pressure (p) (Leake and Prudic, 1991) as: σ΄ ¼ σ −p

ð3Þ

If geostatic stress is assumed to be constant, then: dσ΄ ¼ −dp

ð4Þ

A change in effective stress resulting from a given head change generally differs in unconfined and confined aquifers. If the water table is raised or lowered in an unconfined aquifer, the geostatic pressure will change. The resulting change in effective stress in the unconfined aquifer can be expressed as (Poland and Davis, 1969): Δσ΄ ¼ −γw ð1−n þ nw ÞΔh

ð5Þ

where Δσ´ is the change in effective stress, γw is the unit weight of water, n is porosity, nw is the moisture content above the water table as a fraction of total volume, and Δh is the change in water table. In a confined aquifer, the geostatic stress changes negligibly with changes in head in the confined aquifer owing to the small changes in the unit weight of water associated with the expansion or compaction of water. A change in effective stress caused by a change in a confined aquifer can be described as (Poland and Davis, 1969): Δσ΄ ¼ −γw Δh

ð6Þ

The relation between the void ratio (the ratio of the volume of voids to volume of soils) and the water pressure depends on the rheological behavior of the soil. For cohesive soils, experimental results lead to a relationship of the type (Zeitoun and Wakshal, 2013): e ¼ e −C c log σ΄−σ΄

ð7Þ

Where e° is the void ratio at the effective stress σ´°, e is the void ratio at the effective stress σ´, Cc is the compression index. For many types of sediments, the void ratio, e, decrease linearly with an increase in the

16


Fig. 11. Subsidence rates of the benchmarks (The benchmark location is shown in Fig. 2).

logarithm of effective stress. The relation is (Zeitoun and Wakshal, 2013):

Inelastic compaction, Δbi, and elastic compaction, Δbe, can be computed by the expression (Zeitoun and Wakshal, 2013):

Δe ¼ −C c Δlog 10 σ΄

Δbi ¼

0:434 b C c Δσ΄ ð1 þ e Þσ΄

ð11Þ

Δbe ¼

0:434 b C r Δσ΄ ð1 þ e Þσ΄

ð12Þ

for

σ΄zz ≥ σ΄ zzð maxÞ

ð8Þ

Δe ¼ −C r Δlog 10 σ΄ for

σ΄zz b σ΄ zzð maxÞ

ð9Þ

where Cr is the recompression index and σ 'zz(max) is the preconsolidation stress. These relations are valid for both preconsolidated soil and also overconsolidated soil. Also the compaction of the layer is related to the changes in the voids ratio by the expression (Zeitoun and Wakshal, 2013): Δb ¼ −

b Δe 1 þ e

ð10Þ

where b° is the initial thickness of layer, e° is the initial void ratio, Δe is the change in the void ratio and Δb is the change in layer thickness.

On the other hand, The IBS package uses the Eq. (13) to calculate the change in the thickness (Δb) of the interbed (Chiang, 2005): Δb ¼ Ssk :Δh:b

ð13Þ

where Ssk is skeletal-specific storage, Δh is the change in the hydraulic head, and b is the original thickness of the layers. To account for large changes in skeletal-specific storage when the effective stress exceeds the preconsolidation stress, the following two parameters are often used (Hoffmann et al., 2003b): Ssk ¼ Sske

for

σ΄zz b σ΄zzð maxÞ

ð14Þ

Fig. 12. Vertical components of motion observed by the GPS stations (Time series), a) SAFA station (Apr. to June 2006), b) SAFA station, (Feb. to June 2008), c) AVRZ station (Apr. to June 2006), d) AVRZ station (Feb. to June 2008). Note the rapid subsidence observed in two sites (The GPS stations location is shown in Fig. 2).


17

Fig. 13. Available baseline information for ENVISAT images.

