Apr 25, 2011 - 1) were all located within soils formed on the Tyee Formation, with the exception of. CC which is located in the Elkton Formation (Baldwin 1961) ...
Effects of soil-engineering properties on the failure mode of shallow landslides
Jonathan Peter McKenna, Paul Michael Santi, Xavier Amblard & Jacquelyn Negri
Landslides Journal of the International Consortium on Landslides ISSN 1612-510X Landslides DOI 10.1007/s10346-011-0295-3
1 23
Your article is protected by copyright and all rights are held exclusively by SpringerVerlag (outside the USA). This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your work, please use the accepted author’s version for posting to your own website or your institution’s repository. You may further deposit the accepted author’s version on a funder’s repository at a funder’s request, provided it is not made publicly available until 12 months after publication.
1 23
Author's personal copy Original Paper Landslides DOI 10.1007/s10346-011-0295-3 Received: 25 April 2011 Accepted: 24 August 2011 © Springer-Verlag (outside the USA) 2011
Jonathan Peter McKenna I Paul Michael Santi I Xavier Amblard I Jacquelyn Negri
Effects of soil-engineering properties on the failure mode of shallow landslides
Abstract Some landslides mobilize into flows, while others slide and deposit material immediately down slope. An index based on initial dry density and fine-grained content of soil predicted failure mode of 96 landslide initiation sites in Oregon and Colorado with 79% accuracy. These material properties can be used to identify potential sources for debris flows and for slides. Field data suggest that loose soils can evolve from dense soils that dilate upon shearing. The method presented herein to predict failure mode is most applicable for shallow (depth 8), with few to moderate fines (fine-grained content 0.05), we used a t test that assumes equal variance; when variances were unequal (p value ≤0.05), a t test assuming unequal variance was applied. Probability values (p values) indicate the probability that the two sample population mean values being compared would be truly different from a single large population. For example, a p value of 0.05 indicates that there is a 95% chance that the mean values of the two populations are different. Linear discriminant analysis (LDA) is a statistical method used to define a linear combination of variables which separate two or more dependent variables. LDA was used to identify the principal variables that could be used individually or combined to classify a landslide initiation site as a slide or a flow. For each initiation site, the discriminate function score was computed by simple matrix multiplication. The two Landslides
Type
Open
Hollow
Open
Open
Open
Open
Hollow
Hollow
Hollow
Hollow
Bank failure
Hollow
Hollow
Hollow
