Introduction

With the advancement of global “carbon peaking” carbon neutral’(Hargroves et al. 2016; Le Quéré et al. 2015; Qin et al. 2021; Sovacool 2022), the energy structure is being adjusted in the direction to low-carbon and non-carbonization(Johnstone et al. 2021; Slamersak et al. 2022; Suzuki et al. 2016; Wu et al. 2018). As a significant part of the energy structure, how to use coal resources in a low-carbon, green and clean has become a research hotspot. Underground coal gasification (UCG), a revolutionary technology, may radically transform the traditional coal industry into a clean and environmentally friendly energy industry (Al-Ghussain 2019; Bhutto et al. 2013; Prabu 2015; Xie et al. 2020). In the past decade, the progress of UCG has been increasing and the existing UCG process has been able to meet the requirements of industrialization and large-scale production (Ariyoshi et al. 2016; Friedmann et al. 2008; Walker 2014).

Nevertheless, with the industrialization and large-scale production of UCG, the issues including large-scale surface subsidence and fractured rocks will inevitably occur, which will restrict the reuse of UCG sites and cause serious waste of UCG surface sites. The key to the reuse of UCG sites is to assess the stability of gasification sites (Li et al. 2019; Luan et al. 2020). If the gasification area is evaluated as stable, ground buildings can be constructed. While the gasification area is unstable, the gasification site requires to be regulated. The core of the stability evaluation of the UCG site is to calculate its residual subsidence deformation. By comparing the difference between the residual surface deformation and the evaluation index, it can be determined whether the gasification area site is stable.

However, there is currently no method for predicting the UCG surface residual subsidence, leading to a lack of the scientific basis to evaluate the stability of the gasification area. Nonetheless, some scholars have studied research on the prediction method of residual subsidence in well mining. For example, Salamon and Merwe (Salamon and Madden 1998; Van der Merwe 2003; van der Merwe and Mathey 2013) found that the room-type pillar will suffer progressive instability, causing secondary deformation of the surface. Yu Yang et al. (Yang et al. 2017) deduced a computational method of maximum stripping width for strip mining. Changfu Huang et al. (Huang et al. 2020) explored the residual subsidence in goaf of steeply inclined extra-thick coal seam and established a residual subsidence dynamic prediction function. Guo Guangli et al. (Guang-li et al. 2002) established a stochastic medium model for predicting the residual subsidence of the surface above the deep long-wall goaf. Guo Qingbiao et al. (Guo et al. 2021) employed the probability integral method to establish a prediction model of surface residual subsidence by analyzing the spatial distribution and shape characteristics of voids. Ximin Cui et al. (Cui et al. 2020) proposed a model for calculating the subsidence coefficient of surface residual deformation and quantified the annual residual subsidence, cumulative residual subsidence and future potential cumulative residual subsidence under given geological mining conditions. Meinan Zheng and Donghui Chen (Chen et al. 2020; Zheng et al. 2018) applied the InSAR technology to study the post-mining subsidence. DENG Ka-zhong et al. (Ka-zhong et al. 2012) built the calculating method of residual deformation coefficient of old goaf areas in shallow long walls under the building load action. The research results of the above-mentioned surface residual subsidence prediction method for the well-working mining surface provide an important reference for the construction of the surface residual subsidence model of UCG.

Based on this, this paper combines the UCG process and the geological and mining conditions of the gasification test area and applies the theoretical analysis method to reveal the mechanism of the surface residual subsidence of UCG. Besides, a calculating model of maximum stripping and yielding zone width of “hyperbolic” coal pillar is established and a surface residual subsidence predicting method of UCG considering the coal pillar stripping and yielding is proposed. The research outcomes have a significant theoretical and practical meaning for the stability evaluation of the UCG sites and the reuse of the land resources after UCG.

Overview of underground coal gasification process

The internationally advanced “Strip mining-regional mining” gasifier backward controlled gas injection underground gasification process is located in Ulanqab, China, and four gasification working faces are separated. As shown in Fig. 1, directional drilling and combustion are used to form the gas outlet and ignition column, and drill holes are drilled in the middle of the coal seam by directional drilling to ignite at the starting point of gasification. Next, the backward control of coal seam gasification is adopted until the first working face is gasified, and the gasification operations of the second, third and fourth gasification working faces are, respectively, completed by the above method. The specific gasification process is as follows:

  1. (1)

    The ignition area was ignited, and it took 60 days to form a gas removal channel with a length of 170m long and a width of 5m.

