Introduction

Land subsidence is an environmental geological phenomenon caused by the overexploiting underground resources such as groundwater, which can bring about disasters in severe cases (Hu et al. 2004; Motagh et al. 2008; Galloway and Burbey 2011; Gambolati and Teatini 2015; Guzy and Malinowska 2020). There are 34 countries and about 200 cities around the world which have experienced land subsidence (Herrera-García et al. 2021). For example, the San Joaquin and Santa Clara basins in the USA (Galloway et al. 1998; Pavelko et al. 2006; Jeanne et al. 2019); Tokyo and Osaka in Japan (Cao et al. 2020); Mexico City in Mexico (Strozzi and Wegmuller 1999; Chaussard et al. 2014b); Venice in Italy (Tosi et al. 2007; Teatini et al. 2010); Bangkok in Thailand (Phien Wej et al. 2006); Jakarta in Indonesia (Abidin et al. 2008, 2011); and Shanghai, Tianjin, and Beijing in China (Hu et al. 2009; Xu et al. 2012; Gong et al. 2018).

In China, more than 22 provinces (cities) suffer from land subsidence (Xue et al. 2005). The area with cumulative land subsidence greater than 200 mm added up to 90,000 km2 in 2012 (Ye et al. 2016b). Land subsidence permanently reduces aquifer-system storage capacity, causes earth fissures, damages buildings and civil infrastructure, and increases the susceptibility and risk of flood (Tomas et al. 2011; Pacheco-Martinez et al. 2013; Miller and Shirzaei 2015; Zhu et al. 2015; Zhang et al. 2016; Chen et al. 2020). Land subsidence, which is characteristic of long formation time, wide range of influence, as well as difficulty in prevention and recovery, etc., has become a global and comprehensive environmental geological problem that has a serious impact on the human living environment (Guzy and Malinowska 2020; Herrera-García et al. 2021).

Beijing, capital of China which has a serious shortage of water, is located in North China and has a population of more than 21 million. According to public surveys from the Beijing Water Authority of China, the average available water resource per person is less than 300 cubic meters per year, which is only 1/8 of that of the nation (Shao 2007). There is about 50% to 70% of the water supply comes from groundwater in Beijing (Chen et al. 2020; Lei et al. 2022). Long-term overexploitation of groundwater resources has brought about serious problems of land subsidence in Beijing (Lei et al. 2016; Chen et al. 2019; Zhu et al. 2020). The annual subsidence rate peaked at about 156 mm/year in the eastern part of Beijing Plain from 2010 to 2015 (Zhang et al. 2016). The area affected by a cumulative subsidence larger than 100 cm was more than 300 km2 between 1955 and 2015, which seriously affected the safety of the infrastructure operation (Lei et al. 2016).

The South-to-North Water Diversion Project (SNWDP) is the largest water control project which has ever been built, and the aim of which is to optimize the reallocation of water resources from South China to North China (Bai and Liu 2018). The South-to-North Water Diversion Project Central Route (SNWDP-CR) diverts water from the Danjiangkou reservoir (32° 43′ North, 111° 34′ East) on the Han River via artificial canals that cross Henan and Hebei Provinces to the Tuancheng Lake of Beijing (39° 55′ North, 116° 24′ East). The SNWDP-CR, the total length of which is about 1300 km, spans the four provinces or cities including Henan, Hebei, Beijing, and Tianjin. The SNWDP-CR, which began to be constructed in 2003, and was put into operation in December 2014, is supposed to relieve, to some degree, the partial pressure of water demand in Beijing Plain. The cumulative water volume released to Beijing amounted to 6.0 × 109 m3 by December 2020. From 2014 to 2020, the average of groundwater level rose by 2.9 m in Beijing Plain (Lei et al. 2020).

At present, some scholars have carried out abundant research on the impact of water transfer projects, groundwater exploitation management and artificial recharge on groundwater environment and ecological changes (Yang et al. 2012; Zhao et al. 2017), groundwater level changes (Zhang et al. 2014, 2018; Ye et al. 2014; Li et al. 2017; Chen et al. 2020), and control of land subsidence (Zhang et al. 2015; Wei et al. 2022). Several years after the SNWDP-CR operation, the groundwater level has altered from continuous decline to gradual rise in many areas of the Beijing plain (Zhang et al. 2018; Lei et al. 2020; Du et al. 2021). However, there are few comprehensive analyses on the groundwater flow field and land subsidence during the process of the groundwater level in the Beijing Plain changing from decline to rise before and after the operation of SNWDP-CR. Therefore, a variety of monitoring data, in this study, are used to analyze the groundwater flow field and land subsidence changes in the Beijing Plain before and after the SNWDP-CR operation and to study the stress–strain characteristics and the changes of hydrogeological parameters of soil layers at different depths under different water level change modes. This is of great significance for the further investigation of the mechanism of land subsidence, the determination of the constitutive relationship of soil layer deformation, and realization of the accurate simulation of land subsidence and the scientific regulation of groundwater.

The objectives of this study are as follows: firstly, to compare the evolution of the groundwater flow field and the change of groundwater level by using the regional groundwater level observation data; secondly, to obtain the evolution characteristics of the land subsidence before and after the SNWDP-CR operation by using Persistent Scatterer Interferometry (PSI) technique; and thirdly, to study the deformation characteristics of water bearing sand layers and different compression layer groups under different water level change modes by using long-time series extensometer and groundwater level data. The soil mechanics test is used to simulate and verify the deformation of the soil layer and, fourthly, to analyze the changes of hydrogeological parameters at different stages of soil deformation by calculating the elastic and inelastic skeletal specific storage rate of the sand layer and compressed layer group before and after the SNWDP-CR operation.

Description of the study area

Geology and hydrogeology

Beijing is located on the northwestern edge of the North China Plain. The terrain is generally higher in its northwest part and lower in its southeastern part. It is surrounded by the Taihang Mountains in the west, the Yanshan Mountains in the north, and the inclined plain in the southeast. The geographical coordinates of Beijing are E115.7°–117.4°and N39.4°–41.6°. The total area of Beijing is 16,410 km2, and the plain area is 6400 km2. The plain area accounts for about 39% of the total area of the city (Wei et al. 2008). It is characterized by a continental monsoon climate, with an average annual precipitation of 570 mm/year (1961–2020). Eighty percent of the precipitation is concentrated in the period mid-June to September. The average annual temperature is around 11.7 °C, and the maximum value may reach up to 42.6 °C in summer.