Ssk ¼ Sskv

for

σ΄zz ≥σ΄zzð maxÞ

ð15Þ

where Sske is the elastic skeletal-specific storage, Sskv is the inelastic skeletal-specific storage. According to Leake and Prudic (1991), Δbi and Δbe are related to Δσ΄ by (Chiang, 2005): Δbi ¼

Sskv b Δσ΄ γW

ð16Þ

Δbe ¼

Sske b Δσ΄ γW

ð17Þ

The aquitard deforms elastically when the effective stress is less than the previous maximum effective stress (preconsolidation stress).When the effective stress is greater than the previous maximum effective stress, the aquitard deforms inelastically (Galloway et al., 1998). Sskv ¼ 0:434

C c γw ð1 þ e Þσ΄zz

for

σ΄zz ≥ σ΄zzð maxÞ

ð18Þ

Sske ¼ 0:434

C r γw ð1 þ e Þσ΄zz

for

σ΄zz b σ΄zzð maxÞ

ð19Þ

where Cc is the compression index, Cr is the recompression index, γw is the unit weight of water and e° is the void ratio. Leake (1990) developed the Interbed Storage Package, version 2 (IBS2). IBS2 allows the user to designate arbitrary systems of interbed for which delay in release of water will be calculated (Galloway et al., 2008). The SUB package simulates the delay in release of water from compressible interbeds using 1D diffusion (Cao et al., 2013) as: 2 ∂ h S΄s :∂h ¼ ∂z2 K΄v :∂t

ð20Þ

where S's is the specific storage of the interbed, K'v is the vertical hydraulic conductivity of the interbed, Z is the vertical spatial coordinate, and t is time. 4.1. Model discretization and model conditions Data scarcity remains a major limitation to model applications and to the reliability of their predictions. With the exception of a few heavily-studied major urban centers such as Mexico City, Venice, Las

Vegas, Nevada and Shanghai, and a few non-urban centers such as Antelope Valley, California, and south-central Arizona, subsidence data is often incomplete (Calderhead et al., 2011). The subsidence area in southwestern Tehran plain features a variety of hydrogeological, geotechnic, geoelectric, seismological, InSAR, and GPS data. This data provides a basis for the development of numerical groundwater flow and a subsidence model for the region. The model of study area covers an area of 40 × 23 km discretized in a mesh of 45 rows and 77 columns. The cell dimensions are 500 m by 500 m. The total number of cells is 3465; 1861 cells are active and 1604 cells are inactive. Simulation of groundwater flow was done in a steady state with unsteady state conditions. Land subsidence was simulated only for unsteady state conditions. The simulation of groundwater flow for October 2003 to October 2004 consisted of one stress period with 12 time steps. The length of the stress period was one year (i.e. 3.1536 × 107 s). The stress periods of the land subsidence model were the same as those for the groundwater flow model. The initial heads for the cells were obtained by interpolating the observational data. The initial compaction of all cells was set to zero for the subsidence model. There were 13 observational wells with historical records. Analysis was based on low water level fluctuations under steady-state conditions. The top of the model was the ground surface which was a free surface and the bottom boundary was bedrock. The model consisted of six hydrostratigraphic units of varying thicknesses (Fig. 5) and each model layer represented a hydrostratigraphic unit. The layer properties in the PMWIN package are defined four types, types 0, 1, 2 and 3. Type 0; the layer is strictly confined, and transmissivity of each cell is constant throughout the simulation. Type 1; the layer is strictly unconfined, and transmissivity of each cell varies with the saturated thickness of the aquifer during the simulation (this layer is valid for the first layer only). Type 2; a layer is partially convertible between confined and unconfined. Transmissivity mode of this layer is the same to type 0. Type 3; a layer is fully convertible between confined and unconfined. Transmissivity mode of this layer is the same to type 1. This layer type can be used for all layers of this type that switch between confined and unconfined automatically. For these layers, the initial hydraulic head of a constant head cell should be higher than the elevation of the cell bottom (Chiang, 2005). Thus, the layer type of aquitard (1) is type 1, and other layers are type 3. Recharge is defined by assigning the recharge flux (IR) and recharge flux rate (QR) to each vertical column of cells in the recharge package (Chiang, 2005). Recharge is applied to the most active cell in each vertical column. The recharge flux was computed for these cells. The volume

18


Fig. 14. Interferograms for time spans, a) 20050109–20050320 (2 months), b) 20040926–20050109 (3 months), c) 20040509–20040926 (4 months), d) 20040926–20050320 (6 months), e) 20030803–20040822 (1 year) and f) 20031012–20050424 (1.5 year). One color cycle is 2.8 cm.

of groundwater input and output was calculated for each boundary cell and the recharge flux was then obtained for each cell. MODFLOW uses recharge flux to calculate the recharge flux rate applied to the model cell for simulation as: Q R ¼ IR :DELR:DELC