  2. (2)

    The ignition channel processing took 60 days.

  3. (3)

    UCG was carried out on the first gasification face starting from the ignition channel and ending at the end of the face, which took 90 days and formed a combustion space area with a length of 170m and a width of 16m.

  4. (4)

    After the completion of the first gasification face, the UCG operation of the second gasification face will be conducted. It will take 90 days from the ignition channel to the end of the working face, forming a gasification and combustion space area with a length of 170m in length and a width of 5m.

  5. (5)

    After the second gasification face was completed, the UCG of the third gasification face was performed, starting from the ignition channel and ending at the end of the face, which lasted for 90 days and formed a combustion space area with a length of 170m and a width of 16m.

  6. (6)

    The gasification operation of the fourth gasification working face was carried out, starting from the ignition channel and ending at the end of the face, which took 90 days and formed a combustion space area with a length of 170m and a width of 16m.

  7. (7)

    End the gasification operation and perform furnace shutdown operation.

Fig. 1
figure 1

Schematic diagram of the “Strip mining-regional mining” gasifier backward controlled gas injection underground gasification technology

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Combined with the above-mentioned characteristics of the UCG process, the combustion space area gradually spread from the through holes to the surrounding, forming a “ring runway-like” pattern, while the isolated coal pillar in the middle of the gasifier is “hyperbolic” (Li et al. 2017). The shape of the isolated coal pillar and the gasifier after “Strip mining-regional mining” gasifier backward controlled gas injection underground gasification is shown in Fig. 2.

Fig. 2
figure 2

Morphology of combustion space area after “Strip mining-regional mining” gasifier backward controlled gas injection underground gasification

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Mechanism analysis of surface residual subsidence of UCG

After UCG, surface subsidence occurred and overlying strata were gradually stable after a long time of compaction. However, there still exist phenomena such as insufficient compaction of the falling zone and boundary voids on both sides of the combustion space area. With the decrease of the coal pillar support force and the external additional loads, the overlying rock secondary equilibrium structure will be broken, the combustion space area will awake and surface subsidence will appear. The mechanism of surface residual subsidence after UCG is as follows:

  1. (1)

    When the overlying strata are stable, the unbroken part of the rock formation or the part that does not produce severe deformation, or the part of the stratum that has been broken but can still be neatly arranged, can form arch or beam structure to support the rock above and transfer the overburden pressure to coal pillar on both sides. If the structure is unstable, the overlying strata can move and deform again, and further develop upward to the ground surface, resulting in surface residual subsidence.

  2. (2)

    Under the sustained action of groundwater, efflorescence, and overburden pressure, the inter-grain connection of the coal pillar is destroyed, which reduces the strength of the coal pillar on both sides of the combustion space area. The phenomenon of peeling and yielding appeared on both sides of the "hyperbolic" coal pillar. Thus, the stress area of the coal pillar is continuously fed from both sides to the center, resulting in changes at both ends of the arch or beam, which will increase the movement and deformation of the surface above the combustion space area to a certain extent.

  3. (3)

    The overburden pressure will directly act on the broken rock and gasification residue in the combustion space area. Although the overlying strata trends to be in a stable state, the structural plane of the rock blocks and ash is further compressed and deformed by closure and slippage due to the action of the upper additional load on the upper part. The fractures between the rock blocks, ash, and rock and ash are further compressed. This action is transferred to the surface, causing surface residual subsidence, but the amount of deformation is very limited.

  4. (4)

    Under the support of the arch structure, under-compact areas and residential cavities will appear on both sides of the combustion space area. Under the action of overburden pressure, the under-compact area will be further compressed, and some rock blocks in the under-compact area will be squeezed into the boundary voids. Besides, coal blocks stripped from coal pillars will be scattered into the boundary voids and the overlying strata above the boundary voids will collapse and compact, all of which will cause residual subsidence of surface.

In general, the main reason for the surface residual subsidence of UCG is the stripping and yield softening of the “hyperbolic” coal pillar under the action of the long-term groundwater, efflorescence, overburden pressure, and other factors, as shown in Fig. 3.