The Quaternary stratum of Beijing Plain is mainly formed by the alluvial-diluvial effect of five rivers, which are Yongding, Chaobai, Beiyun, Daqing, and Jiyun rivers. On the top of the alluvial region, the thickness of the Quaternary is about 20–40 m. The lithology is a single layer of sand, gravel, or a thin layer of cohesive soil on the top of sand and gravel in some areas (Cai et al. 2009). In the middle and lower parts of alluvial regions and alluvial plain, the thickness of the sediment increases, the layers increase, and the soil particles gradually change from coarse to fine. The lithology is that sand, gravel, and cohesive soil layers appear alternately, and the cohesive soil is dominant. In the center of the Quaternary sedimentary depression, the thickness of the Quaternary reaches more than 1000 m (Lei et al. 2016, 2022) (Fig. 1).

Fig. 1
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The location of study area and the lithology zone of aquifer. The position of levelling benchmarks, extensometer stations, and groundwater monitoring wells are provided. The SNWDP-CR route is marked with a blue color in the bottom right panel

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The aquifer system in the Beijing Plain can be divided in the vertical direction into three main aquifer groups. The first aquifer group (unconfined aquifer and shallow confined aquifer) are the Quaternary Holocene (Q4) and Upper Pleistocene (Q3) alluvial deposits, the bottom depths of which are about 25 m and 80–120 m respectively. The second aquifer group (medium-deep confined aquifers) is a multi-layered structure of the Quaternary Middle Pleistocene (Q2) strata, the lithology of which is mainly medium-coarse sand, partly with gravel, and the bottom depth of which is about 180 m. The third aquifer group (deep confined aquifers) is the Lower Pleistocene (Q1) stratum of the Quaternary System with a multi-layer structure, which is dominated by medium-coarse sand and gravel, and the bottom boundary of which is the Quaternary basement or about 260–300 m (Jia et al. 2007). At the same time, the division of compression layer group and the division of aquifer group have an obvious corresponding relationship in Beijing Plain (Figs. 2 and 3).

Fig. 2
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Hydrogeological cross-section A–A1 (the location is indicated in Fig. 1)

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Fig. 3
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Hydrogeological cross-section B–B1 (the location is indicated in Fig. 1)

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The history of groundwater exploitation and land subsidence development

The occurrence and development of land subsidence have an obvious corresponding relationship with the history of groundwater exploitation (Fig. 4). The period from 1955 to 1973 was the initial exploitation of groundwater and the formation stage of land subsidence. During this period, the amount of groundwater extraction in Beijing was small. The land subsidence only occurred in the groundwater over-exploitation area, with the land subsidence rate being a few millimeters per year. The period from 1973 to 1983 was the stage of increase of groundwater exploitation and development of land subsidence. During this period, the amount of groundwater exploitation in Beijing remained at 2.5–2.8 billion m3 per year, and the annual average land subsidence rate being 18–30 mm/year. The period from 1983 to 1999 was the stage of stability of groundwater exploitation and expansion of land subsidence. During this period, the amount of groundwater extraction was relatively stable, with an average annual extraction volume of about 2.6 billion m3. The over-extraction area accounted for more than 70% of the plain. The area of land subsidence expanded significantly, with an average annual subsidence rate of 19–24 mm/year. The period from 1999 to 2015 was the rapid development stage of land subsidence. During this period, Beijing experienced the longest dry year in history. The amount of groundwater exploitation declined slightly, but the exploitation horizon gradually extended to deeper layers. During this period, the groundwater in Beijing was severely depleted, and the land subsidence developed rapidly, with a maximum subsidence rate of 156 mm/year (Jia et al. 2018). Since 2015, with the South-to-North Water Diversion Project Central Route was officially operated, the amount of groundwater exploitation in Beijing has decreased, from 2.0 billion m3 in 2014 to 1.35 billion m3 in 2020. At this stage, the land subsidence has been gradually slowing down, with an average annual subsidence rate of 11–19 mm/year (Fig. 5).

Fig. 4
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The relationship between the accumulated storage variables of groundwater and the precipitation and the division of land subsidence in Beijing

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Fig. 5
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Curve of relationship between groundwater extraction volume and average subsidence rate in Beijing

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Dataset and methodology

Dataset

To quantify the impact of the water resource supplied by SNWDP-CR on the Beijing groundwater flow field, groundwater level, land subsidence, soil deformation, and hydrogeological parameters, the remotely sensed measurements, levelling and extensometer data, groundwater level data, geotechnical test, and aquifer recharge management data have been gathered, and the dataset has been revised in the following paragraphs Table 1.

Remotely sensed data

PSI technique outcomes were obtained by processing Radarsat-2 acquisitions. A total of 72 Radarsat-2 images with 30-m resolution and 24-day revisit time acquired in Stripmap mode from January 2013 to December 2020 were processed. These stacks of Synthetic Aperture Radar (SAR) images were used to map land subsidence over the period from 2013 to 2020, respectively. The acquisition parameters of SAR images are presented in Table 2.

Table 1 Acquisition parameters of Radarsat-2 datasets
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In situ deformation data

The different-depth extensometers in the seven land subsidence monitoring stations and thirty levelling benchmarks were used in the study area (Fig. 1). The levelling results were used to calibrate and validate the land movements derived from PSI. The extensometer data recorded from 2006 to 2020 or from 2009 to 2020 were selected to analyze the main subsidence contribution layer and the relationship between layered soil deformation and groundwater level.

Groundwater level data

The comparative maps of the groundwater level of different aquifer groups in the Beijing Plain from 2015 to 2020 are drawn by virtue of the contour data of groundwater level in 2015 and 2020. A long-term series of groundwater level change curves are drawn by means of the monitoring data from 15 groundwater wells in the northern, eastern, and southeastern plains. The change trend of groundwater flow field and groundwater level in different aquifer groups before and after the SNWDP-CR operation has been analyzed. The location of the well is shown in Fig. 1. Well-1, Well-2, and Well-3 are located in a single aquifer group in the northern part of the plain. The lithology is mainly sand and gravel, and the depths of the wells are 45 m, 60 m and 89 m, respectively. Well-4, Well-5, and Well-6 are located near the channel of the Chaobai River in the northern part of the plain. The aquifer group is a single-structure sandy gravel layer, and the depths of the wells are 50 m, 100 m, and 60 m, respectively. D1-1, D1-2, D-3, D-4, and D1-5 wells are located in the Wangsiying land subsidence monitoring station in the eastern part of the plain. The aquifer group is a multi-layer structure composed of sand and cohesive soil, and the depths of the wells are 185 m, 155 m, 102 m, 54 m, and 19 m, respectively. Well-7, Well-8, Well-9, and Well-10 are located in the southeastern part of the plain. The aquifer group is a multi-layer structure composed of sand and cohesive soil, and the depths of the wells are 182 mm, 300 m, 166 m, and 300 m, respectively. At the same time, the groundwater level data of seven land subsidence monitoring stations, recorded from 2006 to 2020 or from 2009 to 2020, are selected to analyze the relationship with the extensometer data.