ð21Þ

where DELR.DELC is the map area of a model cell, QR is the recharge flux rate and IR is the recharge flux. The preconsolidation level (Hp) is the minimum recorded piezometric level corresponding to seasonal fluctuations. It is equivalent to the well-known soil preconsolidation stress used in geotechnical engineering that represents the maximum effective stress experienced by soil (Tomás et al., 2010). Preconsolidation levels for all aquifers were estimated using historical records of groundwater levels in the piezometers of the study area. Preconsolidation levels for the aquitards were interpolated for the groundwater levels in adjacent aquifers assuming that the groundwater levels at the top and bottom of the aquitards are in equilibrium with those in the adjacent aquifers.

4.2. Estimated hydraulic parameters for modeling The hydrogeologic properties of the aquifer system (vertical hydraulic conductivity and storage coefficient) were chosen such that their effect on land subsidence was equivalent to the composite effect of all interbeds. This method is most commonly implemented to simulate the compaction of a multi aquifer system (Teatini et al., 2006). The mean transmissivity in the central of Tehran plain was estimated to be 2500 m2/d (GSI, 2005). Transmissivity decreased from north to south in the plain. To the north, the transmissivity decreased steadily and also decreased to the southwest. In the area south of Shahryar, this value was less than 200 m2/d (GSI, 2005). The low transmissivities in the southern part of the study area resulted from the decrease in the thickness of the saturated layers in the north and northeast of the area and from the decrease in hydraulic conductivity in the south of the study area (GSI, 2005). Horizontal hydraulic conductivity (Kh) was obtained for aquifer units from particle size analysis of the sediment. Kh estimates were


19

Fig. 15. The major subsiding zone of Tehran southwest region (v-shape) is clearly visible on this interferogram.

determined from 399 soil samples from the 6 boreholes with adequate grain-size domains (Chapuis, 2004) as:

K ðcm=sÞ ¼ 2:4622

2 d10 e3

1þe

(2002) show the best predictive capacity (Kpredicted/Kmeasured). K ðcm=SÞ ¼ C P

!0:7825

γw e3þX 1 μ w 1 þ e ρ2 W2X L

ð23Þ

S

ð22Þ

where d10 is the grain size (mm) such that 10% of the soil is composed of grains finer than d10 and e is the void ratio. Kh is obtained using Eq. (23) for the aquitard units (Mbonimpa et al., 2002). Chapuis (2012) showed that, for non-plastic soils and natural inorganic clays, the methods from Chapuis (2004) and Mbonimpa et al.

where Cp = 5.6 g2/m4, Cp is a constant that includes the parameters Ce and λ2 (Cp = Ce/λ2) and Ce is material parameter (unitless) and λ is the function parameter (unitless),γw is the water unit weigth, γw ≈ 9.8 kN/m3, μw is the dynamic viscosity, μw ≈ 10−3 Pa.s, x is the material parameter (unitless), x = 1.5, ρs is in kg.m−3, WL (%) is the liquid limit of the soil, and X is defined as: −3 X ¼ 7:7W −0:15 L

ð24Þ

Fig. 16. Unwrapped and geo-referenced interfrogram a) CD: 70 days (9 January 2005–20 March 2005), b) BD: 175 days (26 September 2004–20 March 2005), and c) AD: 315 days (9 May 2004–20 March 2005). (GSI, 2005), 1: profile 1 and 3: profile 3.

20


Fig. 17. a) subsidence rate along profile 1. This NE–SW profile shows an asymmetrical ‘V’ shape pattern with the highest gradient of displacement affecting the SW of the city of Tehran. The maximum estimated rate is about 15 cm/year, b) subsidence rate along profile 3. This profile shows a ‘V’ shape subsidence pattern. The maximum estimated subsidence rate is about 16 cm/year. (Gaps in the curves correspond to missing data that have not been unwrapped because of signal decorrelation in the interferograms), (GSI, 2005).

Vertical hydraulic conductivity (Kv) values for the aquitards were taken from Neuzil (1994) and Domenico and Schwartz (1998).These values are within the general ranges presented for vertical hydraulic conductivity. Kh is typically 1 to 2 times that of Kv; however, in general, vertical anisotropies are slightly larger for aquifers (Carlson, 2007).

