Structural Feature and Evolution Mechanism of Arch Structure for Thick Unconsolidated Layer

: Traditionally, the study on the bearing structure of overlying strata mainly focuses on bedrock with the effect of the overlying unconsolidated layer. It simply considered as uniformly loading on the top interface of the bedrock, and ignores the bearing structure for unconsolidated layer. Combined with the geological conditions of shallow burial thick unconsolidated layer in Shendong mining area ， the mechanical model of the arch structure for the unconsolidated layers was established. The relationship between the arch height and span was analyzed with theoretical formula and the dynamic evolution mechanism of arch structure was studied with numerical simulation. Besides, formula of arch structure ultimate height was derived. The influence mechanism of arch structure on ground fissures was revealed and criterion was obtained, which was verified by field monitoring data. Furthermore, a classification method of arch structure in thick unconsolidated layers was proposed.

the dynamic evolution mechanism of arch bearing structure in the process of coal mining is studied, and the mining-induced unconsolidated layer structure is classified according to the unconsolidated layer thickness, the research results are verified by the measured data, which has a certain guiding significance for the research on the development law of mining overburden and the development mechanism of ground fissures under the condition of thick alluvium.

The arch structure for thick unconsolidated layer for shallow burial coal seam
After shallow burial coal seam working face was mined, mining-induced overburden structure is broken and then gradually develops upward to the unconsolidated layer. The internal medium of unconsolidated layer deformation occurs, uneven displacement occurs between particles, the transfer effect of the force between the lower and the overlying unconsolidated layer disappeared and separated, and the main axial compressive stress was formed in the particles of the overlying unconsolidated layer. The bearing structure which can not only transfer the load between the particles in different areas of the unconsolidated layer, but also play the bearing role on the mining-induced overburden and protect the working face, is described as unconsolidated layer arch structure. The arch structure of unconsolidated layer is mainly composed of the arch body and the support at the arch base. The arch body of the unconsolidated layer arch structure mainly bears axial compressive stress, while the supporting force at the arch base can bears vertical compressive stress, horizontal thrust and bending moment simultaneously. The bearing structure of the overlying strata is shown in Fig.1. The bearing structure in the bedrock is the structure of key layer, the bearing structure in the unconsolidated layer is the unconsolidated layer arch structure. The bearing structure of unconsolidated layer arch is simplified appropriately and the mechanical model is established (Liu,2011); (1) The thickness of the unconsolidated layer arch is consistent from the arch top to the arch base, the reasonable arch axis of the unconsolidated layer arch is studied by analyzing the middle surface curve; (2) The unconsolidated layer arch structure is simplified as three hinged arch, in other words, the reasonable arch axis of the three hinged arch is taken as the reasonable arch axis of the unconsolidated layer arch structure; (3) The unconsolidated layer arch is filled with the soil, it is under the weight loading of filled soil; (4) Given the shallow burial coal seam, assuming that the horizontal stress is zero.
x The rectangular coordinate system is established with the top point of the arch as the origin, as shown in Fig.2. The distance from the arch top to the surface is the overburden thickness H, arch height is denoted by H, arch span is denoted by L, and the unconsolidated layer arch is subject to soil filling load, Where γ is the bulk density of the unconsolidated layer [N/m 3 ].

Arch structure characteristic equation of unconsolidated layer
The equation of reasonable arch axis for three hinged arch is generally expressed as： where M 0 (x) is the bending moment of simply supported beam under filling load [KN·m], Fh is the reaction force of the horizontal support [KN].
Take the second derivative of both sides of equation (1) The equilibrium differential equation of straight bar segment is approximately applied In Equation (3), it is specified that the Y-axis upward is positive： The general solution of the differential equation can be expressed by hyperbolic function; According to boundary conditions： Therefore, the reasonable arch axis equation can be written as That is, under the action of filled weight loading, the reasonable axis of the three hinged arch is a catenary.

