Analysis on the influence of the water retaining effect of underground structure on land subsidence caused by pumping 

Wang Chengbin   Yu Qingyang

Abstract: Based on Biot consolidation theory, a finite element model of land subsidence was established considering various working conditions including setting water retaining structure and not. The influence of pumping on land subsidence was calculated and analyzed by numerical simulation. Taking maximum land subsidence as index, the structure reliability and the relative sensitivities of several soil parameters considering random distribution were calculated and analyzed by using MATLAB programming. And then, the influence of water retaining structure on soil parameter sensitivity was verified by formulas derivation. The results showed that the deeper the exploited aquifer is, the bigger the maximum land subsidence is. In the sensitivity for land subsidence, the soil parameters from large to small are elastic modulus, permeability coefficient, Poisson’s ratio, density, angle of internal friction, porosity ratio and cohesion. As water retaining structure go deep underground, maximum land subsidence increase, so is differential settlement, and the permeability coefficient and the parameters that related to lateral friction (Poisson’s ratio, angle of internal friction and cohesion) become more sensitive. The structure reliability is reduced when setting water retaining structure or considering the positive correlation between elastic modulus and permeability coefficient.

Keywords: Pumping; Water retaining structure; Land subsidence; Differential settlement; Parameter sensitivity

1 Preface

Land subsidence not only endangers the constructed structures located on the earth’s surface and underground, but also restricts the further development of cities. At a time when the world is facing rising      temperature and rising sea level, land subsidence affects coastal cities and regions especially. There are many human factors that cause land subsidence, such as excavation of foundation pit and tunnel,  construction of high-rise and super high-rise buildings on the earth’s surface, exploitation of groundwater and so on [1-7].With the development of human society, mega-cities and super mega-cities are constantly  emerging. Urban land subsidence is becoming increasingly serious. Especially in recent decades, the development of many cities around the world has been troubled by land subsidence caused by over-exploitation of groundwater. Cai Wenxiao believed that in Dezhou City, the land subsidence caused by over-exploitation of deep groundwater accounted for as much as 90 percent of the total subsidence, and as the deep groundwater continued to be over-exploited, the deep groundwater drop funnel continued to expand vertically and horizontally. Therefore, the influence range of land subsidence caused by over-exploitation of deep groundwater is very large [8].

Based on the principle of effective stress, The decrease of pore water pressure and the increase of effective stress in soil are the reasons of that land subsidence occurs when pumping water from aquifers [9].For the land subsidence caused by pumping water, Ding Demin thought that the calculation results of the seepage-normal stress coupling model for finite element analysis based on Biot consolidation theory   were in good agreement with the actual situation in land subsidence. And the maximum land subsidence occurred in the center of groundwater extraction funnel [10].

A large number of studies had shown that the water retaining structure underground reduces the permeability coefficient of soil [11-14]. About analyzing the influence of water retaining structure on land subsidence, Xu Yaoxing and others calculated the equivalent permeability coefficient by using equivalent medium theory, and then analyzed the influence of water retaining structure on land subsidence. It was concluded that the setting of water retaining structure increased maximum land subsidence [15]. However, this equivalent medium calculation method did not take the influence of location of water retaining structure into account, and it was difficult to accurately monitor or calculate the water head change in different positions of soil. And to calculate the land subsidence caused by pumping water, the widely used analytical solution methods that based on consolidation settlement theory ignored the lateral friction of soil layers [16-17]. Thus, only an approximate solution to the actual situation could be obtained. To analyze the influence characteristics of water retaining structure on land subsidence caused by pumping water, the exact solutions in land subsidence should be obtained. In this paper, numerical calculation method was used to calculate and analyze the influence characteristics of water retaining structure on land subsidence caused by pumping water. The influence of water retaining structure on the sensitivities of soil parameters for maximum land subsidence was analyzed and verified by MATLAB programming and formulas derivation.

2 Establishment of numerical model of land subsidence caused by pumping water

2.1 Mechanical model of land subsidence caused by pumping based on osmotic consolidation theory

On the basis of Terzaghi consolidation theory, Biot derived a true three-dimensional consolidation equation that accurately reflected the relationship between the dissipation of pore water pressure and the consolidation of soil [18]:

       (1)

In the formula, G was shear modulus. µ was Poisson's ratio.γ_w was the unit weight of groundwater. u、v and w were the displacement in the X、Y、Z direction. KX、KY and KZ were the permeability coefficients in the X、Y、Z directions .η² was Laplace operator.