Managed aquifer recharge

The dataset related to the managed aquifer recharge position, duration, and volume of water supplied by the SNWDP-CR were collected from 2015 to 2020. The data were used to analyze the measured changes of the groundwater level. A typical area where the water supplied by the SNWDP-CR was used to recharge the aquifer in the northern plain. The location is shown in Fig. 6. The remote sensing image data in Fig. 6 are downloaded in Google Earth.

Fig. 6
figure 6

The water supplied by the SNWDP-CR was used to recharge the aquifer in the Huai and Chaobai River channels in the northern part of the plain. a The remote sensing image of the rubber dam and river channel before the aquifer recharge in April 2020. b The remote sensing image of the rubber dam and river channel after the aquifer recharge in August 2020. c Rubber dam in Niulanshan. d Recharge the aquifer by using the Chaobai River channel

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Undisturbed soil sample test data

A borehole with a depth of 100 m was constructed in the northern part of the plain, and it was numbered ZK01. Undisturbed soil samples were collected in the borehole for geotechnical tests. The numbers of the tested soil sample were Nos. 4, 6, 7, 9, 13, 16, and 21, respectively. Basic physical property tests and standard consolidation tests were carried out for each soil sample. In addition, loading tests of step by step were carried out in No. 7 and No. 9 soil samples, unloading tests of step by step were carried in No. 4 and No. 13 soil samples, and repeated loading and unloading tests in No. 6, No. 16, and No. 21 soil samples. The depth of soil sample collection and test items are shown in Table 2.

Methodologies

By combining PSI, GIS spatial analysis, stress–strain analysis, mathematical statistics, and geotechnical test methods, this paper studies the changes of groundwater flow field, groundwater level, land subsidence, soil deformation characteristics, and hydrogeological parameters before and after the SNWDP-CR operation. Firstly, the regional groundwater level contour data are utilized to draw the comparative map of the groundwater level of different aquifer groups in the Beijing Plain from 2015 to 2020. By combining the data of multiple groundwater wells, the changes in the groundwater flow field and groundwater level before and after the SNWDP-CR operation are analyzed by means of GIS and mathematical statistics methods. Secondly, Radarsat-2 images, by means of PSI technique, are processed to obtain the long-term sequence of land subsidence distribution characteristics in the Beijing Plain. The relationship between the changes of groundwater level and land subsidence before and after the SNWDP-CR operation is analyzed. Thirdly, by using the extensometer and groundwater level data in the land subsidence monitoring station, the stress–strain analysis method is used to study the deformation characteristics of the sand layer and different compression layer groups under the different groundwater level change mode before and after the SNWDP-CR operation. Verification of soil layer deformation are carried out by using geotechnical tests. Fourthly, the elastic and inelastic skeletal specific storage rate of the sand layer and different compression layer groups are calculated before and after the SNWDP-CR operation. Besides, the changes of related hydrogeological parameters in different stages of soil deformation are analyzed. The overall technical framework is shown in Fig. 7.

Fig. 7
figure 7

The flowchart of methodologies

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PSI technique

The basic idea of PSI is to select those pixels as the research object that maintain high coherence in the long-term sequence of SAR images, and the long-term sequence stability of them enables the accurate phase information to be obtained. By separating the phase of each coherent target point, including the elevation, the orbit, and the phase change of the atmosphere, the surface deformation can be obtained. This method can effectively overcome the influence of space and time decorrelation and atmospheric delay of DInSAR and improve the monitoring accuracy of surface deformation, which can reach the millimeter level. PSI technique was first developed by Ferretti (Ferretti and Prati 2000; Ferretti et al. 2001), and since then it has largely been used to measure movements of Earth surface (Galloway et al. 1998; Hoffmann et al. 2001, 2003; Ng et al. 2012; Gong et al. 2018; Malinowska et al. 2019; Strozzi et al. 2020; Chen et al. 2020). The main steps of the PSI processing chain are as follows: selection of a master image from the available series of SAR scenes, construction of a series of interferograms, selection of permanent scatterers (PS) of the radar signal according to amplitude dispersion index and coherence thresholds, and phase unwrapping. The differential interferometric phase ΦPS of each PS in the interferogram can be expressed as the accumulation of five components (Hooper et al. 2004):

$${\Phi }_{PS}={\Phi }_{def}+{\Phi }_{top}+{\Phi }_{atm}+{\Phi }_{orb}+{\Phi }_{n}$$
(1)

In the formula, Φdef is the deformation phase along the line of sight, Φtop the topographic phase, Φatm the phase component due to atmospheric delay, Φorb the orbital error phase, and Φn the phase noise. The deformation phase Φdef of PS can be separated from the other components. An external DEM with resolution of 30 m is used to remove Φtop from the interferometric phase. The phases due to atmosphere delay and noise are removed through filtering processes (Teatini et al. 2007). In this paper, GAMMA software is used to process 72-scene Radarsat-2 images for time-series differential interference processing and PS point extraction. Interferometric image pairs with a baseline distance of more than 300 m are eliminated, and 30 m resolution SRTM data are used as the reference DEM. After removing the terrain phase, geocoding and transforming the line of sight (LOS) to the vertical projection, the vertical deformation rate of the ground surface in the Beijing Plain area from 2013 to 2020 is obtained. The projection formula of the line of sight (LOS) to the vertical projection is as follows:

$$V=\frac{{V}_{LOS}}{cos\varphi }$$
(2)

where V and \({V}_{LOS}\) represent the displacement rate along the vertical and LOS directions, respectively, and \(\varphi\) is the incidence angle of the InSAR.