Hollow
Hollow
Hollow
Open
Hollow
Hollow
Hollow
Hollow
Hollow
Hollow
Open
Hollow
Hollow
Hollow
Open
Open
Hollow
Hollow
Open
Hollow
Hollow
Sample
BC-1
BC-2
Landslides
CC-1
CC-2
CC-3
CC-4
CHC-1
CHC-10
CHC-11
CHC-12
CHC-13
CHC-14
CHC-15
CHC-16
CHC-17
CHC-18
CHC-19
CHC-2
CHC-20
CHC-21
CHC-22
CHC-23
CHC-24
CHC-25
CHC-3
CHC-4
CHC-5
CHC-6
CHC-7
CHC-8
CHC-9
CHC- LS1
CHC- LS2
CHC- LS3
CHC- LS4
1.24
1.56
1.44
1.65
1.08
1.22
1.29
1.25
1.17
1.10
1.34
1.08
0.95
0.95
0.93
1.11
0.77
1.28
1.24
1.16
1.14
1.17
0.94
1.09
0.99
1.12
1.14
0.99
1.18
1.37
1.42
1.37
1.30
-
1.44
Dry Den., ρd (g/cm3)
31
28
29
28
35
37
40
33
40
29
29
35
44
45
35
35
90
28
43
27
30
34
34
34
49
41
42
50
41
41
38
36
42
34
35
LL
29
26
27
25
39
36
40
32
40
30
28
31
38
40
35
30
NP
25
36
25
28
32
28
31
46
43
44
46
32
29
26
24
27
25
24
PL
1.21
0.43
0.80
0.81
1.16
1.11
0.96
1.15
0.37
1.09
0.10
0.98
0.72
1.96
0.15
0.88
0.41
0.77
2.04
1.79
1.55
1.72
1.49
1.19
0.82
1.38
1.89
1.05
0.56
2.00
0.30
0.30
0.60
0.15
0.74
Depth (m)
Partial
Slide
Slide
Slide
Flow
Slide
Flow
Flow
Slide
Partial
Partial
Flow
Flow
Flow
Flow
Flow
Flow
Partial
Flow
Flow
Flow
Flow
Flow
Flow
Flow
Flow
Flow
Flow
Flow
Slide
Slide
Partial
Partial
Flow
Slide
Failure Mode
0.47 0.48 0.55 0.62 0.57 0.58 0.63 0.59 0.64 0.56 0.57 0.56 0.53 0.52 0.71 0.58 0.65 0.64 0.64 0.59 0.49 0.58 0.56 0.53 0.51 0.54 0.59 0.38 0.46 0.41 0.53
4.03E-04 – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
0.48
0.51
-
0.46
Porosity, n (cm3/cm3)
–
7.20E-04
1.47E-04
-
1.42E-03
Hyd. Cond, ksat (cm/s)
Table 4 Full dataset of geomorphic, soil, and landslide characteristics measured at landslide source sites
40
43
46
40
43
46
46
41
43
46
44
49
48
43
39
46
43
42
47
48
50
49
47
44
50
40
41
43
45
–
38
43
-
55
36
Slope (°)
43.8
81.4
47.3
49.4
60.4
34.3
67.2
34.8
54.4
59.2
69.5
52.9
34.6
67.5
59.4
67.3
75.7
69.3
78.8
77.9
49.4
58.2
52.1
46.2
45.8
72.6
72.1
76.0
42.6
46.8
33.3
41.4
22.4
32.3
46.3
Gravel (%)
43.6
18.4
48.6
40.5
30.4
54.1
27.1
64.8
39.0
28.0
30.1
41.3
58.9
27.0
31.0
23.9
20.9
30.3
16.5
15.7
37.1
28.7
40.4
41.1
47.8
21.6
20.9
19.9
45.7
46.6
64.2
51.6
66.1
62.6
52.7
Sand (%)
9.0
0.2
3.0
7.2
6.6
8.9
4.5
–
3.4
9.0
–
3.9
4.3
4.4
7.4
6.2
2.8
-
3.5
4.0
9.9
10.6
5.4
10.0
4.8
4.2
5.6
3.1
7.8
4.7
1.7
4.7
7.3
4.2
-
Silt (%)
3.7
0.0
1.0
2.9
2.7
2.6
1.2
–
3.2
3.8
–
1.9
2.2
1.1
2.3
2.6
0.6
-
1.3
2.3
3.5
2.5
2.1
2.8
1.5
1.6
1.5
1.0
3.9
1.9
0.8
2.3
4.1
0.9
-
Clay (%)
12.7
0.2
4.0
10.1
9.2
11.6
5.7
0.4
6.6
12.8
0.4
5.8
6.5
5.5
9.6
8.8
3.4
0.4
4.8
6.3
13.4
13.1
7.5
12.7
6.3
5.8
7.1
4.1
11.7
6.7
2.6
7.0
11.4
5.1
1.0
Fines, f (%)
90.0
193.3
76.5
93.3
100.0
21.7
200.0
10.0
109.3
158.3
94.4
32.5
13.3
85.7
144.7
141.2
73.3
111.5
133.3
240.0
83.3
136.8
40.0
93.6
20.8
807.7
163.6
44.4
46.7
26.0
13.2
22.1
16.7
7.5
17.4
Coef. Unifor. Cu
115
24
30
204
63
27
53
372
24
32
4
45
18
13
1
11
14
65
256
249
351
218
30
417
30
181
569
77