Based on Biot consolidation theory, a seepage-normal stress coupling model was constructed to study the influence of water retaining structure on land subsidence caused by pumping water.

2.2 Geometric model of land subsidence caused by pumping

The calculation model with 11 aquifers and weakly permeable aquifers is shown in figure 1. It included one 35 m slightly pressure-bearing aquifer, five aquifers with a thickness of 50 m and five weak permeable layers with a thickness of 50 m. The length, height and thickness of the model were 1500m, 535m and 1m   respectively. The initial groundwater level was 5 m underground. For the model, the sides were constrained in normal direction, the bottom was completely constrained, the top was free, and all boundaries were impervious. There was only one pumping well in the research area, which was in the middle of the model, and its surfaces’ directions were consistent with the wide’s direction. The water retaining structure was set up on the left side of the pumping well, 100m away. In order to avoid the influence of the lateral friction and gravity change caused by the material difference between the water retaining structure and the surrounding soil on land subsidence, the water retaining structure was only considered as an impermeable material compared with the surrounding soil. The soil parameters of the model are shown in Table 1.

Fig.1 Schematic diagram of the calculation model

Table 1The physical and mechanical properties of each soil layer [10, 15]

The calculation model consisted of two types: not setting water retaining structure and a water retaining structure on the left side of the pumping well, 100m away. When there is no water retaining structure, the exploited aquifers were the 1-5 aquifers respectively. When the water retaining structure was set, the exploited aquifer was the second aquifer. Pumping speed was set to 20 m³ / d, and the land subsidence on the earth’s surface was calculated and analyzed when the water retaining structure went deep differently.

3 Analysis on land subsidence caused by pumping water

Soil consolidation and compression in the research area is not only related to the property of soil, but also depends on boundary conditions, pumping conditions and human activities and so on. Under different conditions, the results are often very different. Twenty-four monitoring points were set up on the earth's surface, among which the monitoring points near the pumping well were relatively dense. The following results were the land subsidence after 10 years’ exploitation of the 1-5 aquifers respectively.

3.1 Analysis on land subsidence when no water retaining structure was set

Fig. 2 Vertical cloud of land subsidence when no water retaining structure was set

Fig. 3 Curves of land subsidence when different aquifers were exploited

From figs. 2 and 3, we can see that in the absence of water retaining structure, the amount of land subsidence caused by pumping water increased with the depth of the exploited aquifer. The maximum land subsidence all occurred in the center of groundwater extraction funnel, and the farther away from the   pumping well the place was, the smaller the land subsidence was. The maximum land subsidence was 0.4155m when the fifth aquifer was exploited, which was 2.61 times of that when the first aquifer was exploited. The differential settlement was small. The maximum differential settlement occurred when the second aquifer was exploited, which was only 0.0413m between 0m and 750m away from the pumping well.

3.2 Analysis on land subsidence when the water retaining structure was set

When researching the influence of the inserting depth of water retaining structure, the water retaining structure was set on the left of the pumping well in the model, which was 100 m away from the pumping well. And the second aquifer was exploited. Considering the pumping surfaces’ direction consistent with the wide’s direction in the model and the setting of water retaining structure on the left side of the pumping well had no effect on the land subsidence of the other side. So that only the land subsidence at the 1-15 monitoring points were written down. The land subsidence characteristics were analyzed as the water retaining structures went deep underground.

Fig. 4 Vertical cloud of land subsidence when the water retaining structure went deep into the bottom of the second aquifer

Fig. 5 Curves of land subsidence on the left side of the pumping well when the water retaining structure went deep differently

Fig. 6 Land subsidence at two typical monitoring points as the water retaining structure went deep

The calculation results are as shown in figs. 5 and 6: In the vicinity of the pumping well, the land subsidence increased with the inserting depth of the water retaining structure .When the water retaining structure reached 235m from 225 m underground, that was, when the exploited aquifer was from partially blocked to completely blocked, the increase of maximum land subsidence reached 61.72% of that when no water retaining structure was set. In other cases, as the water retaining structure went deep underground, the increase was relatively small. As shown in figure 6, the place that on the other side of the water retaining structure, which was 650m away from the pumping well, the land subsidence initially increased with the inserting depth of the water retaining structure by small degrees and then when the water retaining structure closed to the bottom of the second aquifer, there was a relatively large decrease in the amount of land subsidence. Lastly, the land subsidence showed a small decreasing trend as the water retaining structure went deep. And on the whole, the differential settlement increased as the water retaining structure went deep.