The outcomes of the Radarsat-2 were calibrated by virtue of the thirty levelling benchmarks shown in Fig. 1 and the calibration was carried out by using the average annual displacement rates over the period of investigation. Because of the lack of PS at the benchmarks, the average movement of the radar targets in a 100 m buffer zone around the levelling points was used as PSI value in the calibration procedure. The difference range of them is from 2 to 8 mm, with the mean square error being 5.16 mm (Table 3).

Table 2 The depth and test items of the soil samples
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Estimation of water storage rate

The water storage rate refers to the amount of water stored or released from a unit volume of soil when the groundwater level rises or falls by one unit. Supposing that the amount of water stored or released by the soil layer is all converted into the volume change of the soil layer, and the soil layer only undergoes vertical displacement, the water storage rate reflects the vertical deformation of the soil layer per unit thickness when the water level changes by one unit and can be used to characterize the potential deformation of the soil layer. However, the concept of the water storage rate depicted above can only quantitatively describe the linear elastic deformation of the soil layer, but cannot describe the general residual deformation of the soil layer. Therefore, the concept of the water storage rate should be expanded and should be divided into the elastic skeletal specific storage rate and the inelastic skeletal specific storage rate (Helm 1975; Liu and Helm 2008a, b). When the effective stress of the aquifer is less than the preconsolidation pressure, the aquifer assumes the recoverable elastic deformation. By contrast, when the effective stress of the aquifer is greater than the preconsolidation pressure, the aquifer shows the irreversible inelastic deformation, that is, the plastic one. Now that the preconsolidation pressure is the largest effective stress in the history of the soil layer; it can correspond to the lowest water level of the aquifer and can be determined through the historical monitoring data. Therefore, if the groundwater level is lower than the water level corresponding to the preconsolidation pressure, the water storage rate is called inelastic skeletal specific storage rate; otherwise, it is called elastic skeletal specific storage rate. The formula can be expressed as follows:

$${S}_{sk}=\left\{\begin{array}{c}{s}_{ske}=\frac{\Delta b}{{b}_{0}\Delta h}\left(h\ge {h}_{min}\right)\\ {S}_{skv}=\frac{\Delta b}{{b}_{0}\Delta h}\left(h<{h}_{min}\right)\end{array}\right.$$
(3)

In the formula, \({S}_{ske}\) is the elastic skeletal specific storage rate (m−1), \({S}_{skv}\) is the inelastic skeletal specific storage rate (m−1), \(\Delta b\) the amount of deformation (m), \(\Delta h\) the amount of water level change (m), \({b}_{0}\) the initial thickness of the soil layer (m), \(h\) the groundwater level (m), and \({h}_{min}\) the lowest groundwater level in the previous period (m). Based on in situ data, Riley showed that aquifer system elastic and inelastic skeletal specific storage rate can be estimated from stress–strain diagrams (Riley 1969). The stress–strain diagram method uses effective stress or water head as the ordinate axis and vertical strain or displacement as the abscissa axis to draw the relationship curve between the stress (water level) and strain (displacement). Then, according to the relationship curve, the elastic skeletal specific storage rate \({S}_{ske}\) and the inelastic skeletal specific storage rate \({S}_{skv}\) are successively calculated. The calculation method can refer to the following documents (Riley 1969; Helm 1975; Liu and Helm 2008a, b; Chaussard et al. 2014a; Motagh et al. 2017).

GIS spatial analysis and stress–strain analysis

The GIS spatial analysis method was used to compile the groundwater level comparison map of different aquifer groups in the Beijing Plain in 2015 and 2020. Combining the data of multiple groundwater wells, the characteristics of groundwater flow field and the changes of groundwater level before and after SNWDP-CR were analyzed. The stress–strain analysis method is used to study the deformation characteristics of the sand layer and different compression layer groups under the different groundwater level change mode before and after SNWDP-CR.

Geotechnical test

In order to further analyze and verify the deformation characteristics of different depths and different lithological soil layers in repeated rise and fall of the groundwater level, the loading, unloading, repeated loading, and unloading test methods are carried out to analyze different soil samples. The test is divided into three groups, and the loading, unloading, and repeated loading and unloading tests are carried out respectively. In each group of tests, clay and silt are used to make comparison, and silty clay is also selected to make comparison in repeated loading and unloading tests. With the load-deformation and deformation-time relationship curves drawn, the deformation characteristics and creep effects of different lithological soil layers under different loading and unloading modes are further analyzed.

No. 7 and No. 9 soil samples are subjected to loading test. The load is added from 25 to 1600 kPa, and the loading ratio is 1, i.e., 25 kPa, 50 kPa, 100 kPa, 200 kPa, 400 kPa, 800 kPa, and 1600 kPa.

No. 4 and No. 13 soil samples are subjected to unloading tests. Firstly, the first-level load imposed on the soil samples is added to 400 kPa and then unloaded to 50 kPa when the soil samples reach deformation stability, i.e., 400 kPa, 300 kPa, 200 kPa, 150 kPa, 100 kPa, and 50 kPa.

No. 6, No. 16, and No. 21 soil samples are subjected to loading and unloading tests. The first loading and unloading cycle is as follows: 100 kPa, 200 kPa, 100 kPa, 200 kPa, and 100 kPa. The second loading and unloading cycle is as follows: 100 kPa, 400 kPa, 200 kPa, 400 kPa, and 200 kPa. The third loading and unloading cycle is as follows: 200 kPa, 800 kPa, 400 kPa, 800 kPa, and 400 kPa. The fourth loading and unloading cycle is as follows: 400 kPa, 1600 kPa, 800 kPa, 1600 kPa, and 800 kPa.

Results and discussion

Changes of groundwater flow field and groundwater level

The comparison of groundwater level of different aquifer groups in 2015 and 2020 are shown in Fig. 8. From 2015 to 2020, the groundwater level of different aquifer groups in most areas of the Beijing Plain rose significantly, such as the northern part of the plain area (Shunyi, Changping, and Pinggu District), the urban area, the eastern part of the plain (parts of Chaoyang), and the northern part of Daxing District. However, the groundwater level of different aquifer groups in the southeast of Tongzhou and the southern part of Daxing continued to decline (Fig. 8). The comparison of groundwater level changes in different aquifers in 2015 and 2020 is shown in Table 4.