Fig. 3
figure 3

Mechanism diagram of surface residual subsidence of UCG

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Calculation method for maximum stripping width and yielding zone width of “Hyperbolic” coal pillar in UCG

Combined with the above-described mechanism of surface residual subsidence of UCG, it can be concluded that the surface residual subsidence is mainly due to the stripping and yielding of coal pillar on both sides of the combustion space area, leading to the increase of the skewback and arch height of the overburden stress balance and causes the surface “secondary” deformation. Therefore, to calculate the surface residual subsidence of UCG, we should calculate the stripping and yielding zone width of the “hyperbolic” coal pillar first. Hence, this section mainly adopts the theoretical analysis method to establish the maximum stripping and yield zone width calculation model of the “hyperbolic” coal pillar of UCG.

Computation approach for maximum stripping width of coal pillar

When the “hyperbolic” coal pillar is subjected to the overburden stress, the stress concentration occurs in the upper curved part of the edge, which is more prone to peeling. On the other hand, the lower bending part is under less pressure and has coal ash to provide lateral pressure, and the degree of peeling is relatively small. The stripped coal block is regarded as a granular medium, and the stripped coal block continuously accumulates in the combustion space area (Yu et al. 2018). Without considering that the pressure on the coal pillar edge decreases gradually from top to bottom, so it is assumed that the coal pillar edge is elliptical after stripping.

The sketch map of the shape of "hyperbolic" coal pillar stripping after UCG is shown in Fig. 4. Assuming that the width of the coal pillar before stripping is T, m; the arch height is a, m; the stripping width at the top of the coal pillar is d, m; the height of the coal pillar is \(m\), m; the ash height is \(h^{\prime}\), m; when the coal pillar stops stripping, the angle between the stacked coal blocks and the horizontal surface is the rest angle, symbolized as θ, (°); the maximum stripping width of the coal pillar is taken as the middle part, defined as b, m. L is the maximum length of coal pillar, m.

Fig. 4
figure 4

Coal pillar stripping model

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It can be seen from Fig. 3 that

$$L = T + 2a.$$
(1)

According to the equivalent mining thickness, the ash formation rate after coal combustion is set as \(k_{p}\). If the ash has been compacted, the real mining height can be written as \(H^{\prime}\):

$$H^{\prime} = m - k_{p} m.$$
(2)

If the coal pillar center is taken as the origin, the horizontal direction is the x-axis, the vertical direction is the y-axis to establish a coordinate system. The boundary of "hyperbola" of the coal pillar must pass through the points \((\frac{L}{2} - a,0)\) and \((\frac{L}{2},\frac{m}{2})\), and the hyperbolic equation can be solved according as

$$\frac{{x^{2} }}{{u^{2} }} - \frac{{y^{2} }}{{v^{2} }} = 1$$
(3)

\({\text{where}}\,u^{2} = \left( {\frac{L}{2} - a} \right)^{2} \,,\,\,v^{2} = \frac{{m^{2} }}{{4\left[ {\frac{{L^{2} }}{{4(\frac{L}{2} - a)^{2} }} - 1} \right]}}.\)

After the coal pillar is peeled off, the boundary ellipse takes the intersection of the original coal pillar edge and the roof plate as the center of the circle. The maximum stripping width and the height of the coal pillar are, respectively, set as the long axis and the short axis, and the equation is

$$\frac{{\left( {x - \frac{L}{2}} \right)^{2} }}{{d^{2} }} + \frac{{\left( {y - \frac{m}{2}} \right)^{2} }}{{m^{2} }} = 1.$$
(4)

Although the lower part of the coal pillar is stripped off by the lateral pressure of ash, expansion capacity is small, and its hulking coefficient is considered to be 1. The volume of stripped coal blocks is

$$V_{p} = k\left( {\frac{\pi md}{4} - V_{s} - V_{t} } \right) + V_{s}$$
(5)
$$V_{p} = \frac{{H^{{\prime}{2}} }}{2\tan \theta } + dh^{\prime} - dm + \frac{\pi md}{4} - V_{r}$$
(6)

where k is the hulking coefficient of the stripped coal blocks:

