Coupling of horizontal joint and topography effects on seismic response of a single face slope

Figures & data

Figure 1. Numerical simulation model setup.

Table 1. Physical and mechanical parameters of rock and joint.

Material Type	Density ρ (kg/m^3)	K (GPa)	G (GPa)	Poisson’s ratio μ	Cohesion c (MPa)	Friction angle φ (°)	kn (MPa/m)	ks (MPa/m)
Rock	2500	27.8	20.8	0.20	/	/	/	/
Joint	/	/	/	/	10	45	Variable	Variable

Figure 2. (a) Time-history acceleration of different ground motions and (b) corresponding Fourier spectrum.

Table 2. Numerical simulation models and the corresponding parameters.

Model No.	Slope height, H (m)	Slope angle, i (°)	Normalized stiffness, K	kn/ks	ξ	Frequency, f (Hz)	Note
1–15	90	45	0.5, 0.6, 0.7, 0.8, 0.9, 1,2, …, 10	1	0.017	5	Effect of K
16–25	90	45	2	1, 2, …, 10	0.017	5	Effect of kn/ks
26–45	90	45	2	2	0.005, 0.006, …, 0.01, 0.02, …, 0.1	5	Effect of spacing
46–50	90	15, 30, 60, 75, 90	2	2	0.017	5	Effect of slope angle
51–56	30, 60, 150, 300, 600, 900	45	2	2	0.017	5	Effect of slope height
57–75	90	45	2	2	0.017	0.32-32	Effect of frequency on Jointed slope
76–94	90	45	2	2	0.017	0.32-32	Effect of frequency on Homogeneous slope
95	/	/	2	2	0.017	5	1D jointed column
96	/	/	/	/	/	5	1D homogeneous column
97	90	45	2	2	0.017	El	Input ground motion of El Centro record
98	90	45	2	2	0.017	WL	Input ground motion of Wolong station record
99	90	45	2	2	0.017	KOBE	Input ground motion of JMA record

Figure 3. Effect of normalized stiffness K on spatial variation of AAF-X of the slope: (a) K=0.5, (b) K=1, (c) K=10, and (d) homogeneous slope.

Figure 4. (a) The AAF-X along the slope surface with different normalized stiffness K and (b) the AAF-X at the slope crest and for different distances behind the slope crest.

Figure 5. Effect of kn/ks on spatial variation of AAF-X of the slope: (a) kn/ks = 1, (b) kn/ks = 6, and (c) kn/ks = 10.

Figure 6. (a) The AAF-X along the slope surface with different kn/ks and (b) the AAF-X at the slope crest and for different distances behind the slope crest.

Figure 7. Effect of normalized joint spacing ξ on spatial variation of AAF-X of the slope: (a) ξ = 0.005, (b) ξ = 0.01, and (c) ξ = 0.1.

Figure 8. (a) The AAF-X along the slope surface with different normalized joint spacing ξ and (b) the AAF-X at the slope crest and for different distances behind the slope crest.

Figure 9. Effect of slope angle i on spatial variation of AAF-X of the slope: (a) i = 15°, (b) i = 30°, (c) i = 45°, (d) i = 60°, (e) i = 75°and (f) i = 90°.

Figure 10. (a) The AAF-X along the slope surface for jointed slope with different slope angle i, (b) the AAF-X along the slope surface for homogeneous slope with different slope angle i, and (c) the AAF-X at the slope crest for jointed and homogeneous slope.

Figure 11. (a) The AAF-X along the slope surface for jointed slope with different slope height H, (b) the AAF-X along the slope surface for homogeneous slope with different slope height H, and (c) the AAF-X at the slope crest with different H/λ by varying the slope height.

Figure 12. Seismogram synthetics of acceleration for different K: (a) K = 0.5, (b) K = 1, (c) K = 3, and (d) K = 10.

Figure 13. Seismogram synthetics of acceleration for different ξ: (a) ξ=0.005, (b) ξ=0.01, (c) ξ=0.02, and (d) ξ=0.1.

Figure 14. The topographic and jointed amplification function: (a) TA_{topo_ho} of the homogeneous model, (b) TA_{topo_jo} of the jointed model, (c) TA_site for 1D and 2D models, and (d) TA_coupled.

Table 3. Recorded PGAs at the free surface of the 1D soil column and 2D slope models.

Slope height, H (m)	Slope angle, i (°)	Recorded PGA (m/s^2)				Atopo_ho	Atopo_jo	Asite_1D	Asite_2D	Acoupled
		a1D_ho	a1D_jo	a2D_ho	a2D_jo
90	15	1.54	1.93	2.03	2.47	1.32	1.28	1.26	1.22	1.61
90	30	1.54	1.93	2.01	3.58	1.31	1.85	1.26	1.78	2.33
90	45	1.54	1.93	2.19	4.01	1.42	2.08	1.26	1.83	2.61
90	60	1.54	1.93	2.20	4.23	1.43	2.19	1.26	1.92	2.75
90	75	1.54	1.93	2.34	4.31	1.52	2.23	1.26	1.84	2.80
90	90	1.54	1.93	2.52	4.21	1.64	2.18	1.26	1.67	2.74

Figure 15. Seismogram synthetics of acceleration for different slope heights. Left (homogeneous slope): (a) H=30m, (b) H=90m, (c) H=300m, and (d) H=900m; Right (jointed slope): (e) H=30m, (f) H=90m, (g) H=300m, and (h) H=900m.

Figure 16. Top (AAF-X along the slope surface): (a) homogeneous slope and (b) jointed slope with different H/λ; bottom (AAF-X at slope crest and behind the slope crest): (c) homogeneous slope and (d) jointed slope.

Figure 17. Seismogram synthetics of acceleration along slope surface. Left (homogeneous slope): (a) H/λ = 0.03, (b) H/λ = 0.22, and (c) H/λ = 0.6; right (jointed slope): (d) H/λ = 0.03, (e) H/λ = 0.22, and (f) H/λ = 0.6.

Data availability statement

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.