Fig. 8
figure 8

Comparison of groundwater levels of different aquifer groups in 2015 and 2020

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Table 3 Calibration of the displacements measured by PSI using levelling records
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The groundwater level change curves of 6 monitoring wells in the northern plain are showed in Fig. 9a, b. It can be seen from the figure that the groundwater level began to rise from 2015. By the end of 2020, the groundwater levels of 1, 2, and 3 wells had risen by 21.62 m, 21.72 m, and 17.24 m, respectively; the groundwater levels of 4, 5, and 6 wells by 2.11 m, 12.59 m, and 23.15 m, respectively. The groundwater level change curves in Wangsiying land subsidence monitoring station in the east of the plain are shown in Fig. 9c. Before 2017, the groundwater level of each aquifer group showed a continuous downward trend, with an average annual decline of 0.13–1.82 m. After 2017, the groundwater level of each aquifer group changed from decline to rise, with an average annual rise of 0.45–1.87 m. This is mainly because after the operation of SNWDP-CR, the reduction and conservation of groundwater were carried out in the emergency-type groundwater source fields of Miyun, Huairou, and Shunyi. The groundwater extraction in these areas decreased by two-thirds. At the same time, the SNWDP-CR supplies water to emergency water source fields through the Chaobai River. By the end of 2020, more than 5 × 108 m3 of groundwater has been recharged in this area. The groundwater level in the northern part of the plain has risen significantly. On the contrary, in parts of Tongzhou and Daxing which are sited in the southeast and south of the plain, the groundwater level was still declining. The groundwater level change curves of 4 monitoring wells in the southeast of Tongzhou are shown in Fig. 9d. From 2010 to 2020, the middle-deep and deep confined water levels continued to decline. An average annual decline was 1.18–1.75 m, and the largest cumulative decline 19.28 m.

Fig. 9
figure 9

Groundwater level change curves in the typical areas. a The groundwater level change curves of Well-1, Well-2, and Well-3, which are located in the northern part of the plain. b The groundwater level change curves of Well-4, Well-5, and Well-6, which are located near the channel of Chaobai River in the northern part of the plain. c The groundwater level change curves of D1-1, D1-2, D-3, D-4, and D1-5 wells, which are located in the Wangsiying land subsidence monitoring station in the eastern part of the plain. d The groundwater level change curves of Well-7, Well-8, Well-9, and Well-10, which are located in the southeastern part of the plain

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Change of land subsidence

The time series information of land subsidence in Beijing Plain from 2013 to 2020 is obtained in this paper by means of PSI technique (Fig. 10). Chaoyang and part of Tongzhou, which are situated in the east of the Beijing Plain, are the most serious land subsidence development areas. Several major land subsidence centers are connected together, and the subsidence center velocity has been above 100 mm/year for many years. The distribution of land subsidence in the northern part of the plain was scattered, and the areas with severe subsidence were mainly distributed in the northern part of Haidian, in the southern part of Changping and part of Shunyi. The time series information of land subsidence show that since the operation of SNWDP-CR at the end of 2014, the land subsidence in Beijing has gradually slowed down. The land subsidence in the northern part of the plain slowed down in 2016, and the area of the subsidence gradually decreased. The land subsidence in the eastern part of the plain mainly slowed down in 2018 Table 5.

From 2013 to 2020, the average land subsidence rate decreased from 21.7 mm/year in 2013 to 10.85 mm/year in 2020, with a decrease of 10.85 mm/year (Fig. 11a). The area of severe subsidence (subsidence rate greater than 50 mm/year) decreased from 572 km2 in 2013 to 45 km2 in 2020, with a decrease of 527 km2 (Fig. 11a). The total volume of land subsidence reduced from 13,210 × 104 m3 in 2013 to 5338 × 104 m3 in 2020, with a decrease of 8120 × 104 m3 (Fig. 11b).

Fig. 10
figure 10

The distribution characteristics of land subsidence in Beijing Plain (2013–2020). a 2013, b 2014, c 2015, d 2016, e 2017, f 2018, g 2019, h 2020

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From the perspective of the vertical distribution of land subsidence, the main subsidence layers of the Beijing Plain are currently concentrated in the second and third compression layer groups, with average subsidence accounting for 34.11% and 57.36% (Table 6). By comparing the annual subsidence of each monitoring station in 2014 and in 2020, it can be found that, except for the increase in the annual subsidence of the Yufa extensometer, the annual subsidence of the extensometers of the other stations decreased significantly. The land subsidence of the extensometer in Zhangjiawan station decreased most, with a decrease of 73.12 mm. As for the groundwater level corresponding to the main subsidence layer, except for Zhangjiawan and Yufa stations, the groundwater levels of the other stations all rose. Among them, the groundwater level of Yufa station declined significantly, especially the deep confined water D7-2 (monitoring depth: 132–169 m) and D7-1 (monitoring depth: 207–295 m), the water level decline of which was 2.76 m and 3.11 m, respectively (Table 7).

Table 4 Comparison of groundwater level changes in different aquifers in 2015 and 2020
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Table 5 Statistics on the proportion of subsidence in each compression layer group of land subsidence monitoring stations
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Through the analysis above, it can be found that since the water from SNWDP-CR entered Beijing in December 2014, the water shortage of Beijing has been alleviated, and the groundwater level in most areas has risen significantly, and the corresponding land subsidence has gradually slowed down. On the whole, the groundwater level in the northern part of the plain had gradually risen since 2015, and land subsidence had gradually decreased since 2016. The groundwater level in the eastern part of the plain began to rise gradually around 2017, and the land subsidence had been significantly decreased since 2018. This is mainly due to the hysteresis in the water release and compression of the cohesive soil layer, and the slowdown of land subsidence will lag behind the rise of the groundwater level for a period of time (Zhang et al. 2007, 2012; Shi et al. 2008; Ye et al. 2016a). However, in the southeastern and southern parts of the plains, groundwater is still over-exploited and the middle-deep and deep confined water levels continue to decline, resulting in continued development of land subsidence in these areas.