$$V_{t} = 2\int_{{\frac{L}{2} - a}}^{\frac{L}{2}} {\left( {v\sqrt {\frac{{x^{2} }}{{u^{2} }} - 1} } \right)} dx$$
(7)
$$V_{r} = \int_{{u\sqrt {1 + \left( {\frac{{\frac{m}{2} - h^{\prime}}}{v}} \right)^{2} } }}^{\frac{L}{2}} {\left[ { - \left( {\frac{m}{2} - h^{\prime}} \right) + v\sqrt {\frac{{x^{2} }}{{u^{2} }} - 1} } \right]{\text{d}}x}$$
(8)
$$V_{s} = \int_{{ - d\sqrt {1 - (\frac{{ - m + h^{\prime}}}{m})^{2} } + \frac{L}{2}}}^{\frac{L}{2}} {\left[ - (\frac{m}{2} - h^{\prime}) + m\sqrt {1 - \left(\frac{{x - \frac{L}{2}}}{d}\right)^{2} } + \frac{m}{2}\right]dx} - V_{r}$$
(9)

\(V_{r}\), \(V_{s}\), \(V_{t}\) are the areas of the regions shown in Fig. 5.

Fig. 5
figure 5

Coal pillar calculation partition

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Combining the above equations yields:

$$d = \frac{{V_{s} + V_{r} - k(V_{t} + V_{s} ) - \frac{{(H^{\prime})^{2} }}{2\tan \theta }}}{{h^{\prime} - m + \frac{\pi m}{4} - \frac{k\pi m}{4}}}$$
(10)
$$b = \frac{T}{2} - \left( { - d\sqrt{\frac{3}{4}} + \frac{L}{2}} \right) = \frac{{V_{s} + V_{r} - k(V_{t} + V_{s} ) - \frac{{(H^{\prime})^{2} }}{2\tan \theta }}}{{h^{\prime} - m + \frac{\pi m}{4} - \frac{k\pi m}{4}}}\sqrt{\frac{3}{4}} - a.$$
(11)

Calculation method of yield zone width of coal pillar

Considering the geometric characteristics and forces of the coal pillar without shaft-type UCG, to apply the Coulomb criterion to simplify and derive the yield zone width of the coal pillar from an ideal angle. The calculation model of the yield zone width of the coal pillar is simplified as a plane problem perpendicular to the gasification direction. Meanwhile, the coal pillar is regarded as a uniform, continuous and isotropic ideal elastic–plastic material. The plane is symmetrical, and the mechanical model is shown in Fig. 6.

Fig. 6
figure 6

Coal pillar mechanical model after UCG

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From the Mohr–Coulomb strength criterion, it follows a cut plane, such that:

$$\tau_{zx} = - (C + \sigma_{z} \tan \varphi )$$
(12)

where \(\tau_{zx}\) is the shear stress at the coal seam interface(kpa), pointing in the negative direction of x, C is the cohesive force between the coal seam and the top and bottom plates(kpa), \(\sigma_{z}\) is the vertical stress above the coal pillar (kpa), and \(\varphi\) is the internal friction angle between the coal seam and the top and bottom layers(°).When \(x = x_{0}\), it has:

$$\left[ {\sigma_{z} } \right]_{{x = x{}_{0}}} = K\gamma Z,\,\,\sigma_{x} = A\left[ {\sigma_{z} } \right]_{{x = x_{0} }}$$
(13)

where K is the stress concentration coefficient of the coal pillar, \(\gamma Z\) is the original rock stress (kPa), and A is the lateral pressure coefficient between the elastic zone and the plastic zone.

The contact surface between the coal pillar and the ash is a curved surface, and the contact surface is regarded as a slope to simplify the calculation. The horizontal passive earth pressure on the coal pillar is (Jian et al. 2009)

$$P = - \frac{{\gamma^{\prime}h^{{\prime}{2}} }}{2w}$$
(14)

where \(h^{\prime}\) is the height of ash, and \(\gamma^{\prime}\) is the average gravity density of ash:

$$w = \frac{\tan \delta - \tan \alpha }{{\tan \alpha + \cot \theta^{\prime}}} + \frac{{(\tan \phi - \cot \theta^{\prime})(1 + \tan \delta \tan \alpha )}}{{(\tan \phi + \cot \theta^{\prime})(1 + \tan \delta \tan \alpha )}}$$
(15)

where \(\theta^{\prime}\) is the inclination angle of the most dangerous sliding surface, \(\alpha\) is the angle between coal pillar and vertical plane, \(\delta\) is the coal pillar and ash friction angle, and \(\phi\) is the internal friction angle of ash.