Mechanical model of unconsolidated layer arch structure
,then the reaction of the horizontal support is : According to the moment balance equation of hinge Point C   0 Substituting equation (8) and equation (9) into equation (10) and simplified: According to the Taylor expansion of the hyperbolic function (11) Formula (12) to calculate the value of m, Substituting it to Formula (11) to calculate the ε* of the relative error limit ε*, The expression is The change of relative error ε* with parameters H and H is shown in Fig.4 and Fig.5.
(1)The relative error ε* increases with the increase of arch height H and decreases with the increase of overburden thickness H； (2)When h and H vary within a certain range, The relative error ε*<<1,equation (12) is right.  (9), it can be simplified as:

Analysis of arch structure stability of unconsolidated layer
According to the research results of K. Terzaghi (Terzaghi,1960) for the unconsolidated layer arch，the condition of the arch structure stability for the unconsolidated layer is: Where φ is the internal friction angle of the unconsolidated layer,[°]; C is the cohesion of the unconsolidated layer,[Pa]。 Substituting equation (13) and (14) into equation (15), the arch height h of the unconsolidated layer under the ultimate state can be obtained as:

The formation condition and limit height
(1) The formation condition of unconsolidated layer arch structure According to the Mohr-Coulomb strength criterion, the maximum and minimum principal stress of the arch foundation should be satisfied in order to form the arch with stable bearing capacity: Where σ1 is the maximum principal stress, σ3 is the minimum principal stress. Through theoretical analysis, the maximum and minimum ultimate principal stress at the arch foundation of the unconsolidated layer is obtained: Where σ1f is the maximum ultimate principal stress at the arch foundation of the unconsolidated layer, σ3f is the minimum ultimate principal stress at the arch foundation of the unconsolidated layer, δ is the thickness of the unconsolidated layer.
Substituting equation (19) into equation (18), the arch thickness of the unconsolidated layer is obtained As shown in Fig.1,when the sum of unconsolidated layer thickness ∑H is greater than the sum of unconsolidated layer arch height H and one half of arch thickness δ/2, the unconsolidated layer is arched. Otherwise, no "arch" structure will be formed in the unconsolidated layer: (2) Limit height of unconsolidated arch structure ① Minimum arch height of unconsolidated layer arch The span when the working face appears first weighting is defined as l 初 . Uneven subsidence of unconsolidated layer is happened. The bearing structure of unconsolidated layer arch is formed for the first time， The minimum arch height of the unconsolidated layer arch is Where l 初 is the arch span of unconsolidated layer when the working face appears first weighting, ② Ultimate arch height of unconsolidated layer With the advance of the working surface and the periodic fracture of the key strata, the arch bearing structure of the unconsolidated layer collapsed and developed upward. When the advanced distance is greater than the working face length, according to the plane strain theory (Xu, 2016), the unconsolidated arch structure will no longer develop upward. As shown in Fig.8     Taking ShendongHaragou coal mine as research background, the dynamic evolution law of unconsolidated layerarch was analyzed by using UDEC numerical software. The corresponding length and height of numerical model is 100m×60 m， as shown in Fig.9. Physical and mechanical parameters of rock layer are shown in Table 1.