Fig. 19. Vertical displacement rates from leveling (1995–2004) and InSAR (2003–2005) on leveling benchmarks along AB (a), CD (b) and EF (c) profiles.

Fig. 18. Interference image (D-InSAR technique) of southwestern Tehran (From 10 January 2007 to 17 January 2010) — Each color fringe indicated subsidence is 11.8 cm (Sharifikia, 2010).


21

Table 7 Summary of the hydraulic parameters of each model layers used in the simulation. Model layer no.

Horizontal hydraulic conductivity Kh (m/s)

Vertical hydraulic conductivity Kv (m/s)

Specific storage Ss (1/m)

Specific yield Sy(−)

Storage coefficient

Elastic skeletal specific storage Sske (1/m)

Inelastic skeletal specific storage Sskv (1/m)

Aquitard 1 Aquifer 1 Aquitard 2 Aquifer 2 Aquitard 3 Aquifer 3

5.10 × 10−10 4.83 × 10−06 3.30 × 10−10 1.17 × 10−05 2.09 × 10−10 2.61 × 10−05

3.40 × 10−10 3.86 × 10−06 2.20 × 10−10 9.36 × 10−06 1.40 × 10−10 2.08 × 10−05

1.25 × 10−03 1.61 × 10−04 1.37 × 10−03 1.61 × 10−04 1.57 × 10−03 1.61 × 10−04

0.03 0.25 0.03 0.25 0.03 0.25

0.051 0.010 0.030 0.020 0.046 0.020

1.23 × 10−03 – 1.36 × 10−03 – 1.55 × 10−03 –

1.90 × 10−03 – 2.10 × 10−03 – 3.8 × 10−03 –

Fig. 20. Example of consolidation test results of the Tehran plain clay, Cc = 0.19 and Cr = 0.13 (GSI, 2008b).

Specific storage was determined (Cooper, 1966) as: Ss

¼ ρw :g ðα þ nβw Þ

ð25Þ

where ρw is the density of the water, g is the acceleration of gravity, α is vertical skeletal compressibility, n is porosity, and βw is the compressibility of water. Specific yield (Sy) is a function of porosity (and is not necessarily equal to porosity). Typically, 0.01 b Sy b 0.3 (Freeze and Cherry, 1979). This parameter is 0.03 for fine-grained materials such as clay and 0.25 for sand and silty sand. Layers of types 0, 2 and 3 require the confined storage coefficient (Chiang, 2005). Confined storage coefficient was determined using Freeze and Cherry (1979) equation as: S ¼ Ss :b

ð26Þ

Table 8 Estimated parameters for each aquitard. Layer

Kv (m/s)

Equivalent thickness (m)

Sskv (1/m)

τ (year)

Aquitard1 Aquitard2 Aquitard3

3.40 × 10−10 2.20 × 10−10 1.40 × 10−10

17.21 22.10 29.39

1.90 × 10−3 2.10 × 10−3 2.38 × 10−3

13.12 36.95 116.40

where Ss is the specific storage and b is the thickness of the aquifer or aquitard. For layer 1, storage coefficient was determined using Freeze and Cherry (1979) as: S ¼ Sy þ Ss :b

ð27Þ

where Sy is the specific yield. The final values for the hydro-mechanical parameters selected for simulation of the model layers are presented in Table 7. The elastic and inelastic skeletal specific storage (Sske and Sskv) can be obtained from consolidation experiments using the compression index (cc) and recompression index (cr) (Calderhead et al., 2011). On the other hand, the elastic skeletal specific storage has been computed as a percentage of inelastic skeletal specific storage. The ratio between the recompression index and compression index (cr/cc), these are comparable to Sske and Sskv parameters (Tomás et al., 2010). These parameters were obtained by observation of the e-logσ´ curves from consolidation tests on Tehran plain clay. By observing Fig. 20 and other elogσ´ curves from consolidation tests of Tehran plain clays (GSI, 2008b), can be said that there is not much different between the two parameters cc and cr. As a result, cr/cc ≈ 0.65 for the Tehran plain. Therefore, the estimated elastic skeletal specific storage (Sske) of the aquitards varied from 1.23 × 10−03 to 1.55 × 10−03 and the estimated inelastic skeletal specific storage (Sskv) varied from 1.90 × 10−03 to

22


Fig. 21. The calibration of model using InSAR data and piezometric levels for period 2003–2005 at four selected piezometric wells (dashed lines (– – – – –): piezometric level, continuous lines (___): subsidence, dotted lines (….): subsidence predicted); (see piezometers wells location in Fig. 8).

