Introduction

Land subsidence is an environmental phenomenon resulting from consolidation of the ground. It is generally a relatively slow movement, but may break pipelines and result in differential settlement/tilting of buildings. The causes of land subsidence include natural factors (e.g. the collapsing of loess, drainage or organic-rich soils, karst development) and human activities (e.g. underground construction, removal of liquid and/or solids from the ground). In the coastal urban region of China, groundwater extraction is the primary cause of land subsidence (Chai et al. 2004, 2005; Gu 1998; Li et al. 2000).

In recent years, land subsidence has occurred in over 90 cities and counties in China, including Shanghai, Tianjin, Jiangsu Province, Shanxi Province; the total area of subsidence is reported as 93,885 km2 (Cui 2008). Shanghai was one of the first cities to experience land subsidence. In the 80 years from 1921 to the end of 2001, the total accumulative subsidence had reached 2.7 m (Zhang and Wei 2002; Xue et al. 2005; Tang et al. 2008a). Initially, this was mainly due to the irrational withdrawal of groundwater but from the 1960s, the withdrawal of groundwater was restricted and from the end of the 1970s, the pumping of groundwater was strictly controlled in the urban area of Shanghai. As a consequence, the quantity of water recharged into the subsurface was always greater than that extracted by pumping, such that the subsidence caused by pumping and recharging was limited. During the 1990s, however, with the development of the economy, a variety of municipal works and high-rise buildings were constructed and land subsidence appeared to accelerate in Shanghai (Tang et al. 2008b; Cui et al. 2009).

In this paper, the “geology-environmental capacity” refers to the optimum inter-relationship between the needs of human society, the economy and the engineering structure in a certain geological area. The geology-environmental capacity is finite, e.g. there is a limit to the weight of the buildings that the ground can sustain in a certain geological situation if particular environmental criteria are to be met. In the soft soils of Shanghai, land subsidence caused by the engineering-environmental effect has resulted in great economic loss to the city, hence this has become an important factor, restricting the scale of construction. In Shanghai, therefore, building is mainly controlled by land subsidence.

Factors affecting land subsidence

Shanghai is situated on the Yangtze River delta where the alluvial deposits generally reach 250–300 m in the urban area (Fig. 1). The upper 150 m of the alluvium is mainly of grey, “soft-plastic” clay and sands. The lower horizon has a wider range of colours and is mainly “hard-plastic” clay alternating with layers of sand and gravel (Tang et al. 2008b).

Fig. 1
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Hydrostratigraphy along the cross section of Fengtang-Yaoguang Road-Zhangjiang

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In recent years, records indicate that the main subsidence below 70 m is related to pumping/recharge while the soil deformation above this depth was mainly caused by engineering works. In this upper horizon there are three distinct thick layers of soft soil, see Table 1.

Table 1 Geological layers (above 70 m)
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Based on population density, engineering construction, hydraulic engineering, flood control etc., the area of Shanghai is divided into a basically stable region and a land subsidence region which contains two sub-regions as shown in Table 2.

Table 2 Distribution of land subsidence in Shanghai
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Density of construction

The floor area ratio is the ratio of the total floor area within an individual structure to the area of land on which the construction has taken place. The building density is the ratio of the basement area of the building to the area of land on which the construction has taken place.

As shown in Table 3 (Yan et al. 2002) the building areas of four typical regions, Lujiazui, Xujiahui, Zhongyuan and Changqiao increased from 1980 to 1999. It can be seen that the built area increased in the 1980s and 1990s relative to that in the previous decade. In most areas, the floor space more than doubled. In the same period, land subsidence increased rapidly (Table 4), again more than doubling between the 1980s and 1990s.

Table 3 Building area of four typical regions (Unit: ×106 m2)
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Table 4 Land subsidence of four typical regions (Unit: mm)
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Table 5 indicates the number of high rise buildings constructed in the four areas together with the total floor areas. The value of the floor area ratio is derived from the proportion of the number of the high-rise buildings to the total number of buildings.

Table 5 The floor area ratio of four typical regions
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The adaptive neuro-fuzzy inference system

The adaptive neuro-fuzzy inference system (ANFIS) combines artificial neural networks (Mamdani and Assilian 1975; Jacobs 1988; Hoke and Brown 1997) with the (Sugeno) fuzzy logic inference. The typical fuzzy logic rule is as follows.