Ignoring the volume force, the basic equation of the mechanical model is

$$\left\{ \begin{gathered} \frac{{\partial \sigma_{z} }}{\partial z} + \frac{{\partial \tau_{xz} }}{\partial x} = 0 \hfill \\ \frac{{\partial \sigma_{x} }}{\partial x} + \frac{{\partial \tau_{xz} }}{\partial z} = 0 \hfill \\ \tau_{zx} = - \left( {C + \sigma_{z} \tan \varphi } \right) \hfill \\ \end{gathered} \right..$$
(16)

Inserting Eq. (12) into Eq. (16), the basic equation of the mechanical model becomes:

$$- \frac{{\partial \sigma_{z} }}{\partial x}\tan \varphi + \frac{{\partial \sigma_{z} }}{\partial z} = 0.$$
(17)

From the mathematical equation, we can set:

$$\sigma_{z} = f(x)g(z) + B_{1} .$$
(18)

Inserting Eq. (18) into Eq. (17):

$$- f^{\prime}(x)g(z)\tan \varphi + f(x)g^{\prime}(z) = 0.$$
(19)

After the simplification, it can attain that:

$$\frac{{f^{\prime}(x)}}{f(x)}\tan \varphi = \frac{{g^{\prime}(z)}}{g(z)}.$$
(20)

There exists a constant B, such that

$$\left\{ \begin{gathered} \frac{{f^{\prime}(x)}}{f(x)}\tan \varphi = B \hfill \\ \frac{{g^{\prime}(z)}}{g(z)} = B \hfill \\ \end{gathered} \right..$$
(21)

Solving for the original function gives

$$\left\{ \begin{gathered} f(x) = B^{\prime}_{1} e^{{\frac{B}{\tan \varphi }x}} \hfill \\ g(z) = B^{\prime}_{2} e^{Bz} \hfill \\ \end{gathered} \right..$$
(22)

Therefore

$$\sigma_{z} = B^{\prime}_{1} B^{\prime}_{2} e^{{\frac{B}{\tan \varphi }x}} e^{Bz} + B_{1}$$
(23)
$$\tau_{xz} = - [(B^{\prime}_{1} B^{\prime}_{2} e^{Bz} e^{{\frac{Bx}{{\tan \varphi }}}} + B_{1} )\tan \varphi + C].$$
(24)

By substituting the parameter \(z = \frac{m}{2}\) into Eq. (24), it can be deduced that:

$$B_{0} = B_{1}^{\prime } B_{2}^{\prime } e^{\frac{Bm}{2}} .$$
(25)

Therefore

$$\left\{ \begin{gathered} \sigma_{z} = B_{0} e^{{\frac{Bx}{{\tan \varphi }}}} + B_{1} \hfill \\ \tau_{xz} = - [(B_{0} e^{{\frac{Bx}{{\tan \varphi }}}} + B_{1} )\tan \varphi + C] \hfill \\ \end{gathered} \right..$$
(26)

Considering the coal pillar to be continuous and in an equilibrium state, according to the equilibrium differential equations, Eq. (27) can be derived:

$$mA[\sigma_{z} ]_{{x = x_{0} }} + 2\int_{0}^{{x_{0} }} {[\tau_{xz} ]} dx - P = 0.$$
(27)

The derivative of the above equation yields:

$$mA\frac{{d[\sigma_{z} ]_{{x = x_{0} }} }}{{dx_{0} }} + 2[\tau_{xz} ]_{{x = x_{0} }} = 0.$$
(28)

Inserting Eq. (12)

$$mA\frac{{d[\sigma_{z} ]_{{x = x_{0} }} }}{{dx_{0} }} - 2\tan \varphi [\sigma_{z} ]_{{x = x_{0} }} - 2C = 0.$$
(29)

The solution is

$$[\sigma_{z} ]_{{x = x_{0} }} = B^{\prime}e^{{\frac{2\tan \varphi }{{mA}}x_{0} }} - \frac{C}{\tan \varphi }.$$
(30)