2.38 × 10−03. The storage values for aquitards are specified in the model by their skeletal storage coefficient, S΄ke = Sske b° and S΄kv = Sskv b° . The estimated elastic skeletal storage coefficient (S'ke) varied from 2.17 × 10−3 to 6.35 × 10−2 and the estimated inelastic skeletal storage coefficient (S'kv) varied from 1.33 × 10−2 to 9.75 × 10−2. The compaction time constant (τ) is the time after which about 93% of the water will drain from storage in the layer due to the equilibration of head (equivalent pore-fluid pressure) in a saturated aquifer with uniform initial head where only vertical flow is permitted in response to a specified instantaneous step change in head at the top and bottom of the aquitard. It is also the time after which 93% of the ultimate compaction of an aquitard is caused by step decreases in the heads of adjacent aquifers (Galloway and Hoffmann, 2007). This time constant for this type of aquitard is (Riley, 1969; Helm, 1975; Pavelko, 2004):

τ ¼ Sskv

2 b =K V 2

ð28Þ

where Sskv is aquitard inelastic skeletal specific storage, b is the thickness of the aquitard, and Kv is aquitard vertical hydraulic conductivity. The τ value ranged from 1 to 1000 years, which indicated that delayed compaction and land subsidence will continue to occur long after the head declines in adjacent aquifers (Galloway and Hoffmann, 2007). Ireland et al. (1984) estimated that τ for the San Joaquin Valley ranged from 5 to 1350 years. This parameter for Antelope Valley, California was 3.8 to 285 years (Hoffmann et al., 2003a) and for Las Vegas, Nevada was 100 to 1300 years (Pavelko, 2004). On the other hand, residual compaction is the inelastic aquitard compaction that would occur because of an increase in effective stress, but has not yet occurred because aquitard heads have not equilibrated to heads in adjacent aquifers and are still draining and compacting (Poland et al., 1972). Flow in interbeds is not simulated in IBS1 where no-delayed drainage is specified. Therefore, IBS1 (not delay option) does not simulate delayed compaction directly. Thus, if delayed drainage is not simulated, compaction occurs instantaneously with changes in head in the aquifer and its interbeds (Galloway and Sneed, 2013). Consequently, the interbeds systems are assumed to

Fig. 22. Sensitivity analysis for hydraulic conductivity and specific yield.


23

Fig. 23. a) Comparison between measured and simulated heads at observation wells, and b) comparison between measured and simulated subsidence rates.

kind of no-delay interbeds for simulating. Table 8 shows the thicknesses and τ values estimated (using Eq. (28), and not simulated) for each aquitard of the study area. This table shows that aquitard 1 requires the least time to ultimate compaction and aquitard 3 requires the most time to consolidation. The parameters for modeling included the thicknesses of the aquifer and aquitard units, hydraulic conductivity, specific storage, storage coefficient, porosity, specific yield, preconsolidation head, elastic and inelastic storage coefficients, and discharge rate of wells. The discharge rate data for more than 1200 wells were entered into the model and the well package was used to simulate discharge wells. 4.3. Model calibration, sensitivity analysis and verification Model calibration and validation were achieved using autocalibrated and manual trial-and-error procedures by matching the observed head and subsidence values with simulated values to determine a set of best-fit parameters. The hydraulic head was fit by varying specific storage, hydraulic conductivity, and intensity of pumping.

Model calibration can be performed for steady-state conditions, unsteady conditions, or both. Calibration of every model should first set a target with acceptable error; its range will depend mainly on the purpose of the model. During calibration, the user should focus on parameters that have been determined with less accuracy or are assumed and only slightly change those parameters that are more certain. Most other parameters are less sensitive and need only to be changed within a specific realistic range (Kresic and Mikszewski, 2013). The model was calibrated using land subsidence data and historical records of piezometric level from 2003 to 2005 (Fig. 21). A good agreement can be observed between the observed and calculated subsidence. After calibrating the model for steady state conditions, it was executed in an unsteady state. PMWIN allows performing steady state or transient flow simulations. During unsteady state or transient groundwater flow, the fluid mass per unit volume of aquifer changes as the head changes. Simulating unsteady state was done for calculating subsidence of an aquifer due to changes of hydraulic heads (Chiang, 2005). Unsteady calibration typically involves water levels recorded in wells during pumping tests or long-term aquifer exploitation. On the other hand,

Fig. 24. Piezometric level evolution for several wells. Continuous line: observed level, Dotted level: calculated level.