8
3374
8
2
13
4
53
Volume (m3)
SM
GP
SP
SP-SM
GP-GM
SP-SM
GP-GM
SP
GP-GM
GM
GP
GP-GM
SP-SM
GP-GM
GP-GM
GP-GM
GP
GP
GP
GP-GM
SM
GM
GP-GM
SM
SP-SM
GP-GM
GP-GM
GP
SP-SM
SP-SM
SP
SW-SC-SM
SP-SM-SC
SP-SC
SP
USCS Class
Author's personal copy
Original Paper
Type
Open
Hollow
Hollow
Hollow
Hollow
Hollow
Hollow
Hollow
Hollow
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Hollow
Hollow
Hollow
Open
Open
Hollow
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Hollow
Sample
FR-DATA
FR-DF-1
FR-DF-2
FR-DF-3
FR-DF-4
FR-DF-5
FR-DF-6
FR-DF-7
FR-LS-1
FR-LS-2
FR-LS-3
FR-LS-4
FR-LS-5
FR-LS-6
FR-LS-7
FR-LS-8
FR-LS-9
FR-LS-10
FP-1
FP-2
FP-3
FP-4
FP-5
IV-1
IV-10
IV-11
IV-2
IV-3
IV-4
IV-5
IV-6
IV-7
IV-9
IVB-1
IVB-2
IVB-3
IVB-20
IVB-5
Table 4 (continued)
1.17
1.35
1.36
1.07
1.08
1.28
1.38
1.33
1.25
1.19
1.26
1.11
1.07
1.20
1.23
1.29
1.20
1.47
1.21
1.17
1.58
1.80
1.48
1.68
1.33
1.59
1.61
1.87
1.37
1.56
1.52
1.38
1.08
1.56
1.28
1.58
1.40
1.64
Dry Den., ρd (g/cm3)
27
26
-
29
35
27
27
47
31
28
28
29
27
27
35
33
29
32
25
31
24
18
25
24
23
21
30
26
22
37
31
24
22
25
27
22
38
21
LL
23
22
-
23
26
22
23
34
24
25
23
23
22
22
25
-
25
22
25
26
18
16
23
20
18
13
18
13
14
18
18
NP
19
17
20
17
19
19
PL
0.56
0.91
0.30
0.64
0.35
0.44
0.35
0.37
0.60
0.26
0.80
0.33
1.20
0.51
0.53
0.65
0.66
4.70
0.59
0.66
0.45
0.37
0.70
0.40
0.50
0.66
0.88
0.70
0.82
1.07
0.60
0.46
0.34
0.76
0.82
0.76
1.00
0.45
Depth (m)
Flow
Flow
Slide
Flow
Slide
Flow
Partial
Flow
Flow
Flow
Flow
Slide
Flow
Flow
Flow
Flow
Flow
Slide
Slide
Slide
Slide
Slide
Slide
Slide
Slide
Slide
Slide
Slide
Slide
Slide
Flow
Flow
Flow
Flow
Flow
Flow
Flow
Flow
Failure Mode
0.47 0.40 0.52 0.41 0.59 0.48 0.42 0.41 0.48 0.30 0.39 0.40 0.50 0.37 0.44 0.32 0.40 0.56 0.54 0.44 0.55 0.51
– – – – – – – – – – – – – – – – – – – – – –
0.56
0.49
– 4.09E-04
0.59 0.49
1.35E-04
0.59
0.52
0.48
0.50
0.53
0.55
0.52
0.58
0.59
0.55
–
9.16E-04
2.35E-04
1.66E-03
1.66E-03
9.42E-04
1.90E-04
2.46E-03
1.29E-02
8.16E-05
-
0.54
0.38
–
8.79E-04
Porosity, n (cm3/cm3)
Hyd. Cond, ksat (cm/s)
41
–
–
39
35
40
-
33
38
39
44
37
40
36
37
29
39
41
23
20
26
27
28
25
29
26
27
29
38
32
24
25
25
31
37
32
42
26
Slope (°)
5.5
19.2
–
4.7
4.0
17.1
56.8
49.4
11.8
5.2
20.6
4.7
48.0
30.3
36.5
16.7
1.9
0.0
1.0
1.7
13.6
44.9
44.8
14.9
64.0
30.5
24.1
63.3
28.3
16.4
49.5
21.5
17.6
12.2
62.1
24.6
50.7
58.0
Gravel (%)
91.5
62.8
–
91.7
92.1
70.0
38.5
39.5
78.0
77.0
68.3
85.6
46.0
59.2
53.9
11.7
11.4
1.6
11.5
12.5
71.4
54.1
34.9
84.8
30.5
57.2
62.2
20.1
64.0
17.6
38.7
45.6
48.4
56.4
28.0
53.0
30.6
22.7
Sand (%)
2.1
10.9
0.8
7.1
–
–
– –
0.7
5.2
1.3
3.1
3.1
5.0
3.7
3.1
1.7
3.0
18.0
–
3.6
4.0
12.9
4.7
11.0
10.3
17.8
11.1
9.7
6.0
10.5
9.6
– 4.9
71.7
86.7
98.4
87.5
85.7
14.9
1.0
20.3
0.3
5.5
12.3
13.7
10.5
7.7
66.0
11.8
33.0
34.1
31.4
9.9
22.4
18.8
19.3
Fines, f (%)
17.9
19.9
28.0
14.7
15.0
6.5
0.0
2.5
0.0
1.8
4.3
5.9
2.6
2.5
33.2
6.3
