This paper presents a dynamic modeling method to test and examine the minimum mass of pressurized pore-gas for triggering landslides in stable gentle soil slopes.A stable gentle soil slope model is constructed with a dry cement powder core,a saturated clay middle layer,and a dry sand upper layer.The test injects H_(2)O_(2)solution into the cement core to produce new pore-gas.The model test includes three identical H_(2)O_(2)injections.The small mass of generated oxygen gas(0.07%of slope soil mass and landslide body)from the first injection can build sufficient pore-gas pressure to cause soil upheaval and slide.Meanwhile,despite the first injection causing leak paths in the clay layer,the generated small mass of gas from the second and third injections can further trigger the landslide.A dynamic theoretical analysis of the slope failure is carried out and the required minimum pore-gas pressure for the landslide is calculated.The mass and pressure of generated gas in the model test are also estimated based on the calibration test for oxygen generation from H_(2)O_(2)solution in cement powder.The results indicate that the minimum mass of the generated gas for triggering the landslide is 2 ppm to 0.07%of the landslide body.Furthermore,the small mass of gas can provide sufficient pressure to cause soil upheaval and soil sliding in dynamic analysis.
Let A=kQ/I be a finite-dimensional basic algebra over an algebraically closed field k,which is a gentle algebra with the marked ribbon surface(SA,MA,ΓA).It is known that SAcan be divided into some elementary polygons{Δi|1≤i≤d}byΓA,which has exactly one side in the boundary of SA.Let■(Δi)be the number of sides ofΔibelonging toΓAif the unmarked boundary component of SAis not a side ofΔi;otherwise,■(Δi)=∞,and let f-Δbe the set of all the non-co-elementary polygons and FA(resp.f-FA)be the set of all the forbidden threads(resp.of finite length).Then we have(1)the global dimension of A is max1≤i≤d■(Δi)-1=maxΠ∈FAl(Π),where l(Π)is the length ofΠ;(2)the left and right self-injective dimensions of A are 0,if Q is either a point or an oriented cycle with full relations.masΔi∈f-Δ{1,■(Δi)-1}=max n∈f-F_(A)l(П),otherwise,As a consequence,we get that the finiteness of the global dimension of gentle algebras is invariant under AvellaGeiss(AG)-equivalence.In addition,we get that the number of indecomposable non-projective Gorenstein projective modules over gentle algebras is also invariant under AG-equivalence.