Theoretically, as the water retaining structure went deep underground, the pumping amount on the far side of the pumping well decreased and the land subsidence decreased. According to the land subsidence characteristics described above when the 1-5 aquifers were exploited respectively, as shown in fig. 3, we can know that the initial increase of land subsidence with the inserting depth of the water retaining structure at the place that 650 m away from the pumping well, where the influence of lateral friction was small, was due to the fact that when the water retaining structure just begun going deep underground, the exploitation of the shallow aquifers decreased, and that of the deep aquifer increased accordingly. In addition, near the water retaining structure, the land subsidence increased with the inserting depth of the water retaining structure. When the water retaining structure completely blocked the other side of the pumping well, that was, the water retaining structure went deep into the ground for 535m, the land subsidence near the water retaining structure increased by 29.95% compared with that when no water retaining was set. However, the land subsidence on the left side of the water retaining structure should decrease in theory because the decrease of the groundwater head was reduced. The analysis showed that this was mainly due to the influence of lateral friction produced by larger settlement at the place near the pumping well.

4 Analysis on relative sensitivities of soil parameters and structure reliability for maximum land subsidence based on quadratic response surface method

4.1 Theory of quadratic response surface method

It was very difficult to obtain the explicit function of large and complex structure using traditional analytic method, and the derived functions were generally restrictive and approximate in application. In this case, on the basis of not changing the meaning of the original equation, the polynomial response surface method, which could replace the display function in the sense of probability, came into being [19]. The polynomial response surface method was used to simulate the unknown limit state surface in the real case by a series of numerical simulations. The response surface function of quadratic polynomials without crossover terms was widely used to analyze nonlinear structures. This paper also selected this method:

                         （2）

X_i was the sample point of parameters related to Z. The coefficients a, b_i and c_i were obtained by selecting 2n sample points.

4.2 JC algorithm for structure reliability

The complexity of underground soil determines that the soil parameters could not be accurately obtained, and the structure reliability obtained by considering the random distribution of soil parameters was of practical significance.

The JC algorithm was also called the checking point method or the improved first-order second- moment method. The probability distribution of variable was considered on the basis of the center point method, and variables that did not conform to normal distribution should be transformed into equivalent normal distributions [20].The tangent plane of structure at the checking point was used to replace the limit state surface, and the improved first-order second-moment method was used to calculate structure reliability.

The limit state function of structure could be expressed as:

                                        （3）

If the checking point  is at the failure interface,  would be satisfied. At this time,

                              （4）

                                （5）

In the upper form,

                                （6）

From the definition of reliability，we could know that

                                           （7）

Combining the formulas（4）-（7）,we could get that

                     （8）

The checking point for this equation was

                                （9）

The new checking point of quadratic response surface method could be got

                 （10）

In the upper form, Xi was the initial iteration point of JC algorithm.

The new checking point was then used to recalculate until the difference between the front and back β values met requirement.

4.3 Method for calculating relative sensitivities of soil parameters

In this paper,  and  were used to analyze the relative sensitivities of soil parameters considering random distribution [21].This method eliminate the unit of parameter sensitivity and make the sensitivities with different unit comparable.

              （11）

                              （12）

For the X,  and  were the mean and variance of parameter considering random distribution. X^* was the checking point. C_X=σ_Xρ_Xσ_X was the covariance matrix.ρ_X was the correlation coefficient matrix.

4.4 Analysis on relative sensitivities of soil parameters and structure reliability for maximum land subsidence

Two typical working conditions of no setting water retaining structure and the water retaining structure going deep into the ground at 235m (that was completely block the second aquifer) were selected as the objects of study, and the second aquifer was exploited. The selection of the parameters distribution characteristics was combined with related document, and the mean values of the parameters were got by weighting the design values of each soil layer.

Table 2 Distribution characteristics of the soil parameters [22]

Random variances	Units	Distribution	Mean value	Coefficient of variation
Elastic modulus(E)	kPa	Normal distribution	69592.7	0.3
Permeability coefficient(K)	m/d	Normal distribution	2.5038	0.3
Density(ρ)	Kg/m3	Normal distribution	1902.3	0.3
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