6.0
10.1
9.0
4.0
6.9
9.8
3.6
Clay (%)
3.2
7.7
3.4
7.9
7.1
12.8
7.5
6.5
4.3
5.6
9.6
53.7
66.7
70.4
72.8
70.7
8.4
1.0
17.8
0.3
3.7
8.0
7.9
14.1
5.2
32.8
5.5
27.0
23.9
22.4
5.9
15.5
8.9
15.7
Silt (%)
4.3
50.0
–
2.8
4.0
11.8
35.7
1025.0
4.3
10.6
6.1
6.7
38.2
23.3
20.0
70.0
45.0
377.8
23.0
2.8
12.5
36.5
616.7
2.7
944.4
7.6
19.6
160.0
4.7
680.0
400.0
21.3
28.3
33.3
800.0
30.0
5814.0
116.7
Coef. Unifor. Cu
51
92
4
43
11
30
13
17
19
4
20
10
329
137
82
467
131
1444
49
92
485
781
521
889
5770
1191
5926
9067
764
400
210
66
190
320
137
256
596
24
Volume (m3)
SP
SW
SP
SP
SP
SM
GP
SP-SM
SP-SM
SW-SM
SP-SM
SP-SM
SP-SM
SP-SM-SC
SW-SM
ML-OL
ML-OL
CL
ML-OL
ML-OL
SW
SP
SM
SP
GP-GM-GC
SW-SC
SW-SC
GP-GC
SP-SC
CL
SP-SC
SP
SW
SP
GP-GM
SP
GP
GP
USCS Class
Author's personal copy
Landslides
Landslides
Open
Open
Open
Hollow
Open
Open
Open
Open
Hollow
Hollow
Open
Open
Open
Open
Open
Open
Open
Hollow
Open
Hollow
Open
Open
Open
MR-1
MR-2
MR-3
MR-4
MR-5
MR-6
PH-2
PH-3
PH-4
SC-1
SC-2
SC-3
SC-4
SC-5
SC-6
SC-8
SC-9
TM-1
TM-2
TM-3
TM-4
TM-5
TM-6
1.17
1.28
1.07
1.34
1.15
1.06
1.16
1.11
1.29
1.48
1.48
1.46
1.45
0.95
1.32
1.11
1.07
1.39
1.57
1.22
1.43
1.34
1.32
Dry Den., ρd (g/cm3)
35
34
32
27
27
34
37
39
28
25
31
33
31
34
34
52
39
24
20
28
34
29
29
LL
30
37
38
20
NP
22
32
32
29
NP
26
25
26
NP
12
33
27
18
17
23
26
21
22
PL
0.55
1.10
0.65
0.60
0.31
0.40
0.59
0.37
0.47
0.53
0.48
0.59
1.33
0.53
1.68
0.98
0.75
0.35
0.76
0.37
0.40
0.35
0.57
Depth (m)
Slide
Slide
Slide
Flow
Flow
Flow
Slide
Flow
Slide
Slide
Slide
Slide
Slide
Flow
Flow
Slide
Slide
Slide
Slide
Flow
Flow
Flow
Slide
Failure Mode
0.47 0.59 0.58 0.50
– – – –
0.56 0.50 0.60 0.52 0.56
1.26E-02 – – –
0.60
0.56
0.58
0.51
0.44
0.44
0.45
0.45
–
4.93E-03
1.26E-02
3.59E-04
8.08E-04
2.18E-03
1.22E-02
1.12E-02
2.36E-03
0.64
0.41
–
4.03E-04
0.54
0.46
0.49
0.50
Porosity, n (cm3/cm3)
3.40E-04
4.93E-04
1.26E-04
9.55E-04
Hyd. Cond, ksat (cm/s)
34
36
36
38
29
39
43
41
41
39
39
38
40
46
32
33
42
–
–
35
40
44
39
Slope (°)
98.8
58.2
59.5
72.3
29.8
50.1
59.6
47.9
24.3
75.5
49.7
63.7
66.0
60.4
28.5
73.5
13.5
14.4
28.2
33.2
57.9
10.6
7.9
Gravel (%)
0.8
35.6
40.2
27.5
53.3
49.4
39.5
43.9
73.0
19.9
48.8
31.5
29.7
34.9
58.2
23.7
71.5
67.7
62.0
66.2
41.1
89.1
88.0
Sand (%)
–
4.8
–
–
1.3
–
0.0
–
– 0.2
0.0
0.2
0.7
0.8
0.5
0.8
7.4
2.0
0.5
–
– 4.1
0.6
0.6
0.8
6.1
1.2
5.9
5.8
4.1
0.0
0.2
4.2
3.7
3.9
7.2
1.7
9.1
12.1
5.7
0.6
0.8
0.7 –
3.4
Clay (%)
–
Silt (%)
0.3
6.2
0.3
0.2
16.9
0.5
0.9
8.2
2.7
4.7
1.5
4.8
4.3
4.7
13.3
2.9
15.0
18.0
9.8
0.6
1.0
0.3
4.1
Fines, f (%)
11.2
230.0
114.3
73.2
24.3
34.0
2.8
37.8
8.8
166.7
18.8
150.0
107.1
116.7
28.8
105.9
20.5
27.5
9.0
3.9
25.0
3.7
3.7
Coef. Unifor. Cu
10
21
36
87
–
76
61
33
25
66
98
76
69
110
4344
690
893
14
32
21
35
21
31
Volume (m3)
GP
GP-GM
GP
GP
SM
GP
GP
SP-SM
SP
GP
SP
GP
GP
GP
SC
SP
SM
SC
SP-SC
SP
GP
SP
SP
USCS Class