Deformation characteristics of soil layers

Since the change form of the groundwater level in the soil layer reflects the change process of the effective stress, it will directly affect the deformation behavior of the soil layer (Shi et al. 2008; Zhang et al. 2015). Therefore, after the operation of the SNWDP-CR, the aquifer and its corresponding compression layer will also show different deformation characteristics when the groundwater level changes from falling to rising in the plain. In this paper, the extensometer and groundwater level observation data of 7 land subsidence monitoring stations are used to study the deformation characteristics of soil layers with different lithologies and different depths before and after the SNWDP-CR operation. The representative soil layer deformation characteristics are selected for analysis, and the soil layers with similar characteristics are grouped. Since the unconfined water is easily affected by many external factors, the first compression layer groups are characteristic of complex deformation. At the same time, the subsidence of the second and third compression layer groups accounts for about 92% of the total subsidence, and they are the main subsidence layers (Table 6). Therefore, the deformation characteristics of the second and third compression layer groups and sand layer are analyzed in the next paragraph. In Figs. 12–18, the negative value of the cumulative deformation represents soil compression, and the positive value rebound.

Fig. 11
figure 11

Statistics maps of average subsidence rate, subsidence area and volume (2013–2020). a Statistics of average land subsidence rate and subsidence area from 2013 to 2020. b Statistics of land subsidence volume from 2013 to 2020

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Sand layers

The monitoring layer of extensometer F3-8 in Tianzhu Station is 49–65 m, with a total thickness of 16 m. It is a confined aquifer which is mainly composed of fine sand and medium-coarse sand and whose top is covered with a 2 m thick clay layer. It can be seen from Fig. 12a that from 2006 to 2016, the average annual water level showed an overall downward trend over time, and the annual water level was dominated by seasonal fluctuations. The average annual water level dropped from −4.37 m in 2006 to −8.73 m in 2016, a drop of 4.36 m. The extensometer F3-8 compressed by 5.19 mm cumulatively. From 2017, the groundwater level began to gradually rise. By the end of 2020, the average annual water level rose to −3.00 m, an increase of 5.73 m. The extensometer F3-8 rebounded by 1.94 mm. From 2006 to 2016, the sand layer showed an almost synchronous compression-rebound as the groundwater level decreased or increased in an annual cycle. After 2017, when the groundwater level changed from fall to rise, there was a slight hysteresis in the deformation of the sand layer. It can be seen from Fig. 12b that from 2006 to 2016 the loading and unloading curves of the sand layer under slow cyclic loading were very close, showing basically synchronous elastic deformation. After 2017, the groundwater level began to rise, but the sand layer did not rebound immediately, there being a hysteresis in deformation. This may be related to the creep deformation of the clay layer which covers the top of the sand layer.

Second compression layer group

The monitoring layer of extensometer F3-5 in Tianzhu Station is 102–117 m, with a total thickness of 15 m. The lithology is mainly cohesive soil with a 2-m-thick fine sand layer in between. As shown in Fig. 13a, from 2006 to 2016, the groundwater level showed an overall downward trend, and the water level rose at the end of 2017. Before 2017, the groundwater level cyclically reciprocated. In each cycle, the water level fell more than it rose. Correspondingly, the soil layer bore the effects of loading and unloading, and each increase in stress was greater than the decrease in unloading, which means that the effective stress that the soil layer bore on the whole continued to increase. The soil layer was continuously compressed at a rate of about 10.3 mm/year. After 2017, although the groundwater level began to rise, the soil layer continued to compress, but the compression rate has slowed down. It can be seen from Fig. 13b that with the continual drop of the groundwater level, the compression curve developed toward the lower right, and the soil layer was rapidly compressed. Meanwhile, the soil layer showed plastic deformation, with the residual deformation relatively large. When the groundwater level rose, the soil layer still continued to compress, there being a hysteresis in deformation. This shows that this section of the soil layer did not only have plastic deformation with large residual deformation, but also contained creep deformation which related to the time development. It can be concluded that with the change of the groundwater level, the soil layer exhibits the characteristics of viscoplastic deformation.

Fig. 12
figure 12

Relationship between cumulative deformation of sand layer with groundwater level at F3-8 of Tianzhu station. a Time series curve of relationship between groundwater level and cumulative deformation. b Relationship curve between groundwater level and cumulative deformation

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The monitoring layer of extensometer F1-3 in Wangsiying Station is 66–94 m, with a total thickness of 28 m. It is mainly composed of clay layer and sand layer. The sand layer accounts for about 74% of the total thickness of the section, and the clay layer 26%. As shown in Fig. 14a, from 2006 to 2016, the groundwater level showed an overall downward trend. The average annual water level dropped from 1.97 m in 2006 to −7.32 m in 2016, with a drop amount of 9.29 m. The extensometer F1-3 compressed by 81.40 mm cumulatively. Since 2017, the groundwater level has risen significantly. By the end of 2019, the average annual water level had risen to −1.03 m, with an increase amount of 6.29 m. Correspondingly, the compression rate of the extensometer F1-3 slowed down to some degree, and there was a slight rebound in 2019. As shown in Fig. 14b, the monitoring layer was dominated by sand. From 2006 to 2016, with the decline of the groundwater level, the soil layer continued to compress rapidly, with a large amount of plastic deformation and with the phenomenon of hysteresis. This was related to the fact that the dissipation of excess pore water pressure in the soil layer lagged behind the change of the aquifer water level, and it may also be related to the creep deformation. After 2017, when the local water level has risen significantly, the compression rate of the soil layer has slowed down, including plastic and creep deformation. There were elastic deformation occurred in 2019 and 2020. It can be seen that with the change of the groundwater level, the soil layer undergoes a process of changing from viscoplastic deformation to viscoelastic plastic one.

Fig. 13
figure 13

Relationship between cumulative deformation of soil layer with groundwater level at F3-5 of Tianzhu station. a Time series curve of relationship between groundwater level and cumulative deformation. b Relationship curve between groundwater level and cumulative deformation

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Third compression layer group

The monitoring layer of extensometer F1-2 in Wangsiying Station is 94–148 m, with a total thickness of 54 m. It is mainly composed of cohesive soil layer and sand layer, and the cohesive soil layer accounts for about 77% of the total thickness of this section. As shown in Fig. 15a, from 2006 to 2016, the groundwater level showed a downward trend year by year. The average annual water level dropped from −5.80 m in 2006 to −20.76 m in 2016, with a drop amount of 14.96 m. The extensometer F1-3 compressed by 241.10 mm cumulatively. Since 2017, the groundwater level has risen significantly. By the end of 2020, the average annual water level had risen to −14.46 m, with an increase amount of 6.30 m. The compression rate of extensometer F1-2 slowed down to some degree. As shown in Fig. 15b, the groundwater level continued to drop, and the soil layer was compressed rapidly, with the amount of plastic deformation large. When the groundwater level rose, the soil layer continued to compress, there being a hysteresis in deformation. This shows that there was not only plastic deformation with large residual deformation, but also creep deformation which related to the time development. It can be found that with the change of the groundwater level, the soil layer exhibits the characteristics of viscoplastic deformation.