24


Fig. 25. Contour maps of a) observed and b) simulated groundwater level in study area at 2004 (contour interval is 10 m and 5 m, respectively).

steady-state calibration does not involve aquifer storage properties, which are critical for a viable (transient) prediction (Kresic and Mikszewski, 2013). For this purpose, water level data from the observation wells for October 2003 to October 2004 was used (with the maximum water level data available). The groundwater levels recorded on October 2003 were used as the initial condition. Calibration was carried out for hydraulic conductivity and specific yield. Therefore, Horizontal hydraulic conductivity in the steady state condition was optimized and specific yield in the unsteady state condition was optimized. After obtaining optimal values for the parameters, the final values were obtained after numerous executions of the model. Sensitivity analysis was then performed for hydraulic conductivity and specific yield to determine the effect of each parameter on model calibration. Increasing and decreasing the values by a multiplier tested the sensitivity of the

model to changes in these parameters while the other parameters remained constant (Kasmarek and Strom, 2002). Sensitivity was evaluated on the basis of computed variance error. The model was carried out for each stage and the model variance error calculated. The most sensitive parameters were those for which a significant percentage of change established a maximum variance error. The results of analysis indicated that the model was more sensitive to decreases than increases in hydraulic conductivity, and conversely, were more sensitive to increases than decreases in specific yield (Fig. 22). In the next step, the model was verified for October 2003 to October 2004. The groundwater levels recorded from 13 observation wells were used to calibrate and verify the model. The calculated and observed hydrographs at the observation wells showed similar trends in general and the calculated heads agreed well with the observed data (Fig. 23a).


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Fig. 26. Contours of the subsidence rates at the end of 2004, a) measured result, b) simulated result.

The first stage of calibration typically ends when there is a good visual match between the calculated and measured hydraulic heads at the observation wells. The next step involves quantification of model error for different statistical parameters (Kresic and Mikszewski, 2013). The simulation parameters were evaluated against measured values by comparison of means, root mean square error (RMSE), coefficient of determination (R2) and coefficient of efficiency (E) as suggested by Nash and Sutcliffe (1970). Both R2 and E tests were performed to evaluate the accuracy of the generated predictive equations. Model performance was regarded as acceptable when R2 ≥ 0.6 and E ≥ 0.5 during calibration and validation (Zhang et al., 2010). The results obtained in this study were RMSE = 0.64, R2 N 0.99, and E = 0.99 for calculated and measured hydraulic heads at the observation wells. The simulations were constrained by remote sensing results

(InSAR) and field data. The 26 points selected for validation were distributed throughout the study area and the observed and calculated land subsidence rates were determined at all piezometric wells and boreholes at points A, B, C, D and E, Sabashahr and Eslamshahr. Fig. 23b compares the simulated and observed subsidence rates for the end of 2004. R2 for the observed and simulated land subsidence rates was 0.98 and E equaled 0.92. The RMSE was 1.15 cm for the 26 observations. These results confirmed the accuracy of the model. For more validation of model, the simulation of groundwater flow was done for the 20 year period of 1991–2010. The total simulation period was divided into 40 stress period with 6 months in each stress period. The temporal evolution of piezometric level changes shows a good relationship between observed and calculated piezometric levels for several wells (Fig. 24).

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Fig. 27. Contours of the subsidence rates prediction at the end of 2018 (simulated result).