BC Big Creek, CC Camp Creek, CHC Charlotte Creek, FP Forest Park, FR Florida River, IV Island View, IVB Island View B, MR Maupin Road, PH Powder House, SC Sulphur Creek, TM Tyee Mountain, USCS Unified Soil Classification System, LL is liquid limit, PL is plastic limit
The first two letters indicated the study site where the sample was collected and are shown in Fig. 1
Type
Sample
Table 4 (continued)
Author's personal copy
Original Paper
Author's personal copy
SLIDE FLOW
Fig. 3 Example of an open-slope slide (center of picture) that failed just above an open-slope flow in the IVB study site (see Fig. 1 for location)
scores were then compared, and the sample was assigned to the group (slide or flow) with the highest score. The variables tested using this method included: coefficient of curvature (Cc), coefficient of uniformity (Cu), various grain-size distribution parameters (D10, D30, D50, D60, and gravel, sand, silt, clay, and fine-grained percentage [f]), ρd, ksat, slope (°), and 2 D Atterberg limits (LL, PL, PI). The variable, Cc Cc ¼ D10 30D60 , is a measure of the shape of the grain-size distribution curve and the variable, Cu Cu ¼ DD1060 , is an indicator of the range of particles for a given soil. The grain-size distribution parameter (D) refers to the apparent grain-size diameter (mm) and the subscripts
(10, 30, 50, 60) refer to the percent of the soil mass that is finer than that diameter. The variable f consists of the percentage of the total dry soil mass passing the #200 sieve (silt+clay). The soil testing program was designed to test the hypothesis that material properties can be used to explain why some landslides mobilized into flows (flows) while others did not mobilize into flows (slides). The failure mode of landslides that initiate in hollows may be affected by hydrologic conditions and morphological influences such as angle of entry of failure to the channel, channel gradient, and volume of in-channel stored sediment. Landslides that initiate on open slopes are not affected by these factors. Therefore, to reduce potential geomorphic influences and to isolate the effects of material properties on landslide failure mode, we analyzed open-slope landslides (open-slope data set) separately from our analysis of the full dataset. Partial flows were not included in our analyses of the full data to further limit the analyses to material properties affecting only slide and flow landslide failure modes. We also test the applicability of AMI for predicting the failure mode. Results Table 2 provides a summary of field and laboratory results, Tables 5 and 6 contain the results of the predictive models that we tested, and Tables 7 and 8 contain a summary of the calculated statistics for the variables tested. The apparent influence of measured variables on landslide failure mode for the open-slope and full datasets follows.