Fig. 14
figure 14

Relationship between cumulative deformation of soil layer with groundwater level at F1-3 of Wangsiying station. a Time series curve of relationship between groundwater level and cumulative deformation. b Relationship curve between groundwater level and cumulative deformation

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The monitoring layer of extensometer F6-3 in Zhangjiawan Station is 126–193 m, with a total thickness of 67 m. It is mainly composed of cohesive soil layer and sand layer. The cohesive soil layer accounts for about 52% of the total thickness of the section, and the sand layer 48%. As shown in Fig. 16a, from 2009 to 2017, the groundwater level showed an overall downward trend, and the groundwater level rose in 2018. Before 2018, with the decline of the groundwater level, the soil layer was compressed continuously. After 2018, the groundwater level rose, and the soil layer still compressed, but the compression rate slowed down. Meanwhile, there was a slight rebound in 2019 and 2020. As shown in Fig. 16b, the curve always developed toward the right with the continual decline of the groundwater level. There was very small rebound of the soil, or there was no rebound, and there was a hysteresis in the deformation of the soil. This shows that there was not only plastic deformation with large residual deformation, but also creep deformation in this section of the soil. After 2018, when the local water level rose, the curve still developed towards the right, there being plastic deformation and creep deformation. At the same time, there appeared a hysteresis loop in 2019 and 2020, indicating that there were still the characteristics of elastic deformation.

Fig. 15
figure 15

Relationship between cumulative deformation of soil layer with groundwater level at F1-2 of Wangsiying station. a Time series curve of relationship between groundwater level and cumulative deformation. b Relationship curve between groundwater level and cumulative deformation

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What has been discussed above is the typical deformation curves of long-term series of different depths and lithological soil layers in different water level change modes in land subsidence monitoring stations. It can be found that most of the middle-deep and deep confined groundwater levels continued to decline before 2017 and gradually rose after 2017. Therefore, the year 2017 can be regarded as the time node. Under the comprehensive consideration of different groundwater level change modes, the deformation characteristics of different compression layer groups and sand layer can be summarized as shown in Table 8. The groundwater levels corresponding to the second and third compression layer groups continued to decline at a rapid rate before 2017 and then gradually rose after 2017. The second and third compression layer groups showed the (I) deformation type before 2017, and the different lithological soil layers showed the (II) and (III) deformation types after 2017. The groundwater level corresponding to the sand layer decreased slightly before 2017 and gradually rose after 2017. The sand layer showed the (IV) deformation type.

Table 6 The subsidence of each monitoring station and the main compression layer correspond to the change of groundwater level in 2014 and 2020
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Geotechnical test of soil deformation

On the basis of obtaining the deformation characteristics of the soil layer, the loading, unloading, and repeated loading and unloading test methods are used to compare different lithological soil samples. The deformation characteristics and creep effects of different lithological soil layers under different loading and unloading modes are analyzed. In the test process above, each level of load is applied or removed instantaneously, to observe the stability of the deformation under each level of load, and the deformation less than 0.005 mm/h is regarded as the stability standard (Zhang et al. 2012, 2016). The location of the soil sample is shown in Fig. 1. The physical and mechanical properties of the soil sample are shown in Table 9.

Table 7 Deformation characteristics of different compression layer groups and sand layers before and after SNWDP-CR operation under different water level change modes
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It can be seen from Fig. 17a that firstly, after each level of pressure is loaded, the deformation of the soil sample is basically stable after about 120 min; secondly, the total deformation of the clay sample and the silt sample is 2.822 mm and 1.0 mm, respectively. Under the same load condition, the deformation of clay is greater than that of silt. As the pressure increases, the difference in the amount of deformation becomes larger and larger. It can be seen from Fig. 17b as follows: Firstly, after the soil sample is loaded with 400 kPa and reaches the stable deformation, with the gradual unloading, the total rebound of the clay sample and the silt sample is 0.277 mm and 0.121 mm. The rebound of clay is more than the silt obviously under the same load. Secondly, since the unloading of the soil sample is completed instantaneously, the instantaneous rebound of the soil sample is very obvious after each level of unloading. With the progress of the test, when the effective stress gradually approaches the load borne by the soil, the rebound amount of the soil sample gradually decreases and tends to a constant value. Thirdly, the smaller the unloading pressure of the soil sample is, the longer time will be taken for the soil sample to complete the rebound and achieve stable deformation.

Fig. 16
figure 16

Relationship between cumulative deformation of soil layer with groundwater level at F6-3 of Zhangjiawan station. a Time series curve of relationship between groundwater level and cumulative deformation. b Relationship curve between groundwater level and cumulative deformation

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Repeated loading and unloading tests are carried out on No. 6, No. 16, and No. 21 soil samples to simulate the deformation characteristics of soil layer during the rise and decline of groundwater level. It can be seen from Fig. 18 is as follows: Firstly, the deformation of the clay in the first loading and unloading is greater than the second, and the deformation of the latter two loading and unloading gradually increases and is greater than the first loading and unloading. The main reason is the large porosity of the clay. During the first loading and unloading, the soil sample is pressurized and drained, easy to compress and deform greatly. During the second loading and unloading, however, because the load of the soil sample is still small and it has already gone through one loading and unloading cycle, the soil sample’s creep increases, and the amount of deformation is small. The loads of the third and fourth cycles are larger, and the creep amount of the soil sample becomes larger and larger until the soil sample is destroyed. So there is a large amount of deformation. Secondly, the deformation of silty clay and silty soil in each loading, and unloading cycle is greater than the previous cycle. This is mainly because after the porosity of the soil sample reduces, the soil sample is not easy to be compressed, and it is easy to reach a consolidated state, and the amount of creep is small. When the maximum load gradually increases, the amount of deformation also gradually increases. Thirdly, the time effect of creep is as follows: clay > silty clay > silt. It shows that the larger porosity, the more creep deformation is likely to occur.