In the formula

$$\left\{ \begin{gathered} B = \frac{{2\tan^{2} \varphi }}{mA} \hfill \\ B_{1} = - \frac{C}{\tan \varphi } \hfill \\ B_{0} = B^{\prime} \hfill \\ \end{gathered} \right..$$
(31)

Inserting Eq. (31) into Eqs. (26) and (27):

$$\left\{ \begin{gathered} B_{0} e^{{\frac{2\tan \varphi }{{mA}}x_{0} }} - \frac{C}{\tan \varphi } = k\gamma Z \hfill \\ 2\int_{0}^{{x_{0} }} {\tau_{xz} dx} + mAk\gamma Z - P = 0 \hfill \\ \end{gathered} \right..$$
(32)

With the above derivation:

$$\int_{0}^{{x_{0} }} {\tau_{xz} dx = \frac{{B_{0} mA}}{2}\left( {1 - e^{{\frac{2\tan \varphi }{{mA}}x_{0} }} } \right)}$$
(33)
$$\left\{ \begin{gathered} B_{0} e^{{\frac{2\tan \varphi }{{mA}}x_{0} }} - \frac{C}{\tan \varphi } = k\gamma Z \hfill \\ mAB_{0} (1 - e^{{\frac{2\tan \varphi }{{mA}}x_{0} }} ) + Ak\gamma Zm - P = 0 \hfill \\ \end{gathered} \right..$$
(34)

It can be solved that

$$B_{0} = \frac{C}{\tan \varphi } + \frac{P}{mA}.$$
(35)

Inserting Eqs. (35) and (31) into Eq. (30):

$$\sigma_{z} = \left( {\frac{C}{\tan \varphi } + \frac{P}{mA}} \right)e^{{\frac{2\tan \varphi }{{mA}}x_{0} }} - \frac{C}{\tan \varphi } = K\gamma Z.$$
(36)

To sum up, the yield zone width in a balanced stress state is

$$x_{0} = \frac{mA}{{2\tan \varphi }}\ln \left( {\frac{{k\gamma Z + \frac{C}{\tan \varphi }}}{{\frac{C}{\tan \varphi } + \frac{P}{mA}}}} \right).$$
(37)

Application and example

Prediction method for surface residual subsidence of low-carbon gasification coal mining

The steps to predict the surface residual subsidence and deformation extreme value in the mining area of a single short working face are as follows:

  1. (1)

    Employing the probability integral method (PIM) to predict the surface subsidence and deformation values before yielding and stripping of the coal walls on both sides of the combustion space area.

  2. (2)

    Calculation of the sum of maximum stripping and yielding width of the coal pillar based on the proposed model.

  3. (3)

    Using the PIM to predict the surface subsidence and deformation values after yielding and stripping of coal walls.

  4. (4)

    The predicted surface subsidence and deformation values before and after yielding and stripping of the "hyperbolic" coal pillar are compared to obtain the surface residual deformation of UCG, and then the residual deformation prediction of the surface of the gasification site is realized.

Overview of the study area

The UCG area in the Ulanqab Mine is located in the central part of Inner Mongolia Autonomous Region, China, which is owned by Xin’ao Gasification Coal Mining Technology Co. As shown in Fig. 7, the terrain in this area is flat, with the convenient transportation. The area where the working face is located is mostly covered by the Quaternary, and a small amount of Tertiary basalt is exposed in the western part of the mining area. The 2# coal seam is a gasification coal seam, with a depth of 273 ~ 278.5 m, and the average burial depth is 275.75 m. In addition, the thickness of the coal seam is 5 m, the width of the coal pillar is 24 m, and the width of the gasification working face is 16 m. The coal in this seam is mainly lignite, and its ash yield is 12.88 ~ 42.54%, with an average of 27.85%. The percentage of silica in coal ash is the highest, and the general proportion is 2.96 ~ 62.48%, with an average proportion of 49.48%.

Fig. 7
figure 7

Experimental area location

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Application and verification

To calculate the maximum stripping and yield zone width after UCG, the ash generation rate was taken as 0.2785, the stripped coal block hulking coefficient was 1.1, and the rest angle was 45° according to the actual measurement and empirical data. Taking the above data into Eqs. (2) and (11), respectively, it can be calculated that the ash height after gasification is 1.39 m and the maximum stripping width of the coal pillar is 0.91 m.