Slope When analyzing the full dataset, there is a statistically significant difference between the mean slopes of the two failure mode populations (Table 7). The mean slope is greater for flows than for slides suggesting that steeper slopes are more prone to flows. However, by limiting the data to the open-slope dataset, there is no statistical difference between the means of the two populations (Table 8). Volume The distribution of initial failure volumes (Volume, Table 2) is log-normal regardless of failure mode and the median volumes of slides and flows are equal (slide, 70 m3; flow 70 m3). Geomorphic setting Analysis of the full dataset (Table 2) shows that 87% of the slides and only 30% of the flows initiated on open slopes. If geomorphic setting was used as a predictor of failure mode, assuming all slides initiate on open slopes and all flows initiate in hollows, 77% of failure modes would be predicted correctly (Table 5).
Fig. 4 Example of a channelized flow that initiated at the PH study site (see Fig. 1 for locations)
Approximate mobility index The AMI for each landslide in the full dataset is shown in Fig. 5. If AMI is used to predict failure mode by assuming that an AMI1 will result in a flow, 66% of failure modes would be predicted correctly (Table 5) and the mean AMI of the two failure mode populations are statistically different (Table 7). If we constrain the dataset to only landslides that initiate on open slopes, only 45% of failure modes would be predicted correctly using AMI (Table 6) and the mean AMI of the two failure mode populations are not statistically different (Table 8). Landslides
Author's personal copy Original Paper Table 5 Model results using the full dataset to predict landslide failure mode using (a) threshold dry density, (b) AMI, and (c) geomorphic setting
Table 6 Model results using the open-slope dataset to predict landslide failure mode using (a) threshold dry density and (b) AMI
a
Threshold Density: 76.6% Correct (36 of 47) Predicted Flow Slide Observed 12 3 Flow (n=15) (80%) (20%) 8 24 Slide (n=32) (25%) (75%)
Threshold Density: 79.3% Correct (69 of 87) Predicted Flow Slide Observed 41 9 Flow (n=50) (82%) (18%) 9 28 Slide(n=37) (24%) (76%)
a
b AMI: 65.5% Correct (57 of 87) Predicted Observed Flow (n=50) Slide(n=37)
Flow
Slide
44 (88%) 24 (65%)
6 (12%) 13 (35%)
AMI: 44.7% Correct (21 of 47) Predicted Observed Flow (n=15) Slide (n=32)
Values in blue indicate the number of sites for which the predicted behavior matched the observed behavior. Values in red indicate the number of sites where predicted and observed behavior did not match
Dry density, fine-grained content, and saturated hydraulic conductivity Among the individual variables analyzed using LDA, a combination of ρd, ksat, and f showed the highest success rate for predicting failure mode (89% using full dataset; 86% using open-slope dataset). However, the inclusion of the variable, ksat, in this method reduced the sample population (flows: n=27 (full dataset), n=22 (open-slope dataset)). The linear discriminate functions for the two dependent variables (slide and flow) using the full dataset are as follows:
3 (20%) 9 28%)
and 55% of the initiation sites, respectively, using the full dataset. For the open-slope dataset, 65%, 64%, and 36% of failure modes were correctly predicted for the ρd, ksat, and f variables, respectively. Tables 7 and 8 summarize the statistical results (F test, t test) for the individual variables tested. Although a statistically significant difference in the means of the two failure mode populations exists for the individual variables, ρd and ksat, when using the entire dataset (Table 7), there is no statistical difference in the two population means for either variable when using the open-slope dataset. The distribution of landslide failure mode with respect to f and ρd is shown in Fig. 6 (full dataset) and in Fig. 7 (open-slope data set). Figure 6 includes previously published data from large-scale flume experiments (Logan and Iverson 2007; Iverson et al. 2000) and from California field sites (Gabet and Mudd 2006), which are referred to as “Flume” and “G&M,” respectively. These two additional datasets were included because the authors investigated the influence of