If x is A and y is B, then Z = f(x, y), where A and B are the fuzzy set of the inputs and z = f(x, y) is the accurate function of the target. Generally, f(x,y) is polynomial about input variables x, y. If f(x, y) is one-order polynomial, the obtained fuzzy inference system is the one-order Sugeno fuzzy model.

Figure 2 shows the inference process of the one-order Sugeno fuzzy model which has two inputs x, y and one output z, such that it contains two fuzzy “if-then” rules:

Fig. 2
figure 2

The inference process of one-order Sugeno fuzzy system

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$$ {\text{If }}x{\text{ is }}A_{1} {\text{ and }}y{\text{ is }}B_{1} ,{\text{ then }}f_{1} = p_{1} x + q_{1} y + r_{1} . $$
$$ {\text{If }}x{\text{ is }}A_{2} {\text{ and }}y{\text{ is }}B_{2} ,{\text{ then }}f_{2} = p_{2} x + q_{2} y + r_{2} . $$

where A i and B i are fuzzy sets corresponding with input variables.

Supposing that the S type membership functions of input variables x and y are:

$$ S_{{A_{i} }} (x,a_{i} ,b_{i} ) = {\frac{1}{{1 + e^{{ - a_{i} (x - b_{i} )}} }}} $$
(1)
$$ S_{{B_{i} }} (y,c_{i} ,d_{i} ) = {\frac{1}{{1 + e^{{ - c_{i} (x - d_{i} )}} }}} $$
(2)

where i = 1, 2 {a i , b i } and {c i , d i } being two group characteristic parameters of S type membership functions.

S type membership functions are changed with the change of the values of characteristic parameters, that is, the membership functions of A i and B i are changed. The inference process can be equivalent to the ANFIS structure shown in Fig. 3 which consists of five layers.

Fig. 3
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The ANFIS structure equivalent to one-order Sugeno

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The function of the first layer is to compute the fuzzy membership of inputs. Every node of this layer is the adaptive node and has a node function,

$$ O_{1,i} = S_{{A_{i} }} (x,a_{i} ,b_{i} ),\quad i = 1,2 $$
(3)
$$ O_{1,j} = S_{{B_{j - 2} }} (y,c_{j - 2} ,d_{j - 2} ),\quad j = 3,4 $$
(4)

where O 1,i is the No.i output of the first layer and is a member of the corresponding output variable of fuzzy sets A i and B i

The function of the second layer is to compute the fitness of every rule. Every node of this layer is a fixed node labeled ∏. Its output is the product of all input signals:

$$ O_{2,1} = O_{1,1} \cdot O_{1,3} = S_{{A_{1} }} (x,a_{1} ,b_{1} ) \cdot S_{{B_{1} }} (y,c_{1} ,d_{1} ),{\text{marking}}\,W_{1} $$
(5)
$$ O_{2,2} = O_{1,2} \cdot O_{1,4} = S_{{A_{2} }} (x,a_{2} ,b_{2} ) \cdot S_{{B_{2} }} (y,c_{2} ,d_{2} ),{\text{marking}}\,W_{2} $$
(6)

The function of the third layer is to compute the unitary value of fitness. Every node of this layer is a fixed node labeled N. The ratio of the strength of one rule to the sum of all the strengths is obtained:

$$ O_{3,1} = \bar{W}_{1} = {\frac{{W_{1} }}{{W_{1} + W_{2} }}} $$
(7)
$$ O_{3,2} = \bar{W}_{2} = {\frac{{W_{2} }}{{W_{1} + W_{2} }}} $$
(8)

The function of the fourth layer is to compute the output of every rule. Every node of this layer is an adaptive node with a function:

$$ O_{4,1} = \bar{W}_{1} z_{1} = \bar{W}_{1} (p_{1} x + q_{1} y + r_{1} ) $$
(9)
$$ O_{4,2} = \bar{W}_{2} z_{2} = \bar{W}_{2} (p_{2} x + q_{2} y + r_{2} ) $$
(10)

where {p i , q i , r i } (i = 1, 2) is the set of parameters of corresponding nodes, i.e. conclusion parameters.