Table 1 shows the selected coefficients when using the horizontal layer analysis method to solve the ash side pressure.

Table 1 Mechanical parameters between coal pillar and ash
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Substituting into Eq. (14), the lateral pressure of ash is 26.57 kN.

This paper is based on the elastic–plastic limit theory, and the mechanical parameters of coal pillars are shown in the following table.

Substituting into Eq. (37), the maximum yield width of coal pillar is 7.03 m (Table 2).

Table 2 Mechanical parameters of coal pillar
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According to the A. H. Wilson strip coal pillar stability calculation method (Wilson 1983), under the action of the overburden pressure, the edge of the coal pillar undergoes plastic deformation and generates a yield zone. Let the yielding area width be \(Y\)(m), mining depth be \(H\)(m), and mine width be \(w\)(m):

$$Y = 0.0049wH.$$
(38)

Considering the geological mining conditions, the calculated width of the yield zone is 6.76 m.

The calculation method of strip-mining stability has problems caused by simplification, which does not incorporate the side pressure of ash and coal pillar "hyperbolic" characteristics after UCG, so 7.03 m is selected as the width of coal pillar yield zone after UCG is safer and more reliable.

From the most unfavorable conditions, it is considered that the total width of the loss of bearing is the sum of the stripping width and yield zone width of the coal pillars on both sides of the combustion space area, that is: 7.03 + 0.91 = 7.94 m.

From the literatures (Li et al. 2017), PIM is applicable for the surface residual subsidence of UCG. The PIM is developed and established on the basis of the stochastic medium theory, which is the most commonly used method for predicting surface subsidence estimation in the field of mining subsidence. Therefore, this paper also adopts the PIM to calculate the surface subsidence and deformation values of UCG. The predicted parameters of surface subsidence before and after UCG are summarized in Tables 3 and 4.

Table 3 Predicted parameters of surface subsidence before coal pillar stripping and yielding
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Table 4 Predicted parameters of surface subsidence after coal pillar stripping and yielding
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According to the prediction values, the surface residual subsidence contour lines, horizontal residual displacement contour lines, surface tilt contours and surface residual horizontal deformation contours of the UCG experimental area based on the PIM can be drawn. Due to the limited space, only the surface residual subsidence contours of the industrial experiments of UCG are shown in Fig. 8.

Fig. 8
figure 8

Surface subsidence contour lines in the UCG experimental area based on the PIM

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Only one observation points was set up in the industrial experiment of UCG in Ulanqab. Because of the small number of monitoring points, it cannot be used to learn the surface residual subsidence, but it can offer an important real measurement reference for the data comparison for the PIM of surface residual subsidence. This observation point is located in the middle of the second and third gasification working faces, 10 m away from the maximum subsidence point. According to the actual measurement, the measured subsidence value of this point is 36 mm after the UCG is completed. The maximum value of surface subsidence before stripping and yielding is calculated by the PIM to be 39 mm, which is relatively close to the measured value. Considering that the measured point is not the maximum subsidence point, the prediction result is considered reliable, because the measured point is not the maximum sinkage point. The maximum value of surface subsidence after stripping is 74 mm, so the maximum value of surface residual subsidence of the UCG test area is 35 mm.

Conclusion

  1. (1)

    The main reason for the surface residual subsidence of UCG is the stripping and yield softening of the “hyperbolic” coal pillar under the action of long-term groundwater, weathering, overburden pressure, and other factors, resulting in the increase of the arch foot and arch height of the overlying stress balance arch, which in turn causes the “secondary” deformation of the gasification site.

  2. (2)

    Combined with the characteristics of coal pillars and ash accumulation after UCG, the calculation model of the maximum stripping width of “hyperbolic” isolated coal pillars after UCG was established by theoretical analysis method. In addition, an elastic–plastic limit theory was used to derive a model for calculating the maximum yield zone width of the “hyperbolic” coal pillar after UCG, which provides a theoretical basis for the prediction of the surface residual subsidence of the UCG.

  3. (3)

    The method for predicting the residual subsidence on the surface of UCG that considers the stripping and yielding of “hyperbolic” coal pillars is proposed, which solves the problem of predicting the residual deformation on the surface of UCG and is applied to the UCG test area in Ulanqab. It can be concluded that the maximum subsidence value of the surface residual deformation in the gasification test area is 35mm.