Table 7 Statistical summary of p values for F and t tests (α=0.05) for individual variables using the full dataset
ð3Þ
ð4Þ
Scores are calculated using both Eqs. 3 and 4, and the predicted failure mode corresponds to the highest score. For the full dataset, LDA analysis of the individual variables (ρd, ksat, and f) resulted in correct prediction of the failure mode for 71%, 67%, Landslides
12 (80%) 23 (72%)
Values in blue indicate the number of sites for which the predicted behavior matched the observed behavior. Values in red indicate the number of sites where predicted and observed behavior did not match
Geomorphic Setting: 77.3% Correct (68 of 88) Predicted Flow Slide Observed 35 15 Flow (n=50) (70%) (30%) 5 33 Slide (n=38) (13%) (87%)
flow ¼ 337:06ksat þ 72:45d þ :35f 44:81
Slide
b
c
slide ¼ 642:37ksat þ 81:89d þ :13f 56:57
Flow
a
F (p value)
T (p value)
Variable
Population size
ρdev
87
0.13
2.13E-07a
ρd
88
0.19
8.65E-06a
AMI
87
0.21
9.02E-04a
Slope
84
0.42
3.08E-03a
ksat
27
0.02a
0.04a
f
88
9.3E-04a
0.64
Statistically significant figures
Author's personal copy Threshold Dry Density: Full Dataset
Table 8 Statistical summary of p values for F and t tests (α=0.05) for individual variables using the open-slope dataset
Population size
ρdev
47
F (p value)
3.75E-03a
0.32
0.7
T (p value)
0.06
0.09
Slope
43
0.22
0.09
ksat
22
0.10
0.10
AMI
47
0.35
0.17
td
= 8.48x10-6f 3 - 1.33x10-3f 2 + 5.27x10-2f + 1.04
0.6
f a
a
47
9.5E-06
Dry density,
d
48
FLOW 1.1
0.75
1.3 0.5 1.5
Slide
0.4 1.7
material properties on landslide failure mode in a fashion similar to this study. It is apparent in Figs. 6 and 7 that a threshold curve divides the two failure modes, with flows plotting above the threshold curve and slides plotting below the curve. The best-fit curve that divides failure modes and equalizes the number of Type I (predicted slide, observed flow) and Type II errors (predicted flow, observed slide) (Table 5) is the threshold density (ρtd): td ¼ 8:48x106 f 3 1:33x103 f 2 þ 5:27x102 f þ 1:04
ð5Þ
where f is the fine-grained fraction of the soil. In order to analyze the statistical significance of ρtd as a predictor variable for failure mode, we normalized the density measurements with respect to ρtd as follows: dev ¼ td d
ð6Þ
where (ρdev) is the deviation of the sample density (ρd) with respect to ρtd. Positive values for ρdev indicate that ρd ρtd (susceptible to sliding). F and t tests indicate that for the variable ρdev, a statistically significant difference in the means of the two failure mode populations exists for both the full dataset and the open-slope dataset (Tables 7 and 8). Deviation density positively identifies 79% of failure
Partial flow Flow Flume slide
SLIDE
Statistically significant figures 1.9
Porosity, n
ρd
0.9
(g/cm3)
Variable
0.7
0
20
40
60
Flume flow G&M slide
0.3 100
80
G&M flow
Fine-grained content, f (%)
Fig. 6 Dry density threshold boundary (ρtd) defined by Eq. 5 showing the division between slides and flows using the full dataset (Table 2) where f is the silt and clay fraction of the soil. Green symbols are flows, yellow symbols are partial flows, and red symbols are slides. “Flume” data from Logan and Iverson 2007; Iverson et al. 2000; “G&M” data from Gabet and Mudd 2006
modes using the full dataset and 77% using the open-slope dataset. The distribution of soil density at the FR study area (Fig. 2) can provide some insight into the origins of soils looser than the criticalstate value. Figure 2 shows that the debris-flow initiation sites are located within active slide deposits and in most cases are located at slide toes. Density profiles (expressed as ρdev) extending from debrisflow headscarps up to the headscarps of their containing slides (along profile lines P1-P6 in Fig. 2) are shown in Fig. 8. Five of the six profiles show that ρdev is positive, or looser than ρtd, for debris-flow source areas. Generally, ρdev is negative, or denser than ρtd, above the debrisflow headscarp and throughout the corresponding up-hill slide deposit. Discussion Geomorphic setting is a good indicator of landslide failure mode suggesting that slides typically occur on open slopes and flows Threshold Dry Density:Open-Slope Dataset 0.7