Fig. 17
figure 17

Cumulative deformation curve of loading and unloading of clay and silt. a Cumulative deformation curve of loading of clay and silt. b Cumulative rebound curve of unloading step by step of clay and silt after reaching stable deformation from 400 kPa

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Fig. 18
figure 18

Cumulative deformation curves of soil samples with different lithologies after repeated loading and unloading. a Cumulative deformation curve of No. 6 clay sample after repeated loading and unloading. b Cumulative deformation curve of No. 16 silty clay after repeated loading and unloading. c Cumulative deformation curve of No. 21 silt soil after repeated loading and unloading

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Change of elastic and inelastic skeletal specific storage rate

According to the above-mentioned deformation characteristics of soil layers with different lithologies and different depths, the elastic and inelastic skeletal specific storage rates of the sand layer and compressed layer group can be calculated. The average of the results is shown in Table 10. In terms of the results of Galloway and Burbey (2011) when the value of Sske is 5 × 10−4, it is a typical elastic skeletal specific storage coefficient. When the value of Sskv is 5 × 10−3, it is likely to be an inelastic skeletal specific storage rate coefficient during land subsidence. Of course, when the water storage rate is calculated, the water storage coefficient needs to be divided by the initial thickness of the soil layer. At the same time, Hoffmann et al. point out that for aquifers dominated by loose clay and mucky, the value of Sskv is usually tens to hundreds of times larger than that of Sske. It can be seen from Table 10 that the inelastic skeletal specific storage rate in different compression layer groups is 1 to 2 orders of magnitude larger than the elastic skeletal specific storage rate. It shows that when the soil layer is mainly cohesive soil, with the rise of the water level, the soil layer will still have a large residual deformation and will continue to compress without rebound or with small rebound. The F3-5 in the second compression layer group, and the F1-2 and F6-3 in the third compression layer group all show larger residual deformation. It is noticeable that the inelastic skeletal specific storage rate of F6-3 from 2009 to 2016 is 4.88 × 10−5, which is small and close to the elastic skeletal specific storage rate. The reason is that the water-bearing sand layer accounts for 48% of the total thickness of this section, which has a certain influence on the inelastic deformation of the soil layer. Since the inelastic skeletal specific storage rate is greater than the elastic skeletal specific storage rate, there will be residual deformation when the water level is restored (Ye et al. 2016a, b).

Table 8 Statistics of physical and mechanical properties of soil samples
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Table 9 Elastic and inelastic skeletal specific storage rate of compressed layer group and sand layer
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It is noticeable that as for different stages of the soil deformation, the change in water storage rate is not constant, and its value depends on the relationship between the effective stress and the preconsolidation pressure (Hoffmann et al. 2003; Liu and Helm 2008a, b). For example, the extensometer F1-3 with the year 2017 taken as the time nodes, the soil layer changed from plastic deformation to elastic deformation. The water storage rate also changed from inelastic skeletal specific storage rate to elastic skeletal specific storage rate. The rest of the extensometers took the year 2017 as the time node, and the soil water storage rate in different periods also showed different characteristics of change. This further illustrates that after the operation of SNWDP-CR, the deformation characteristics of different lithologies and depths of soil layers have changed, and the corresponding hydrogeological parameters have also changed greatly. Therefore, in order to simulate the land subsidence under the new situation where the groundwater level continues to rise after the operation of the SNWDP-CR, suitable soil constitutive relations and corresponding hydrogeological parameters must be selected according to the deformation characteristics of the soil.

Conclusions

This study has investigated the impact of the 6 years of SNWDP-CR operation on the groundwater and land subsidence in the Beijing Plain. PSI, GIS spatial analysis, stress–strain analysis, mathematical statistics, and geotechnical tests are used for the first time to analyze the changes of the groundwater flow field, groundwater level, land subsidence, soil deformation, and hydrogeology parameters before and after the SNWDP-CR operation. The research results are of great significance for the further determination of the constitutive relationship of soil layer deformation before and after the SNWDP-CR operation and the establishment of an appropriate coupling model of groundwater and land subsidence.

Affected by various measures such as SNWDP-CR, reduction of groundwater exploitation, shut-down of wells, and recharge of aquifers, the groundwater level of the first to fourth aquifer groups in most areas of the Beijing Plain rose significantly from 2015 to 2020, and the corresponding land subsidence has gradually slowed down. The average groundwater level of the four aquifer groups rose by 2.72 m, 3.68 m, 3.31 m, and 1.91 m, respectively. The average land subsidence rate decreased from 18.8 mm/year in 2015 to 10.85 mm/year in 2020, with a decrease of 7.95 mm/year. However, the groundwater level in some areas is still declining, and land subsidence continues to develop.

The main subsidence layers of the Beijing Plain are currently concentrated in the second and third compression layer groups, with average subsidence accounting for 34.11% and 57.36%. Since the operation of SNWDP-CR, except for the increase in the annual subsidence of the Yufa extensometer, the annual subsidence of the extensometers of the other stations decreased significantly. As for the groundwater level corresponding to the main subsidence layer, except for Zhangjiawan and Yufa stations, the groundwater levels of the other stations all rose.

The deformation characteristics of different lithological soil layers under different water level change modes can be summarized into 4 categories before and after the SNWDP-CR operation. The sand layer is mainly characteristic of elastic deformation. The soil deformation characteristics of the second and third compression layer groups are quite different when the groundwater level changes from declining to rising. When the soil layer is dominated by cohesive soil, it always exhibits plastic and creep deformation. If the sand layer is the main one, the soil layer exhibits plastic and creep deformation in the stage of groundwater level decline, and plastic, creep, and elastic deformation in the stage of water level rises.

Under the condition of gradual loading, the deformation of clay was greater than that of silt. With the increase of the pressure, the difference in the amount of deformation increased. Under the condition of gradual unloading, the rebound amount of clay was greater than that of silt. And the rebound amount gradually decreased until it tended to a constant value. Under the condition of repeated loading and unloading, silty clay and silt soil were easier to consolidate than clay, and the amount of creep was smaller. The time effect of creep was as follows: clay > silty clay > silt. It shows that the larger porosity, the more creep deformation is likely to occur.

After the operation of SNWDP-CR, the hydrogeological parameters corresponding to different lithology and soil layers of different depths changed greatly. The change in the elastic and inelastic skeletal specific storage rate of the sand layer and compressed layer group were not constant, but changed with the different deformation characteristics of the soil layer. The inelastic skeletal specific storage rate of different compression layer groups was 1 to 2 orders of magnitude larger than the elastic skeletal specific storage rate. As the groundwater level decreases, the soil skeletal specific storage rate shows a decreasing trend.