4.4. Simulation results for groundwater level and land subsidence Groundwater level and land subsidence under groundwater exploitation at the end 2004 were first simulated. The observed and simulated contour maps for groundwater level for the second aquifer (2) and the third aquifer (Fig. 3) are shown in Fig. 25. The map of simulation shows the contour line for maximum elevation in the northeast area and contour lines for minimum elevation in the southeast area (Fig. 25b). The minimum level of groundwater in the south and southeast is marked by curves at 1010 m and 1040 m, respectively. The maximum groundwater level was observed in the northwest area. The direction of groundwater flow was from the north to the south and southwest of the area (Fig 25a). Fig. 26 shows the measured and simulated land subsidence rates at the end of 2004. The vertical displacement has been calculated using Eq. (1). Thus, InSAR subsidence map has been prepared (Fig. 26a). InSAR displacement values for 26 selected points were estimated using the Fig. 26a. Five patterns of subsidence bowls formed in the study area at points A, B, C, D and E. Points B, C, and D had maximum subsidence rates, respectively, of 16.4, 16.4 and 12.8 cm/year. The results show that these areas are the regions with the thickest clays. The thickness of the clay in the study area is N 85 m (GSI, 2005). These subsidence bowls are consistent with the concentration of discharge wells in the area. The minimum subsidence rate in the study area was b 2 cm/year. The subsidence rate was b2 to 16.4 cm/year (Fig. 26b). The mean subsidence rate was over 5.5 cm/year.

4.5. Model prediction The land subsidence rate was predicted for 2018 assuming that the conditions in the study area do not change (aquifer recharge and discharge rates). InSAR data was used to calibrate and verify the model and predict land subsidence. Based on the calculated results, maximum land subsidence in response to groundwater withdrawals which were ~17 cm in 2004 will reach ~33 cm by 2018.

Four patterns of subsidence bowls formed in the prediction model at points A, B, C and D. Points B and C recorded the maximum subsidence rates of 31 and 33 cm/year, respectively (Fig. 27). Points A and D recorded subsidence rates of 26 and 19 cm/year, respectively (Fig. 25). Two important features of the prediction model for land subsidence can be seen when it is compared with the 2004 model. The critical subsidence zones extended and subsidence rates increased from 2004 to 2018. The minimum subsidence rate in 2004 was as little as 2 cm/year; in 2018 it is predicted to be ≤ 5 cm/year. The mean subsidence rate was N 15 cm/ year. The simulation results well illustrate the development of land subsidence in southwest Tehran plain.

5. Summary and conclusions In this study, leveling, GPS and InSAR techniques are used to detect land subsidence in the southwestern area of Tehran plain. The InSAR results points out that, in 2004, the areas of subsidence encompassed about 415.64 km2 at a maximum rate of 16 cm/year. The leveling results demonstrate that, in 2004, there were the areas of subsidence having maximum rates of 17, 20 and 20.7 cm/year in three directions. From 2003 to 2012, discharge from the wells had doubled. Land subsidence in southwestern Tehran plain is mainly caused by severe groundwater exploitation from three aquifers. This aquifer system is multi-layered. The aquifer system is conceptualized as three aquifers and three aquitards layers. The third unconfined aquifer is the main aquifer under pumping and the third soft layer (third aquitard layer) has the greatest thickness. The soil layers comprising the aquifer system play a major role in the amount of compaction. The thickness of the fine-grained interbeds is the main factor controlling the timing of land subsidence. Consolidation of the aquitards units (especially aquitard 3) induced by lowering of groundwater showed mainly plastic deformation. The third aquitard is the key to the process of land subsidence in the study area. Land subsidence was also dictated by the engineering geological properties and hydrogeological conditions of the aquifer system.