Result and analysis
(1) After coal seam is mined, the immediate roof collapsed primarily. Then the main roof is separated, broken and collapsed. In the process of rock strata movement, uneven displacement occurs between the unconsolidated layers and then forms the "arch shell" structure. It carries the upper loading, while the lower sand layer has broken down. (2) As the working face advances, the first periodic weighting of the main roof occurs, the bedrock block rotates to form the stepped voussoir beam structure. After the arch foot of the unconsolidated layer collapsed, the separated zone for arch-shaped is filled with the gob. The unconsolidated layer arches upward based on the fracture location of the key layer, and then forms a new "arch shell" structure. This arch structure of unconsolidated layer appears repeatedly until the failure height of overburden reaches the maximum value. (3) With the advance of working face, the unconsolidated layer arch continues to develop upward. When the thickness of the unconsolidated layer is less than the sum of the theoretical arch height and half of arch thickness for the unconsolidated layer, namely ∑H<(h+δ/2), the unconsolidated layer arch cannot be formed. But if the strength of surface sandy soil layer is low, when the unconsolidated layer arch develops to a certain height, the upper part of the overlying unconsolidated layer is "beam" while the lower part is "arch", as shown in Fig. 12 (a) and Fig. 12 (b). After the arch beam has fractured, "funnel-shaped" subsidence occurs in the unconsolidated layer, as shown in Fig. 12 (c). Non-uniform subsidence and movement lead to ground fissures appearing at outside of the gob boundary, as shown in Fig. 12 (d). According to the thickness of the unconsolidated layer for shallow burial coal seam, the structure of unconsolidated layer is classified: (1) The type of loading: When 2 δ h H    min , the arch structure of the unconsolidated layer cannot be formed, the unconsolidated layer acts as the loader on the key strata. hmin is the arch height of the arch structure for unconsolidated layer when the working face has first initial weighting.
(2) The type of arch-beam broken: When ℎ + 2 ≤ ∑ < ℎ , the arch structure of unconsolidated layer can be formed. And with the advance of the working face, it develops upward. When ℎ + 2 ≥ ∑ , the bearing structure is no longer formed. And when the unconsolidated layer develops to a certain height, the upper part of the overlying unconsolidated layer is "beam", and the lower part is "arch".
(3) The type of ultimate arched: When ∑ > ℎ , after the arch structure of the unconsolidated layer is formed and reaches the maximum height, it will not develop upward, the structure of unconsolidated layer extends forward in the way of "tunnel".

Prediction and analysis of ground fissures
Before the formation of ground fissures, the "arch beam" is in the state of self-stable. The stress analysis of the right side for the arch structure is shown in Fig.13. The top position of arch is point B, the foot of arch is point C, ρ is the density of sandy soil, g is the gravitational acceleration. The equation of the catenary arch is ( ) = − ℎ √ ，the distance between the arch top and ground surface is H. The stress distribution inside the beam [11] is: The maximum normal stress σmax in the beam is: It can be seen from Table 2 and Fig.15，when the second periodic weighting occurs in Halagou Coal Mine 22207 working face, the unconsolidated layer presents the failure type of "arch-beam". Then the ground fissure appears. The advanced distance of 22207 working face is 58 m at the moment. See Fig.16, Through geology investigation of the ground surface for 22207 working face, it is found that a series of collapsed fissures have formed, which is consistent with the theoretical analysis.

Conclusion
(1) The mechanical model of the arch structure for thick unconsolidated layer under the condition of shallow burial coal seam is established. As the span of arch structure increases, the height of arch structure increases nonlinearly. The greater the thickness of the unconsolidated layer, the greater the ultimate arch height and the ultimate arch span.
(2) The dynamic evolution mechanism of the arch structure for the unconsolidated layer is revealed. During the mining process, the structure of unconsolidated layer develops in the shape of "arch" from the bottom to the top. The "arch-beam" failure type is formed with "beam" at the top and "arch" at the bottom. The formulas for calculating the minimum height and ultimate height of the arch structure are obtained.
(3) The influence mechanism of arch structure on ground fissures is revealed, and the calculation formula of working face advanced distance when ground fissure appears for the first time is obtained: (4) According to different thickness of the unconsolidated layer, the arch structure of the unconsolidated layer is divided into three types:①The type of loading: the bearing structure fails to form, and the unconsolidated layer acts on the bedrock as the load;②The type of arch-beam broken: the bearing structure is formed inside the unconsolidated layer, it finally failure as the type of "arch-beam" with the advance of the working face;③The type of ultimate arched: the arch structure is formed inside the unconsolidated layer, and the arch height will not change when it reaches the ultimate value.

Data availablity statement
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.