The function of the fifth layer is to compute the output of the fuzzy system. The single node of this layer is a fixed node (∑) which computes the sum of all the incoming signals:

$$ O_{5} = z = \sum {\bar{W}_{i} z_{i} = } \bar{W}_{1} z_{1} + \bar{W}_{2} z_{2} $$
(11)

This network consists of undetermined characteristic parameters (a i , b i , c i , d i (i = 1, 2) of membership functions and p i , q i , r i (i = 1, 2) conclusion parameters). ANFIS dynamically adjusts these parameters in the trained process.

ANFIS model based on the floor area ratio

Land subsidence S, the building density D, the geological disaster district C, the exploitation of groundwater K, the re-circulation of groundwater H and the type of the geology structure J were selected as the variables to infer the floor area ratio R in this paper, that is, X = (S, D, C, K, H, J). The relationship between R and X is,

$$ R = F(\{ X\} ) $$
(12)

This can be established using ANFIS as follows.

  1. (1)

    The finite groups of the training data are obtained at different places according to the influencing factor X and the floor area ratio R.

  2. (2)

    X and R are taken as the input data and the output data of the initial structure of ANFIS, respectively. After training, the optimum structure model of ANFIS reflecting the global mapping relationship is built up between X and R.

  3. (3)

    Putting the data of four typical regions into this structure model of ANFIS, the output is the predicted optimum value of the floor area ratio.

Nineteen examples were selected as the training data, from different places in Shanghai; the variables are shown in Table 6. The variables of the 16 examples in Table 6 were treated in the standardized way. The S, D, C, K, H and J are the input of the network and the R is the output of the network. A model structure was built up by the subtraction cluster method. The values of the training parameters were

Table 6 ANFIS training data
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$$ {\text{Range of influence }}0.27,{\text{ Squash factor }}1.25,{\text{ Accept ratio }}0.5,{\text{ Reject ratio 0}} . 1 5.$$

Every input variable of the model was automatically endowed with 16 Gauss membership functions. The model structure based on the floor area ratio is shown in Fig. 4. Using the hybrid learning algorithm, the network was trained by the selected data. The training degree was 1,000 times and the smallest root-mean-square deviation of the training data was 0.0030208. The change of the error in the training process is shown in Fig. 5.

Fig. 4
figure 4

The structure of ANFIS

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Fig. 5
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The training error in the training process

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The membership functions of land subsidence S, the building density D, the geological disaster district C, the exploitation of groundwater K, the re-circulation of groundwater H and the type of the geology structure J can be obtained before and after training. The membership function of land subsidence as an example is shown in Fig. 6.

Fig. 6
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The membership function of land subsidence before and after training

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Six pictures of the changing laws between one single input parameter of S, D, C, K, H, J and the output parameter R can be obtained. The changing laws of S-R and D-R as two examples are shown in Figs. 7 and 8. Fifteen pictures of the changing laws between every two input parameters of S, D, C, K, H, J and the output parameter R can also be obtained. The changing laws of S, D-R and S, C-R as two examples are shown in Figs. 9 and 10.

Fig. 7
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The changing law between S and R

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Fig. 8
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The changing law between D and R

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Fig. 9
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The changing law between S, D and R

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Fig. 10
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The changing law between S, C and R

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Evaluation of the geology-environmental capacity of the buildings based on the ANFIS model of the floor area ratios are shown in Figs. 11, 12, 13 and 14. Where the floor area ratios of the regions are bigger, the high-rise buildings are dense and land subsidence is larger. It is inappropriate to continue to plan high-rise construction in these regions. However, where the floor area ratios of the regions are smaller and land subsidence is less, high-rise buildings can be constructed.

Fig. 11
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The floor area ratios of the 1st typical region

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Fig. 12
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The floor area ratios of the 2nd typical region

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Fig. 13
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The floor area ratios of the 3rd typical region

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Fig. 14
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The floor area ratios of the 4th typical region

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Conclusions

The paper has demonstrated that as the geological environmental capacity of a building is mainly controlled by the land subsidence in the Shanghi area, the relationship can be assessed using the floor area ratio. ANFIS was used to evaluate the floor area ratios of four typical areas in the Shanghai region (Lujiazui, Xujiahui, Zhongyuan and Changqiao) in order to offer some guidance in respect of urban planning.