The groundwater level and land subsidence were simulated using PMWIN to validate, analyze, and predict future trends. Numerical simulation was carried out to obtain the groundwater level and land subsidence rate at the end of 2004 and its results were validated using field measurements from observation wells and InSAR data. The distribution of subsidence bowls exhibit good correlation with the concentration of discharge wells. The maximum land subsidence prediction for 2018 caused by groundwater withdrawal will be about 33 cm if the rate of groundwater extraction from wells remains constant. The analysis of this study has shown a progressive trend of land subsidence in study area. Acknowledgments The authors wish to thank the editor, Associate professor Carlos Carrenza-Torres, for his handling of the manuscript and the valuable comments he made. Our special thanks are also offered to MS Devin L. Galloway, Dr. Chih-Tung Chen and four anonymous referees for carefully reading the manuscript and their critical comments which have significantly improved our work. The authors also wish also to thank the Geological Survey of Iran for providing a substantial amount of the data used in this study. References Amighpey, M., Arabi, S., Talebi, A., Djamour, Y., 2006. Elevation Changes of the Precise Leveling Tracks in the Iran Leveling Network. Scientific Report Published in National Cartographic Center (NCC) of Iran (in Persian). Arabi, S., Montazerian, A.R., Maleki, E., Talebi, A., 2005. Study of land subsidence in south-west of Tehran plain basin. J. Nat'l. Cartogr. Center 16 (69), 14–28. Bagha, N., Arian, M., Ghorashi, M., Pourkermani, M., El Hamdouni, R., Solgi, A., 2014. Evaluation of relation tectonic activity in the Tehran basin, central Alborz, northern Iran. Geomorphology 213, 66–87. http://dx.doi.org/10.1016/j.geomorph. 2013.12.041. Biot, M.A., 1941. General theory of three-dimensional consolidation. J. Appl. Phys. 12, 155–164. Bonsignore, F., Bitelli, G., Chahoud, A., Macini, P., Mesini, E., Severi, P., Villani, B., Vittuari, L., 2010. Recent Extensometric Data for the Monitoring of Subsidence in Bologna (Italy). In: Carreon-Freyre, D., Cerca, M., Galloway, D.L., Silva-Corona, J.J. (Eds.), Land Subsidence, Associated Hazards and the Role of Natural Resources Development (EISOLS, 2010). IAHS Publ. 339, IAHS Wallingford, UK, pp. 333–338. Buckley, S.M., Rosen, P.A., Hensley, S., Tapley, B.D., 2003. Land subsidence in Houston, Texas, measured by radar interferometry and constrained by extensometers. J. Geophys. Res. 108 (B11), 2542. http://dx.doi.org/10.1029/2002JB001848. Calderhead, A.I., Therrien, R., Rivera, A., Martel, R., Garfias, J., 2011. Simulating pumpinginduced regional land subsidence with the use of InSAR and field data in the Toluca Valley, Mexico. Adv. Water Resour. 34, 83–97. http://dx.doi.org/10.1016/j. advwatres. 2010.09.017. Calderhead, A.I., Martel, R., Garfias, J., Rivera, A., Therrien, R., 2012. Sustainable management for minimizing land subsidence of an over-pumped volcanic aquifer system: tools for policy design. Water Resour. Manag. 26, 1847–1864. http://dx.doi.org/10. 1007/s11269-012-9990-7. Cao, G., Han, D., Moser, J., 2013. Groundwater exploitation management under land subsidence constraint empirical evidence from the Hangzhou–Jiaxing–Huzhou plain, China. Environ. Manag. 51, 1109–1125. http://dx.doi.org/10.1007/ s00267-013-0037-5. Carlson, D., 2007. Estimate of vertical anisotropy of hydraulic conductivity for northern Louisiana aquifers from grain-size data. Proceedings of Baton Rouge Geological Society's 1st Annual Louisiana Groundwater Symposium, Baton Rouge, Louisiana, v.1, pp. 32–42. Chapuis, R.P., 2004. Predicting the saturated hydraulic conductivity of sand and gravel using effective diameter and void ratio. Can. Geotech. J. 41 (5), 787–795. http://dx. doi.org/10.1139/t04-022. Chapuis, R.P., 2012. Predicting the saturated hydraulic conductivity of soils: a review. Bull. Eng. Geol. Environ. 71, 401–434. http://dx.doi.org/10.1007/s10064-0120418-7. Chaussard, E., Amelung, F., Abidin, H., Hong, S.H., 2013. Sinking cities in Indonesia: ALOS PALSAR detects rapid subsidence due to groundwater and gas extraction. Remote Sens. Environ. 128, 150–161. http://dx.doi.org/10.1016/j.rse.2012.10. 015. Chaussard, E., Wdowinski, S., Cabral-Cano, E., Amelung, F., 2014. Land subsidence in central Mexico detected by ALOS InSAR time-series. Remote Sens. Environ. 140, 94–106. http://dx.doi.org/10.1016/j.rse.2013.08.038. Chiang, W.-H., 2005. 3D-Groundwater Modeling with PMWIN, A Simulation System for Modeling Groundwater Flow and Transport Processes. second ed. Springer-Verlag, New York (414 pp.). Cooper Jr., H.H., 1966. The equation of groundwater flow in fixed and deforming coordinates. J. Geophys. Res. 71, 4785–4790.

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