Slide Partial flow Flow
Approximate Mobility Index 0.9
FLOW
td
0.7
= 8.48x10-6f 3 - 1.33x10-3f 2 + 5.27x10-2f + 1.04
1.1
0.6
1
Dry density,
AMI
2
1.3 0.5 1.5
Porosity, n
(g/cm3)
Slide Partial Flow Flow
d
3
0.4 1.7
SLIDE 1.9
0
20
40
60
80
0.3 100
Fine-grained content, f(%)
0
Fig. 5 AMI according to landslide failure mode
Fig. 7 Dry density threshold boundary (ρtd) defined by Eq. 5 showing the division between slides and flows using the open-slope dataset (Table 2). Green symbols are flows, yellow symbols are partial flows, and red symbols are slides
Landslides
Author's personal copy
Deviation from threshold dry Density,
dev
(g/cm3)
Original Paper Density Profiles above Debris-flow Headscarps 0.8
P1 P2
P3 P4
P5 P6
0.6 0.4 0.2 Threshold dry density (
0
td)
< Soils susceptible to flowing > Soils suceptible to sliding
-0.2 -0.4 -0.6 -0.8 0
25
50
75
100
Distance above debris-flow headscarp (m)
Fig. 8 Density profiles for Florida River sample locations along profile lines (P1–P6) shown in Fig. 2. The trend line corresponds to all data on the plot. The threshold density (ρtd) corresponds to ρdev =0; positive values for ρdev indicate soils susceptible to flowing; negative values for ρdev indicate soils susceptible to sliding
typically occur in hollows. Likely explanations for this spatial occurrence are that flows may initiate from dilated slide debris in locations where water is abundant. Hollows are indicated by topographic concavities marking the beginning of the stream channel, and open slopes are generally indicated by parallel topographic contours that form the hillslopes above hollows (Hack and Goodlet 1960). Sources of dilated material are likely upslope from hollows on open slopes where slides are common. The dilated slide deposits may accumulate in the hollow where topographic concavities provide an avenue for groundwater to converge and saturate the soil. Subsequent failure in the saturated soil would be contractive. When contraction rates exceed diffusive pore-pressure rates, pore pressures can increase beyond hydrostatic pressures which can transform some landslides into rapidly moving liquefied flows (Rudiniki 1984; Iverson and LaHusen 1989). Landslide failure mode is predicted with the highest success rate for both the open-slope and full datasets using the initial dry density (ρd) and fine-grained fraction (f) of the soil. The same threshold curve (Eq. 3) divides slide and flow failure modes when using ρd and f as predictor variables for the full dataset (Fig. 6), as well as for the open-slope dataset (Fig. 7). A previously published critical-state density value (ρd =1.51 g/cm3, f=11%) for well-graded material tested at low normal stress at the USGS large-scale flume (Reid et al. 2008) falls on the threshold curve, and the threshold curve is consistent with published field data from California (Gabet and Mudd 2006). Among all the variables tested, ρdev (which is a function of ρd and f and is shown in Eq. 6) is the only variable that shows a statistically significant difference in the means of the two failure mode populations for both the full and open-slope datasets. The results of the LDA analysis suggest that the principal components for discerning failure modes are ρd, f, and ksat. The inclusion of ρd and f in Eqs. 3 and 4 reinforces the conclusion that these variables can be used to estimate ρtd shown in Figs. 6 and 7 and defined by Eq. 5. The inclusion of ksat in Eqs. 3 and 4 supports the physical-based theory that contractive soils will cause increased pore pressures only when the contraction rate exceeds the pore-pressure Landslides
diffusion rate of the soil (Rudnicki 1984; Iverson and LaHusen 1989). When pore pressures increase beyond hydrostatic pressures, complete liquefaction leading to flow behavior rather than slide behavior is very likely. Therefore, contraction and pore-pressure diffusion rates are of paramount importance in the liquefaction process. More than 85% of the samples shown in Table 2 have LL8 (well-graded), and f
